checkpoint 2025-08-27

Cargo.lock

@@ -1004,6 +1004,18 @@ version = "1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a3d8a32ae18130a3c84dd492d4215c3d913c3b07c6b63c2eb3eb7ff1101ab7bf"
 
+[[package]]
+name = "enum_dispatch"
+version = "0.3.13"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "aa18ce2bc66555b3218614519ac839ddb759a7d6720732f979ef8d13be147ecd"
+dependencies = [
+ "once_cell",
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
 [[package]]
 name = "enumflags2"
 version = "0.7.11"
@@ -1908,6 +1920,7 @@ dependencies = [
  "eframe",
  "egui",
  "egui_graphs",
+ "enum_dispatch",
  "geo",
  "itertools 0.14.0",
  "petgraph",

Cargo.toml

@@ -9,6 +9,7 @@ ecolor = "0.31.1"
 eframe = "0.30"
 egui = "0.30"
 egui_graphs = "0.23.0"
+enum_dispatch = "0.3.13"
 geo = "0.29.3"
 itertools = "0.14.0"
 petgraph = "0.6"

README.md

@@ -0,0 +1,101 @@
+# Maxflow-rs
+
+## Idea
+
+- Generate StableGraph (petgraph)
+    - run algo on that
+- Create a custom to_graph method which displays a maxflow graph
+
+TODOs
+- [x] Implementation of Algos:
+    - [x] Ford-Fulkersson (DFS zur Berechnung des flusserhöhenden/augmentierenden Pfads)
+    - [x] Edmonds-Karp (BFS zur Berechnung des flusserhöhenden/augmnetierenden Pfads)
+    - [x] Dinic
+    - [x] Goldberg-Tarjan/Preflow-Push
+- [x] Step-by-step implementation for all algos
+    - [x] Ford-Fulkerson
+    - [x] Edmonds-Karp
+    - [x] Dinic
+    - [x] Goldberg-Tarjan/Preflow-Push
+- [x] Mark edges which have active flows with a color
+- [x] Move GUI Graph conversion to a trait of StableGraph
+- [ ] Add graph positioning strategy which looks "nicer"
+    - [x] Only insert nodes which are at least a distance of 40 away (default)
+    - [ ] Pseudo-random node positioning strategy
+- [x] Handle residual edges properly
+    - [x] Add display option for residual edges
+- [x] Only show active flows (filter all edges with f=0)
+- [x] Show normal vs residual graph -> not needed, residual graph is shown by default
+- [x] When increasing flows, handle residual path
+- [x] Add unit tests
+    - [x] With small problems to prove correctness
+    - [x] For Benchmarking the algos
+    - [x] Check validity of the generated flows (incoming flows = outgoing flows; flow <= capacity)
+- [x] Add info display pane
+    - [x] is valid flow? (add trait to graph)
+    - [x] current total flow (add trait to calculate)
+    - [x] number of steps (is implemented for stepwise)
+- [x] implement PartialEq for StableGraph (not really possible -> how do you compare graphs?) -> implemented a prune_zero trait & compare node/edge weights for same index
+- [x] Step-by-step vizualisation with choosable time delay
+- [ ] Dinic: add GUI options to show Layer Graph and Blocking flow
+- [ ] Goldberg-Tarjan: show distance labels at nodes
+- [x] change GUI colors to accomodate color-blindness (blue-yellow rather than red-green)
+- [x] remove display option for residual graph -> this should be the default
+
+DFS: Stack
+BFS: Queue
+
+Bugs:
+- [x] if I generate a new graph, the algo runs on the old graph
+- [x] if I click reset & then step, the algo runs in one step
+- [x] when using edmonds karp the updated flow isn't displayed correctly
+- [ ] the capacity on residual edges also gets displayed when using 
+
+Residual Graph:
+- parallel arcs in the same direction can be summarized into a single arc by summing up the capcities
+- 
+
+TODOs:
+- [x] gui colors in yellow blue (should be easy)
+- [x] no residual graph option, residual graph is default (medium, bit of effort)
+    - [ ] do we need to delete the graph field in algos & use residual_graph instead?
+    - [ ] check correctness of all algos by testing a small sample#
+- [ ] gui display options (medium)
+    - [ ] layer graph (done - TODO: check if correct) & blocking flow (for Dinic)
+    - [ ] goldberg-tarjan: push-relabel step - current pre-flow, flow change in every step
+- [x] add time delay for algorithm (hard due to multithreading)
+    - [ ] fix glitchy graph display (somewhere in update_graph function)
+- [ ] implement goldberg tarjan (hard)
+    - [x] fix residual edges: algo pushes flows back but increases flow on the residual edge instead of decreasing the reverse edge
+    - [ ] fix loops: somehow the algo produces loops towards the source node (not critical for calculating the total flow, but should be fixed)
+    - [ ] big tests sometimes fail for goldberg-tarjan (panic when reading node from distance labelling)
+- [x] make MaxflowAlgorithm object-safe (remove from_problem & implement it per struct, then create a generic wrapper which creates new instances for each specific algorithm)
+- [ ] add unit test environment (hard)
+    - [x] callable from gui
+    - [x] several test tuples [number of problems, node count, max capacity]
+    - [x] split MaxflowProblem:new into two functions (one for display, one for test environment)
+    - [x] apply to every algo
+    - [x] große testumgebung
+    - [x] testfunktion in seperatem thread ausführen, damit programm nicht hängt
+    - [ ] check for: 
+        - [x] flusserhaltung
+        - [x] kapazitätsbedingungen
+        - [ ] saturierter schritt
+    - [ ] testumgebung durch änderungen der lösung automatisch überprüfen (korrektheit, optimalität)
+- [x] reduce warnings
+
+
+thread '<unnamed>' panicked at src/graph.rs:191:31
+attempt to subtract with overflow
+note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace
+
+thread '<unnamed>' panicked at src/algorithms/goldberg_tarjan.rs:109:238:
+No distance label found
+note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace
+
+# Code erklären
+
+- Graph generieren (random_generator.rs)
+- GUI, Custom Layout (main.rs, layout.rs)
+- Graph Hilfsfunktionen (graph.rs)
+- Algorithmen (ford_fulkerson.rs, edmonds_karp.rs, dinic.rs, goldberg_tarjan.rs)

src/algorithms.rs

@@ -1,13 +0,0 @@
-// Ford-Fulkerson mit DFS zur Berechnung des flusserhöhenden Pfades,
-// Edmonds-Karp (also Ford-Fulkerson mit BFS statt DFS),
-// Dinic
-// Goldberg-Tarjan (auch Preflow-Push oder Push-Relabel genannt).
-use random_generator::MaxflowProblem;
-
-mod random_generator;
-
-impl FordFulkerson {
-    fn solve(problem: MaxflowProblem) -> ???solution??? {
-
-    }
-}

src/algorithms/common.rs

@@ -0,0 +1,61 @@
+use crate::algorithms::ford_fulkerson::FordFulkerson;
+use crate::algorithms::edmonds_karp::EdmondsKarp;
+use crate::algorithms::dinic::Dinic;
+use crate::algorithms::goldberg_tarjan::GoldbergTarjan;
+
+use std::fmt;
+use enum_dispatch::enum_dispatch;
+use petgraph::stable_graph::StableGraph;
+
+#[enum_dispatch(MaxflowAlgorithmEnum)]
+pub trait MaxflowAlgorithm {
+    // perform a single step; returns true if the algorithm terminates
+    fn step(&mut self) -> bool;
+
+    // runs the whole algorithm in a single step
+    fn run(&mut self) -> StableGraph<(f32, f32), (u64, u64)>;
+
+    // returns the current graph
+    fn graph(&mut self) -> StableGraph<(f32, f32), (u64, u64)>;
+
+    // resets the current flow to the zero flow
+    fn reset(&mut self);
+
+    // returns the algorithm name
+    fn name(&self) -> &'static str;
+}
+
+pub fn available_capacity(edge: (u64, u64)) -> u64 {
+    edge.1 - edge.0
+}
+
+#[enum_dispatch]
+pub enum MaxflowAlgorithmEnum {
+    FordFulkerson,
+    EdmondsKarp,
+    Dinic,
+    GoldbergTarjan
+}
+
+impl PartialEq for MaxflowAlgorithmEnum {
+    fn eq(&self, other: &Self) -> bool {
+        match (self, other) {
+            (&MaxflowAlgorithmEnum::FordFulkerson(_), &MaxflowAlgorithmEnum::FordFulkerson(_)) => true,
+            (&MaxflowAlgorithmEnum::EdmondsKarp(_), &MaxflowAlgorithmEnum::EdmondsKarp(_)) => true,
+            (&MaxflowAlgorithmEnum::Dinic(_), &MaxflowAlgorithmEnum::Dinic(_)) => true,
+            (&MaxflowAlgorithmEnum::GoldbergTarjan(_), &MaxflowAlgorithmEnum::GoldbergTarjan(_)) => true,
+            _ => false,
+        }
+    }
+}
+
+impl fmt::Display for MaxflowAlgorithmEnum {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match &self {
+            &MaxflowAlgorithmEnum::FordFulkerson(_) => write!(f, "Ford-Fulkerson"),
+            &MaxflowAlgorithmEnum::EdmondsKarp(_) => write!(f, "Edmonds-Karp"),
+            &MaxflowAlgorithmEnum::Dinic(_) => write!(f, "Dinic"),
+            &MaxflowAlgorithmEnum::GoldbergTarjan(_) => write!(f, "Goldberg-Tarjan"),
+        }
+    }
+}

src/algorithms/dinic.rs

@@ -0,0 +1,148 @@
+use std::cmp::min;
+use std::collections::VecDeque;
+
+use petgraph::{stable_graph::{NodeIndex, StableGraph}, visit::{EdgeRef, VisitMap, Visitable}, Direction};
+use crate::{algorithms::common::{available_capacity, MaxflowAlgorithm}, graph::FlowGraph, random_generator::MaxflowProblem};
+
+pub struct Dinic {
+    graph: StableGraph<(f32, f32), (u64, u64)>,
+    source: NodeIndex,
+    sink: NodeIndex,
+    residual_graph: StableGraph<(f32, f32), (u64, u64)>,
+    layer_graph: StableGraph<(f32, f32), (u64, u64)>,
+}
+
+impl Dinic {
+    pub fn from_problem(p: &MaxflowProblem) -> Self {
+        Self {
+            residual_graph: p.g.residual(),
+            graph: p.g.clone(),
+            layer_graph: StableGraph::default(),
+            source: p.s,
+            sink: p.t,
+        }
+    }
+
+    // BFS
+    fn layer_graph(&self) -> StableGraph<(f32, f32), (u64, u64)> {
+        // filter graph for edges with no remaining capacity
+        let mut layer_graph = self.residual_graph.filter_map(|_, n| {
+            Some(*n)
+        }, |_, &e| {
+            match available_capacity(e) {
+                0 => None,
+                _ => Some(e),
+            }
+        });
+
+        // filter graph for s-t paths
+        let mut visited = layer_graph.visit_map();
+        let mut queue = VecDeque::from([(self.source, 0)]);
+        while let Some((node, layer)) = queue.pop_front() {
+            //let outgoing_edges = layer_graph.edges_directed(node, Direction::Outgoing).collect::<Vec<_>>();
+            let outgoing_edges = layer_graph.edges_directed(node, Direction::Outgoing).map(|e| e.id()).collect::<Vec<_>>();
+            visited.visit(node);
+
+            for edge in outgoing_edges {
+                let neighbor = layer_graph.edge_endpoints(edge).expect("edge index not found").1;
+                // if neighbor is unvisited, this is the shortest path to neighbor -> keep the edge
+                if !visited.is_visited(&neighbor) {
+                    visited.visit(neighbor);
+                    // stop traversing this path if destination is reached
+                    if neighbor == self.sink {
+                        continue;
+                    } else {
+                        // add neighbor to queue if destination is not reached
+                        queue.push_back((neighbor, layer+1));
+                    }
+                } else {
+                    // if neighbor was visited before this edge is not on the shortest path -> remove it
+                    layer_graph.remove_edge(edge);
+                }
+            }
+        }
+
+        layer_graph
+    }
+
+    // Runs a depth Depth First Search (DFS) which returns an augmenting path from source to destination if possible
+    fn dfs(&self) -> Option<Vec<NodeIndex>> {
+        let mut visited = self.layer_graph.visit_map();
+        let mut stack = VecDeque::from([(self.source, vec![self.source])]);
+
+        // work through the main stack
+        while let Some((node, path)) = stack.pop_front() {
+            let outgoing_edges = self.layer_graph.edges_directed(node, Direction::Outgoing);
+            visited.visit(node);
+
+            // iterate over all outgoing edges & add neighboring nodes to the stack
+            for edge in outgoing_edges {
+                let neighbor = edge.target();
+                if !visited.is_visited(&neighbor) && available_capacity(*edge.weight()) > 0 {
+                    visited.visit(neighbor);
+                    let mut new_path = path.clone();
+                    new_path.push(neighbor);
+                    if neighbor == self.sink {
+                        return Some(new_path);
+                    } else {
+                        stack.push_front((neighbor, new_path));
+                    }
+                };
+            }
+        }
+        None
+    }
+}
+
+impl MaxflowAlgorithm for Dinic {
+    fn step(&mut self) -> bool {
+        // construct layer graph (from s to t)
+        self.layer_graph = self.layer_graph();
+    
+        // construct a blocking flow in the layer graph using a DFS
+        // continue while there are augmenting paths
+        if let Some(path) = self.dfs()  {
+            // find all edges along the path
+            let edges: Vec<petgraph::prelude::EdgeIndex> = path.windows(2).map(|w| self.residual_graph.find_edge(w[0], w[1]).expect("edge not found")).collect();
+            // find bottleneck capacity along path
+            let bottleneck_capacity = edges.iter().fold(u64::MAX, |m, x| {
+                let edge = self.residual_graph.edge_weight(*x).expect("edge index not found");
+                min(m, edge.1 - edge.0)
+            });
+    
+            // increase flow with bottleneck capacity along the augmenting path
+            for edge in edges {
+                self.residual_graph.add_flow(edge, bottleneck_capacity);
+            }
+            false
+        } else {
+            true
+        }
+    }
+
+    fn reset(&mut self) {
+        // set all flows in graph to 0
+        for edge in self.graph.edge_indices().collect::<Vec<_>>() {
+            let weight = self.graph.edge_weight_mut(edge).expect("edge not found");
+            (*weight).0 = 0;
+        }
+        // reset the residual & layer graph as well
+        self.residual_graph = self.graph.residual();
+        self.layer_graph = StableGraph::default();
+    }
+
+    fn run(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        while !self.step() {
+            continue;
+        }
+        self.residual_graph.clone()
+    }
+    
+    fn graph(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        self.residual_graph.clone()
+    }
+
+    fn name(&self) -> &'static str {
+        "Dinic"
+    }
+}

src/algorithms/edmonds_karp.rs

@@ -0,0 +1,100 @@
+use std::cmp::min;
+use std::collections::VecDeque;
+
+use petgraph::{stable_graph::{NodeIndex, StableGraph}, visit::{EdgeRef, VisitMap, Visitable}, Direction};
+use crate::{algorithms::common::{available_capacity, MaxflowAlgorithm}, graph::FlowGraph, random_generator::MaxflowProblem};
+
+pub struct EdmondsKarp {
+    graph: StableGraph<(f32, f32), (u64, u64)>,
+    source: NodeIndex,
+    sink: NodeIndex,
+    residual_graph: StableGraph<(f32, f32), (u64, u64)>,
+}
+
+impl EdmondsKarp {
+    pub fn from_problem(p: &MaxflowProblem) -> Self {
+        Self {
+            residual_graph: p.g.residual(),
+            graph: p.g.clone(),
+            source: p.s,
+            sink: p.t,
+        }
+    }
+
+    // Runs a depth Breadth First Search (BFS) and returns an augmenting path from source to destination if possible
+    fn bfs(&mut self) -> Option<Vec<NodeIndex>> {
+        let mut visited = self.residual_graph.visit_map();
+        let mut queue = VecDeque::from([(self.source, vec![self.source])]);
+        //queue.push_back((source, vec![source]));
+
+        // work through the main queue
+        while let Some((node, path)) = queue.pop_front() {
+            let outgoing_edges = self.residual_graph.edges_directed(node, Direction::Outgoing);
+            visited.visit(node);
+
+            for edge in outgoing_edges {
+                let neighbor = edge.target();
+                if !visited.is_visited(&neighbor) && available_capacity(*edge.weight()) > 0 {
+                    visited.visit(neighbor);
+                    let mut new_path = path.clone();
+                    new_path.push(neighbor);
+                    visited.visit(neighbor);
+                    if neighbor == self.sink {
+                        return Some(new_path);
+                    } else {
+                        queue.push_back((neighbor, new_path));
+                    }
+                }
+            }
+        }
+        None
+    }
+}
+
+impl MaxflowAlgorithm for EdmondsKarp {
+
+    fn step(&mut self) -> bool {
+        if let Some(path) = self.bfs()  {
+            // find all edges along the path
+            let edges: Vec<petgraph::prelude::EdgeIndex> = path.windows(2).map(|w| self.residual_graph.find_edge(w[0], w[1]).expect("edge not found")).collect();
+            // find bottleneck capacity along path
+            let bottleneck_capacity = edges.iter().fold(u64::MAX, |m, x| {
+                let edge = self.residual_graph.edge_weight(*x).expect("edge index not found");
+                min(m, edge.1 - edge.0)
+            });
+
+            // increase flow with bottleneck capacity along the augmenting path
+            for edge in edges {
+                self.residual_graph.add_flow(edge, bottleneck_capacity);
+            }
+            false
+        } else {
+            true
+        }
+    }
+
+    fn reset(&mut self) {
+        // set all flows in graph to 0
+        for edge in self.graph.edge_indices().collect::<Vec<_>>() {
+            let weight = self.graph.edge_weight_mut(edge).expect("edge not found");
+            (*weight).0 = 0;
+        }
+        // reset the residual graph as well
+        self.residual_graph = self.graph.residual();
+    }
+
+    fn run(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        while !self.step() {
+            continue;
+        }
+        self.residual_graph.clone()
+    }
+    
+    fn graph(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        self.residual_graph.clone()
+    }
+
+    fn name(&self) -> &'static str {
+        "Edmonds-Karp"
+    }
+}

src/algorithms/ford_fulkerson.rs

@@ -0,0 +1,99 @@
+use std::cmp::min;
+use std::collections::VecDeque;
+use petgraph::{stable_graph::{NodeIndex, StableGraph}, visit::{EdgeRef, VisitMap, Visitable}, Direction};
+use crate::{algorithms::common::{available_capacity, MaxflowAlgorithm}, graph::FlowGraph, random_generator::MaxflowProblem};
+
+pub struct FordFulkerson {
+    graph: StableGraph<(f32, f32), (u64, u64)>,
+    source: NodeIndex,
+    sink: NodeIndex,
+    residual_graph: StableGraph<(f32, f32), (u64, u64)>,
+}
+
+impl FordFulkerson {
+    pub fn from_problem(p: &MaxflowProblem) -> Self {
+        Self {
+            residual_graph: p.g.residual(),
+            graph: p.g.clone(),
+            source: p.s,
+            sink: p.t,
+        }
+    }
+
+    // Runs a depth Depth First Search (DFS) which returns an augmenting path from source to destination if possible
+    fn dfs(&mut self) -> Option<Vec<NodeIndex>> {
+        let mut visited = self.residual_graph.visit_map();
+        let mut stack = VecDeque::from([(self.source, vec![self.source])]);
+    
+        // work through the main stack
+        while let Some((node, path)) = stack.pop_front() {
+            let outgoing_edges = self.residual_graph.edges_directed(node, Direction::Outgoing);
+            visited.visit(node);
+    
+            // iterate over all outgoing edges & add neighboring nodes to the stack
+            for edge in outgoing_edges {
+                let neighbor = edge.target();
+                if !visited.is_visited(&neighbor) && available_capacity(*edge.weight()) > 0 {
+                    visited.visit(neighbor);
+                    let mut new_path = path.clone();
+                    new_path.push(neighbor);
+                    if neighbor == self.sink {
+                        return Some(new_path);
+                    } else {
+                        stack.push_front((neighbor, new_path));
+                    }
+                };
+            }
+        }
+    
+        None
+    }
+}
+
+impl MaxflowAlgorithm for FordFulkerson {
+    fn step(&mut self) -> bool {
+        // continue while there are augmenting paths
+        if let Some(path) = self.dfs() {
+            // find all edges along the path
+            let edges: Vec<petgraph::prelude::EdgeIndex> = path.windows(2).map(|w| self.residual_graph.find_edge(w[0], w[1]).expect("edge not found")).collect();
+            // find bottleneck capacity along path
+            let bottleneck_capacity = edges.iter().fold(u64::MAX, |m, x| {
+                let edge = self.residual_graph.edge_weight(*x).expect("edge index not found");
+                min(m, edge.1 - edge.0)
+            });
+
+            // increase flow with bottleneck capacity along the augmenting path
+            for edge in edges {
+                self.residual_graph.add_flow(edge, bottleneck_capacity);
+            }
+            false
+        } else {
+            true
+        }
+    }
+
+    fn reset(&mut self) {
+        // set all flows in graph to 0
+        for edge in self.graph.edge_indices().collect::<Vec<_>>() {
+            let weight = self.graph.edge_weight_mut(edge).expect("edge not found");
+            (*weight).0 = 0;
+        }
+        // reset residual graph as well
+        self.residual_graph = self.graph.residual();
+    }
+
+    fn run(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        while !self.step() {
+            continue;
+        }
+        self.residual_graph.clone()
+    }
+    
+    fn graph(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        self.residual_graph.clone()
+    }
+
+    fn name(&self) -> &'static str {
+        "Ford-Fulkerson"
+    }
+}

src/algorithms/goldberg_tarjan.rs

@@ -0,0 +1,161 @@
+use std::cmp::min;
+use std::collections::{VecDeque, HashMap};
+
+use itertools::Itertools;
+use petgraph::{stable_graph::{NodeIndex, StableGraph}, visit::{EdgeRef, NodeRef, VisitMap, Visitable}, Direction};
+use crate::{algorithms::common::{MaxflowAlgorithm}, graph::FlowGraph, random_generator::MaxflowProblem};
+
+pub struct GoldbergTarjan {
+    graph: StableGraph<(f32, f32), (u64, u64)>,
+    source: NodeIndex,
+    sink: NodeIndex,
+    residual_graph: StableGraph<(f32, f32), (u64, u64)>,
+    first_iteration: bool,
+    pub distance_label: Option<HashMap<NodeIndex, u64>>
+    // psi?
+}
+
+impl GoldbergTarjan {
+    pub fn from_problem(p: &MaxflowProblem) -> Self {
+        Self {
+            residual_graph: p.g.residual(),
+            graph: p.g.clone(),
+            source: p.s,
+            sink: p.t,
+            first_iteration: true,
+            distance_label: None
+        }
+        // initialize with a valid preflow (max flow on all outgoing edges of s)
+        // assign height/label to every node using the labeling/height function (using BFS)
+    }
+
+    fn active_node(&self) -> Option<(NodeIndex, u64)> {
+        for node in self.residual_graph.node_indices() {
+            // s and t are ne
+            if node == self.source || node == self.sink {
+                continue;
+            }
+            let outgoing_flows: u64 = self.residual_graph.edges_directed(node, Direction::Outgoing).map(|e| e.weight().0).sum();
+            let incoming_flows: u64 = self.residual_graph.edges_directed(node, Direction::Incoming).map(|e| e.weight().0).sum();
+            if (incoming_flows - outgoing_flows) > 0 {
+                // this node has an excess flow - return node index & excess flow
+                return Some((node, incoming_flows - outgoing_flows));
+            }
+        }
+        None
+    }
+
+    // performs a BFS from sink to source and labels all nodes with their distance to the sink
+    fn compute_distances(&mut self) {
+        let mut distance_label = HashMap::new();
+        let mut visited = self.residual_graph.visit_map();
+        let mut queue = VecDeque::from([(self.sink, 0 as u64)]);
+        visited.visit(self.sink);
+        
+        while let Some((node, distance)) = queue.pop_front() {
+            // first, visit nodes in queue
+            let outgoing_edges = self.residual_graph.edges_directed(node, Direction::Outgoing);
+            
+            for edge in outgoing_edges {
+                let neighbor = edge.target();
+                if !visited.is_visited(&neighbor) {
+                    visited.visit(neighbor);
+                    distance_label.insert(neighbor, distance + 1);
+                    queue.push_back((neighbor, distance + 1));
+                }
+            }
+        }
+
+        // set d(source) := |V|
+        distance_label.insert(self.source, self.residual_graph.node_count() as u64);
+        // set d(target) := 0
+        distance_label.insert(self.sink, 0);
+
+        assert!(distance_label.len() == self.residual_graph.node_count(), "Distance mapping is incomplete");
+        self.distance_label = Some(distance_label);
+    }
+}
+
+impl MaxflowAlgorithm for GoldbergTarjan {
+    fn step(&mut self) -> bool {
+        // Initialization: if this is the first iteration, set the current flow on all outgoing edges of the source to their capacity
+        if self.first_iteration {
+            for edge in self.residual_graph.edges_directed(self.source, Direction::Outgoing).map(|e| e.id()).collect::<Vec<_>>() {
+                let (source, target) = self.residual_graph.edge_endpoints(edge).expect("edge not connected");
+                // set all outgoing edges to their maximum capacity
+                let weight = self.residual_graph.edge_weight_mut(edge).expect("edge id not found");
+                let capacity = (*weight).1.clone();
+                (*weight).0 = capacity;
+                // increase capacity of the residual edge of the with the calculated bottleneck value
+                let residual_edge = self.residual_graph.find_edge(target, source).expect("residual edge not found");
+                let residual_weight: &mut (u64, u64) = self.residual_graph.edge_weight_mut(residual_edge).expect("edge not found");
+                (*residual_weight).1 += capacity;
+            }
+            self.first_iteration = false;
+            return false;
+        } 
+        // if the distance labels were not already computed, compute them now
+        if self.distance_label == None {
+            self.compute_distances();
+        }
+        
+        // Main loop: while there is an active node, continue
+        if let Some((node, excess)) = self.active_node() {
+            // find all outgoing edges with available capacity
+            let valid_edges: Vec<petgraph::prelude::EdgeIndex> = self.residual_graph
+                .edges_directed(node, Direction::Outgoing)
+                .filter(|e| (e.weight().1 - e.weight().0) > 0 )
+                .filter(|e| self.distance_label.as_ref().expect("distance labelling not present").get(&e.target().id()).expect("No distance label 1 found") < self.distance_label.as_ref().expect("distance labelling not present").get(&node).expect("No distance label 2 found") )
+                .map(|e| e.id())
+                .collect::<Vec<_>>();
+            if valid_edges.len() > 0 {
+                // node has valid edges -> push (move min[excess, capacity] to first valid edge)
+                let edge = valid_edges[0];
+                let available_capacity = self.residual_graph.edge_weight(edge).expect("Invalid edge index").1 - self.residual_graph.edge_weight(edge).expect("Invalid edge index").0;
+                let additional_flow = min(excess, available_capacity);
+                self.residual_graph.add_flow(edge, additional_flow);
+                
+            } else {
+                // node has no valid edges -> relabel (increase node distance label to min[neighbors] + 1)
+                let neighbors = self.residual_graph
+                    .edges_directed(node, Direction::Outgoing)
+                    .filter(|e| (e.weight().1 - e.weight().0) > 0 )
+                    .sorted_by_key(|e| self.distance_label.as_ref().expect("distance labelling not present").get(&e.target()))
+                    .map(|e| e.target())
+                    .collect::<Vec<_>>();
+                assert!(neighbors.len() > 0);
+                let lowest_distance = self.distance_label.as_ref().expect("distance labelling not present").get(&neighbors[0]).expect("No distance label found").clone();
+                self.distance_label.as_mut().expect("distance labelling not present").insert(node, lowest_distance + 1);
+            }
+            false
+        } else {
+            // algorithm terminates if there are no more active nodes
+            true
+        }
+    }
+
+    fn reset(&mut self) {
+        // set all flows in graph to 0
+        for edge in self.graph.edge_indices().collect::<Vec<_>>() {
+            let weight = self.graph.edge_weight_mut(edge).expect("edge not found");
+            (*weight).0 = 0;
+        }
+        // reset the residual & layer graph as well
+        self.residual_graph = self.graph.residual();
+    }
+
+    fn run(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        while !self.step() {
+            continue;
+        }
+        self.residual_graph.clone()
+    }
+    
+    fn graph(&mut self) -> StableGraph<(f32, f32), (u64, u64)> {
+        self.residual_graph.clone()
+    }
+
+    fn name(&self) -> &'static str {
+        "Goldberg-Tarjan"
+    }
+}

src/algorithms/mod.rs

@@ -0,0 +1,13 @@
+mod common;
+mod ford_fulkerson;
+mod edmonds_karp;
+mod dinic;
+mod goldberg_tarjan;
+
+pub use common::MaxflowAlgorithm;
+pub use common::MaxflowAlgorithmEnum;
+
+pub use ford_fulkerson::FordFulkerson;
+pub use edmonds_karp::EdmondsKarp;
+pub use dinic::Dinic;
+pub use goldberg_tarjan::GoldbergTarjan;

src/graph.rs

@@ -0,0 +1,268 @@
+use egui_graphs::{DefaultNodeShape, Graph, default_edge_transform, default_node_transform, to_graph_custom};
+use petgraph::{algo::has_path_connecting, stable_graph::{EdgeIndex, NodeIndex, StableGraph}, visit::{EdgeRef, VisitMap, Visitable}, Directed, Direction};
+use egui::{Pos2};
+use std::collections::{HashMap, HashSet, VecDeque};
+use std::cmp::min;
+use crate::layout::CustomEdgeShape;
+use egui::Color32;
+
+// All methods which convert the graph into a GUI representations
+pub trait GuiGraph {
+    fn to_gui_graph(&self, s: NodeIndex, t: NodeIndex) -> Graph<(f32, f32), (u64, u64), Directed, u32, DefaultNodeShape, CustomEdgeShape>;
+    fn to_gui_graph_distance(&self, s: NodeIndex, t: NodeIndex, distance_labels: HashMap<NodeIndex, u64>) -> Graph<(f32, f32), (u64, u64), Directed, u32, DefaultNodeShape, CustomEdgeShape>;
+}
+
+impl GuiGraph for StableGraph<(f32, f32), (u64, u64)> {
+    fn to_gui_graph(&self, s: NodeIndex, t: NodeIndex) -> Graph<(f32, f32), (u64, u64), Directed, u32, DefaultNodeShape, CustomEdgeShape> {
+        let mut graph = to_graph_custom(&self,
+            |n| {
+                let (x, y) = *n.payload();
+                default_node_transform(n);
+                n.set_location(Pos2::new(x, y));
+                n.set_label(String::from(""));
+            },
+            |e| {
+                let (flow, capacity): (u64, u64) = *e.payload();
+                default_edge_transform(e);
+                e.set_label(format!("{flow}:{capacity}"));
+                if flow > 0 {
+                    e.set_selected(true);
+                }
+            }
+        );
+        graph.node_mut(s).expect("node index not found").set_label(String::from("s"));
+        graph.node_mut(t).expect("node index not found").set_label(String::from("t"));
+        graph.node_mut(s).expect("node index not found").set_color(Color32::BLUE);
+        graph.node_mut(t).expect("node index not found").set_color(Color32::ORANGE);
+        graph
+    }
+
+    fn to_gui_graph_distance(&self, s: NodeIndex, t: NodeIndex, distance_labels: HashMap<NodeIndex, u64>) -> Graph<(f32, f32), (u64, u64), Directed, u32, DefaultNodeShape, CustomEdgeShape> {
+        let mut graph = to_graph_custom(&self,
+            |n| {
+                let (x, y) = *n.payload();
+                default_node_transform(n);
+                n.set_location(Pos2::new(x, y));
+                if let Some(d) = distance_labels.get(&n.id()) {
+                    if n.id() == s {
+                        n.set_label(format!("s ({})", d));
+                    } else if n.id() == t {
+                        n.set_label(format!("t ({})", d));
+                    } else {
+                        n.set_label(format!("{}", d));
+                    }
+                } else {
+                    n.set_label(String::from(""));
+                }
+            },
+            |e| {
+                let (flow, capacity): (u64, u64) = *e.payload();
+                default_edge_transform(e);
+                e.set_label(format!("{flow}:{capacity}"));
+                if flow > 0 {
+                    e.set_selected(true);
+                }
+            }
+        );
+        graph.node_mut(s).expect("node index not found").set_color(Color32::BLUE);
+        graph.node_mut(t).expect("node index not found").set_color(Color32::ORANGE);
+        graph
+    }
+}
+
+// all methods specific to MaxFlow problems
+pub trait FlowGraph {
+    fn filter_empty_flows(&self) -> StableGraph<(f32, f32), (u64, u64)>;
+
+    fn reset_flow(&mut self);
+
+    fn prune_zero(&self) -> StableGraph<(f32, f32), (u64, u64)>;
+
+    fn valid_flow(&self, source: NodeIndex, sink: NodeIndex) -> bool;
+
+    fn total_flow(&self, source: NodeIndex, sink: NodeIndex) -> u64;
+
+    fn available_capacity(&self, edge: EdgeIndex) -> u64;
+
+    fn layer_graph(&self, source: NodeIndex, sink: NodeIndex) -> StableGraph<(f32, f32), (u64, u64)>;
+
+    fn add_flow(&mut self, edge: EdgeIndex, flow: u64);
+
+    fn residual(&self) -> StableGraph<(f32, f32), (u64, u64)>;
+}
+
+impl FlowGraph for StableGraph<(f32, f32), (u64, u64)> {
+    fn filter_empty_flows(&self) -> StableGraph<(f32, f32), (u64, u64)> {
+        self.filter_map( |_, n| {
+            Some(*n)
+        },
+        |_, &e| {
+            match e.0 {
+                0 => None,
+                _ => Some(e),
+            }
+        })
+    }
+
+    fn layer_graph(&self, source: NodeIndex, sink: NodeIndex) -> StableGraph<(f32, f32), (u64, u64)> {
+        // filter graph for edges with no remaining capacity
+        let mut layer_graph = self.filter_map(|_, n| {
+            Some(*n)
+        }, |_, &e| {
+            match e.1 - e.0 {
+                0 => None,
+                _ => Some(e),
+            }
+        });
+
+        // filter graph for s-t paths
+        let mut visited = layer_graph.visit_map();
+        let mut queue = VecDeque::from([(source, 0)]);
+        while let Some((node, layer)) = queue.pop_front() {
+            //let outgoing_edges = layer_graph.edges_directed(node, Direction::Outgoing).collect::<Vec<_>>();
+            let outgoing_edges = layer_graph.edges_directed(node, Direction::Outgoing).map(|e| e.id()).collect::<Vec<_>>();
+            visited.visit(node);
+
+            for edge in outgoing_edges {
+                let neighbor = layer_graph.edge_endpoints(edge).expect("edge index not found").1;
+                // if neighbor is unvisited, this is the shortest path to neighbor -> keep the edge
+                if !visited.is_visited(&neighbor) {
+                    visited.visit(neighbor);
+                    // stop traversing this path if destination is reached
+                    if neighbor == sink {
+                        continue;
+                    } else {
+                        // add neighbor to queue if destination is not reached
+                        queue.push_back((neighbor, layer+1));
+                    }
+                } else {
+                    // if neighbor was visited before this edge is not on the shortest path -> remove it
+                    layer_graph.remove_edge(edge);
+                }
+            }
+        }
+
+        layer_graph
+    }
+
+    // set all flows back to zero
+    fn reset_flow(&mut self) {
+        for edge in self.edge_indices().collect::<Vec<_>>() {
+            let weight = self.edge_weight_mut(edge).expect("edge not found");
+            (*weight).0 = 0;
+        }
+    }
+
+    // removes all edges where the current flow is zero & returns a pruned graph
+    fn prune_zero(&self) -> StableGraph<(f32, f32), (u64, u64)> {
+        let mut zero_graph = self.clone();
+        for edge in zero_graph.edge_indices().collect::<Vec<_>>() {
+            let weight = zero_graph.edge_weight(edge).expect("edge not found");
+            if weight.0 == 0 {
+                zero_graph.remove_edge(edge);
+            }
+        }
+
+        zero_graph
+    }
+
+    // check if flow is valid:
+    // - for every edge, the flow doesn't exceed the capacity
+    // - for every node, the amount of incoming flows is equal to the amount of outgoing flows
+    fn valid_flow(&self, source: NodeIndex, sink: NodeIndex) -> bool {
+        // capacity isn't exceeded
+        for edge in self.edge_indices().map(|e| e).collect::<Vec<_>>() {
+            if self.edge_weight(edge).expect("edge index not found").0 > self.edge_weight(edge).expect("edge index not found").1 {
+                return false;
+            }
+        }
+        // sum incoming flows = sum outgoing flows
+        for node in self.node_indices().map(|n| n).collect::<Vec<_>>() {
+            let outgoing_flows: u64 = self
+                .edges_directed(node, Direction::Outgoing)
+                .map(|e| e.weight().0)
+                .sum();
+            let incoming_flows: u64 = self
+                .edges_directed(node, Direction::Incoming)
+                .map(|e| e.weight().0)
+                .sum();
+            if incoming_flows != outgoing_flows {
+                if node != source && node != sink {
+                    // println!("invalid flow at {:?} incoming flows: {} outgoing flows: {}", node, incoming_flows, outgoing_flows);
+                    return false;
+                }
+            }
+        }
+        true
+    }
+
+    fn total_flow(&self, source: NodeIndex, sink: NodeIndex) -> u64 {
+        let outgoing_flows_source: u64 = self.edges_directed(source, Direction::Outgoing).map(|e| e.weight().0).sum();
+        let incoming_flows_source: u64 = self.edges_directed(source, Direction::Incoming).map(|e| e.weight().0).sum();
+        let outgoing_flows_sink: u64 = self.edges_directed(sink, Direction::Outgoing).map(|e| e.weight().0).sum();
+        let incoming_flows_sink: u64 = self.edges_directed(sink, Direction::Incoming).map(|e| e.weight().0).sum();
+        let total_flow_source = outgoing_flows_source - incoming_flows_source;
+        let total_flow_sink = incoming_flows_sink - outgoing_flows_sink;
+        if total_flow_sink != total_flow_source {
+            return 0;
+        }
+        return total_flow_source;
+    }
+
+    fn residual(&self) -> StableGraph<(f32, f32), (u64, u64)> {
+        let mut res_graph = self.clone();
+
+        for edge in res_graph.edge_indices().map(|e| e).collect::<Vec<_>>() {
+            let (source, target) = res_graph.edge_endpoints(edge).expect("edge not connected");
+            if let Some(reverse_edge) = res_graph.find_edge(target, source) {
+                let (flow, capacity) = *res_graph.edge_weight(edge).expect("forward edge not found");
+                let (reverse_flow, _reverse_capacity) = *res_graph.edge_weight(reverse_edge).expect("reverse edge not found");
+                // update the edge
+                res_graph.update_edge(source, target, (flow, capacity + reverse_flow));
+            } else {
+                // add a residual edge with a flow of 0 if the reverse edge doesn't exist
+                res_graph.add_edge(target, source, (0, 0));
+            }
+        }
+        res_graph
+    }
+    
+    fn available_capacity(&self, edge: EdgeIndex) -> u64 {
+        self.edge_weight(edge).expect("edge not found").1 - self.edge_weight(edge).expect("edge not found").0
+    }
+    
+    // adds the specified flow to the edge of a residual graph
+    fn add_flow(&mut self, forward_edge: EdgeIndex, flow: u64) {
+        // search for reverse edge
+        let (source, target) = self.edge_endpoints(forward_edge).expect("edge not connected");
+        let reverse_edge = self.find_edge(target, source).expect("reverse edge not found");
+        
+        // calculate how much flow needs to be added on the reverse edge
+        let current_reverse_flow = self.edge_weight(reverse_edge).expect("reverse erge not found").0;
+        // maximum flow we can subtract from reverse edge
+        let reverse_flow = min(current_reverse_flow, flow);
+        let forward_flow = flow - reverse_flow;
+        if reverse_flow > 0 {
+            // decrease reverse flow
+            let reverse_weight: &mut (u64, u64) = self.edge_weight_mut(reverse_edge).expect("reverse edge not found");
+            (*reverse_weight).0 -= reverse_flow;
+            assert!(reverse_weight.0 <= reverse_weight.1);
+            // decrease forward capacity 
+            let forward_weight: &mut (u64, u64) = self.edge_weight_mut(forward_edge).expect("edge not found");
+            (*forward_weight).1 -= reverse_flow;
+            assert!(forward_weight.0 <= forward_weight.1);
+        }
+
+        // add remaining flow to forward edge
+        if forward_flow > 0 {
+            // increase forward flow
+            let forward_weight: &mut (u64, u64) = self.edge_weight_mut(forward_edge).expect("edge not found");
+            (*forward_weight).0 += forward_flow;
+            assert!(forward_weight.0 <= forward_weight.1);
+            // increase reverse capacity
+            let reverse_weight: &mut (u64, u64) = self.edge_weight_mut(reverse_edge).expect("reverse edge not found");
+            (*reverse_weight).1 += forward_flow;
+            assert!(reverse_weight.0 <= reverse_weight.1);
+        }
+    }
+}

src/layout.rs

@@ -0,0 +1,353 @@
+use std::f32::consts::PI;
+
+use egui::{
+    epaint::{CubicBezierShape, QuadraticBezierShape, TextShape}, Color32, FontFamily, FontId, Pos2, Shape, Stroke, Vec2
+};
+
+use petgraph::{matrix_graph::Nullable, stable_graph::IndexType, EdgeType};
+
+use egui_graphs::{DisplayEdge, EdgeProps, DisplayNode, Node, DrawContext};
+
+
+#[derive(Clone)]
+pub struct CustomEdgeShape {
+    pub order: usize,
+    pub selected: bool,
+
+    pub width: f32,
+    pub tip_size: f32,
+    pub tip_angle: f32,
+    pub curve_size: f32,
+    pub loop_size: f32,
+    pub label_text: String,
+}
+
+impl<E: Clone> From<EdgeProps<E>> for CustomEdgeShape {
+    fn from(props: EdgeProps<E>) -> Self {
+        Self {
+            order: props.order,
+            selected: props.selected,
+            label_text: props.label,
+
+            width: 1.,
+            tip_size: 6.,
+            tip_angle: std::f32::consts::TAU / 20.,
+            curve_size: 10.,
+            loop_size: 3.,
+        }
+    }
+}
+
+impl<N: Clone, E: Clone, Ty: EdgeType, Ix: IndexType, D: DisplayNode<N, E, Ty, Ix>>
+    DisplayEdge<N, E, Ty, Ix, D> for CustomEdgeShape
+{
+    // helper functions
+    // copied from: https://github.com/SeverinAlexB/pknames/blob/d042b6843ee503d92ae36742bab81b14574d9ad3/cli/src/visualization/edge_vis.rs
+    fn is_inside(
+        &self,
+        start: &Node<N, E, Ty, Ix, D>,
+        end: &Node<N, E, Ty, Ix, D>,
+        pos: egui::Pos2,
+    ) -> bool {
+        if start.id() == end.id() {
+            return is_inside_loop(start, self, pos);
+        }
+
+        let pos_start = start.location();
+        let pos_end = end.location();
+
+        if self.order == 0 {
+            return is_inside_line(pos_start, pos_end, pos, self);
+        }
+
+        is_inside_curve(start, end, self, pos)
+    }
+
+    fn shapes(
+        &mut self,
+        start: &Node<N, E, Ty, Ix, D>,
+        end: &Node<N, E, Ty, Ix, D>,
+        ctx: &DrawContext,
+    ) -> Vec<egui::Shape> {
+        // fixed properties
+        let edge_color = match self.selected {
+            true => Color32::LIGHT_BLUE,
+            false => Color32::LIGHT_GRAY
+        };
+        let label_color = Color32::DARK_GRAY;
+        //let label_visible = true;
+        //let style = ctx.ctx.style().visuals.widgets.inactive;
+
+        // calculate coordinates
+        let dir = (end.location() - start.location()).normalized();
+        let start_connector_point = start.display().closest_boundary_point(dir);
+        let end_connector_point = end.display().closest_boundary_point(-dir);
+        let tip_end = end_connector_point;
+        let edge_start = start_connector_point;
+        let edge_end = end_connector_point;
+
+        // draw curved edge
+        let stroke_edge = Stroke::new(self.width * ctx.meta.zoom, edge_color);
+        let dir_perpendicular = Vec2::new(-dir.y, dir.x);
+        let center_point = (edge_start + edge_end.to_vec2()).to_vec2() / 2.;
+        let control_point = (center_point + dir_perpendicular * self.curve_size as f32).to_pos2();
+        let tip_dir = (control_point-tip_end).normalized();
+        //println!("edge_start: {:?} edge_end {:?} center_point {:?} dir_p {:?} control_point {:?}", edge_start, edge_end, center_point, dir_perpendicular, control_point);
+
+        let arrow_tip_dir_1 = rotate_vector(tip_dir, self.tip_angle) * self.tip_size;
+        let arrow_tip_dir_2 = rotate_vector(tip_dir, -self.tip_angle) * self.tip_size;
+        let tip_start_1 = tip_end + arrow_tip_dir_1;
+        let tip_start_2 = tip_end + arrow_tip_dir_2;
+
+        let edge_end_curved = point_between(tip_start_1, tip_start_2);
+        let line_curved = QuadraticBezierShape::from_points_stroke(
+            [
+                ctx.meta.canvas_to_screen_pos(edge_start),
+                ctx.meta.canvas_to_screen_pos(control_point),
+                ctx.meta.canvas_to_screen_pos(edge_end_curved),
+            ],
+            false,
+            Color32::TRANSPARENT,
+            stroke_edge,
+        );
+
+        // draw tip/arrow
+        let stroke_tip = Stroke::new(0., edge_color);
+        let line_curved_tip = Shape::convex_polygon(
+            vec![
+                ctx.meta.canvas_to_screen_pos(tip_end),
+                ctx.meta.canvas_to_screen_pos(tip_start_1),
+                ctx.meta.canvas_to_screen_pos(tip_start_2),
+            ],
+            edge_color,
+            stroke_tip,
+        );
+
+
+        // draw label
+        let size = (::egui_graphs::node_size(start, dir) + egui_graphs::node_size(end, dir)) / 2.;
+        let galley = ctx.ctx.fonts(|f| {
+            f.layout_no_wrap(
+                self.label_text.clone(),
+                FontId::new(ctx.meta.canvas_to_screen_size(size), FontFamily::Monospace),
+                label_color,
+            )
+        });
+
+        let flattened_curve = line_curved.flatten(None);
+        let median = *flattened_curve.get(flattened_curve.len() / 2).unwrap();
+
+        let label_width = galley.rect.width();
+        let label_height = galley.rect.height();
+        let pos = Pos2::new(median.x - label_width / 2., median.y - label_height);
+
+        let label_shape = TextShape::new(pos, galley, label_color);
+        
+        vec![line_curved.into(), line_curved_tip, label_shape.into()]
+    }
+
+    fn update(&mut self, state: &egui_graphs::EdgeProps<E>) {
+        self.order = state.order;
+        self.selected = state.selected;
+        self.label_text = state.label.to_string();
+    }
+
+}
+
+// Everything below is copied from:
+// https://github.com/SeverinAlexB/pknames/blob/d042b6843ee503d92ae36742bab81b14574d9ad3/cli/src/visualization/edge_vis.rs
+fn shape_looped(
+    node_size: f32,
+    node_center: Pos2,
+    stroke: Stroke,
+    e: &CustomEdgeShape,
+) -> CubicBezierShape {
+    let center_horizon_angle = PI / 4.;
+    let y_intersect = node_center.y - node_size * center_horizon_angle.sin();
+
+    let edge_start = Pos2::new(
+        node_center.x - node_size * center_horizon_angle.cos(),
+        y_intersect,
+    );
+    let edge_end = Pos2::new(
+        node_center.x + node_size * center_horizon_angle.cos(),
+        y_intersect,
+    );
+
+    let loop_size = node_size * (e.loop_size + e.order as f32);
+
+    let control_point1 = Pos2::new(node_center.x + loop_size, node_center.y - loop_size);
+    let control_point2 = Pos2::new(node_center.x - loop_size, node_center.y - loop_size);
+
+    CubicBezierShape::from_points_stroke(
+        [edge_end, control_point1, control_point2, edge_start],
+        false,
+        Color32::default(),
+        stroke,
+    )
+}
+
+fn shape_curved(
+    pos_start: Pos2,
+    pos_end: Pos2,
+    size_start: f32,
+    size_end: f32,
+    stroke: Stroke,
+    e: &CustomEdgeShape,
+) -> QuadraticBezierShape {
+    let vec = pos_end - pos_start;
+    let dist: f32 = vec.length();
+    let dir = vec / dist;
+
+    let start_node_radius_vec = Vec2::new(size_start, size_start) * dir;
+    let end_node_radius_vec = Vec2::new(size_end, size_end) * dir;
+
+    let tip_end = pos_start + vec - end_node_radius_vec;
+
+    let edge_start = pos_start + start_node_radius_vec;
+    let edge_end = pos_end + end_node_radius_vec;
+
+    let dir_perpendicular = Vec2::new(-dir.y, dir.x);
+    let center_point = (edge_start + tip_end.to_vec2()).to_vec2() / 2.0;
+    let control_point =
+        (center_point + dir_perpendicular * e.curve_size * e.order as f32).to_pos2();
+
+    QuadraticBezierShape::from_points_stroke(
+        [edge_start, control_point, edge_end],
+        false,
+        stroke.color,
+        stroke,
+    )
+}
+
+fn is_inside_loop<E: Clone, N: Clone, Ix: IndexType, Ty: EdgeType, D: DisplayNode<N, E, Ty, Ix>>(
+    node: &Node<N, E, Ty, Ix, D>,
+    e: &CustomEdgeShape,
+    pos: Pos2,
+) -> bool {
+    let node_size = node_size(node);
+
+    let shape = shape_looped(node_size, node.location(), Stroke::default(), e);
+    is_point_on_cubic_bezier_curve(pos, shape, e.width)
+}
+
+fn is_inside_line(pos_start: Pos2, pos_end: Pos2, pos: Pos2, e: &CustomEdgeShape) -> bool {
+    let distance = distance_segment_to_point(pos_start, pos_end, pos);
+    distance <= e.width
+}
+
+fn is_inside_curve<
+    N: Clone,
+    E: Clone,
+    Ty: EdgeType,
+    Ix: IndexType,
+    D: DisplayNode<N, E, Ty, Ix>,
+>(
+    node_start: &Node<N, E, Ty, Ix, D>,
+    node_end: &Node<N, E, Ty, Ix, D>,
+    e: &CustomEdgeShape,
+    pos: Pos2,
+) -> bool {
+    let pos_start = node_start.location();
+    let pos_end = node_end.location();
+
+    let size_start = node_size(node_start);
+    let size_end = node_size(node_end);
+
+    let shape = shape_curved(
+        pos_start,
+        pos_end,
+        size_start,
+        size_end,
+        Stroke::default(),
+        e,
+    );
+    is_point_on_quadratic_bezier_curve(pos, shape, e.width)
+}
+
+fn node_size<N: Clone, E: Clone, Ty: EdgeType, Ix: IndexType, D: DisplayNode<N, E, Ty, Ix>>(
+    node: &Node<N, E, Ty, Ix, D>,
+) -> f32 {
+    let left_dir = Vec2::new(-1., 0.);
+    let connector_left = node.display().closest_boundary_point(left_dir);
+    let connector_right = node.display().closest_boundary_point(-left_dir);
+
+    (connector_right.x - connector_left.x) / 2.
+}
+
+/// Returns the distance from line segment `a``b` to point `c`.
+/// Adapted from https://stackoverflow.com/questions/1073336/circle-line-segment-collision-detection-algorithm
+fn distance_segment_to_point(a: Pos2, b: Pos2, point: Pos2) -> f32 {
+    let ac = point - a;
+    let ab = b - a;
+
+    let d = a + proj(ac, ab);
+
+    let ad = d - a;
+
+    let k = if ab.x.abs() > ab.y.abs() {
+        ad.x / ab.x
+    } else {
+        ad.y / ab.y
+    };
+
+    if k <= 0.0 {
+        return hypot2(point.to_vec2(), a.to_vec2()).sqrt();
+    } else if k >= 1.0 {
+        return hypot2(point.to_vec2(), b.to_vec2()).sqrt();
+    }
+
+    hypot2(point.to_vec2(), d.to_vec2()).sqrt()
+}
+
+/// Calculates the square of the Euclidean distance between vectors `a` and `b`.
+fn hypot2(a: Vec2, b: Vec2) -> f32 {
+    (a - b).dot(a - b)
+}
+
+/// Calculates the projection of vector `a` onto vector `b`.
+fn proj(a: Vec2, b: Vec2) -> Vec2 {
+    let k = a.dot(b) / b.dot(b);
+    Vec2::new(k * b.x, k * b.y)
+}
+
+fn is_point_on_cubic_bezier_curve(point: Pos2, curve: CubicBezierShape, width: f32) -> bool {
+    is_point_on_bezier_curve(point, curve.flatten(Option::new(10.0)), width)
+}
+
+fn is_point_on_quadratic_bezier_curve(
+    point: Pos2,
+    curve: QuadraticBezierShape,
+    width: f32,
+) -> bool {
+    is_point_on_bezier_curve(point, curve.flatten(Option::new(0.3)), width)
+}
+
+fn is_point_on_bezier_curve(point: Pos2, curve_points: Vec<Pos2>, width: f32) -> bool {
+    let mut previous_point = None;
+    for p in curve_points {
+        if let Some(pp) = previous_point {
+            let distance = distance_segment_to_point(p, pp, point);
+            if distance < width {
+                return true;
+            }
+        }
+        previous_point = Some(p);
+    }
+    false
+}
+
+/// rotates vector by angle
+fn rotate_vector(vec: Vec2, angle: f32) -> Vec2 {
+    let cos = angle.cos();
+    let sin = angle.sin();
+    Vec2::new(cos * vec.x - sin * vec.y, sin * vec.x + cos * vec.y)
+}
+
+/// finds point exactly in the middle between 2 points
+fn point_between(p1: Pos2, p2: Pos2) -> Pos2 {
+    let base = p1 - p2;
+    let base_len = base.length();
+    let dir = base / base_len;
+    p1 - (base_len / 2.) * dir
+}

src/lib.rs

@@ -0,0 +1,5 @@
+pub mod algorithms;
+pub mod graph;
+pub mod random_generator;
+pub mod layout;
+pub mod testing;

src/main.rs

@@ -1,47 +1,295 @@
 use eframe::{run_native, App, CreationContext, NativeOptions, Frame};
-use egui::{CentralPanel, SidePanel, Context};
-use egui_graphs::{GraphView, Graph, SettingsStyle, LayoutRandom, LayoutStateRandom};
-
+use egui::{CentralPanel, CollapsingHeader, ComboBox, Context, ScrollArea, SidePanel, Slider, Window};
+use egui_graphs::{DefaultNodeShape, Graph, GraphView, LayoutRandom, LayoutStateRandom, SettingsStyle};
+use petgraph::{stable_graph::{StableGraph}, Directed};
+use std::{sync::{Arc, Mutex}, thread, thread::JoinHandle, time::Instant};
 use random_generator::MaxflowProblem;
-use algorithms::{ford_fulk
-//use petgraph::stable_graph::StableGraph;
+use layout::CustomEdgeShape;
+use crate::algorithms::{MaxflowAlgorithm, MaxflowAlgorithmEnum, FordFulkerson, EdmondsKarp, Dinic, GoldbergTarjan};
+use graph::{GuiGraph, FlowGraph};
+use testing::{run_small_tests,run_large_tests};
 
 mod random_generator;
 mod algorithms;
+mod layout;
+mod graph;
+mod testing;
+
+//type MaxflowFn = fn(StableGraph<(f32, f32), (u64, u64)>, NodeIndex, NodeIndex) -> StableGraph<(f32, f32), (u64, u64)>;
 
 pub struct MaxflowApp {
-    g: Graph<(), u64>,
-    p: MaxflowProblem,
+    gui_graph: Arc<Mutex<Graph<(f32, f32), (u64, u64), Directed, u32, DefaultNodeShape, CustomEdgeShape>>>,
+    problem: MaxflowProblem,
+    current_graph: StableGraph<(f32, f32), (u64, u64)>,
     node_count: u64,
     max_capacity: u64,
+    algorithm: MaxflowAlgorithmEnum,
+    display_active_flows: bool,
+    display_layer_graph: bool,
+    algorithm_finished: bool,
+    num_steps: u64,
+    test_thread: Option<JoinHandle<String>>,
+    test_results: String,
+    test_results_open: bool,
+    delay: u64,
+    animation_runnning: bool,
+    last_update: Instant
 }
 
 impl MaxflowApp {
     fn new(_: &CreationContext<'_>) -> Self {
-        let problem = MaxflowProblem::new(10, 10);
-        Self { g: problem.g.clone(), p: problem, node_count: 10, max_capacity: 5 }
+        let problem = MaxflowProblem::new_planar_graph(10, 10);
+        Self {
+            current_graph: problem.g.clone(),
+            gui_graph: Arc::new(Mutex::new(problem.g.to_gui_graph(problem.s, problem.t))),
+            algorithm: FordFulkerson::from_problem(&problem).into(),
+            problem,
+            node_count: 10,
+            max_capacity: 5,
+            display_active_flows: false,
+            display_layer_graph: false,
+            algorithm_finished: false,
+            num_steps: 0,
+            test_thread: None,
+            test_results: String::default(),
+            test_results_open: false,
+            delay: 200,
+            animation_runnning: false,
+            last_update: Instant::now()
+        }
+    }
+
+    // reinitialize the current algorithm & reset its internal state
+    fn reset_state(&mut self) {
+        // undo finished run
+        self.algorithm_finished = false;
+        // set steps to zero
+        self.num_steps = 0;
+        // reinitialize the current graph from the problem
+        self.current_graph = self.problem.g.clone();
+        // assign new maxflow problem to the graph
+        match self.algorithm {
+            MaxflowAlgorithmEnum::FordFulkerson(_) => self.algorithm = FordFulkerson::from_problem(&self.problem).into(),
+            MaxflowAlgorithmEnum::EdmondsKarp(_) => self.algorithm = EdmondsKarp::from_problem(&self.problem).into(),
+            MaxflowAlgorithmEnum::Dinic(_) => self.algorithm = Dinic::from_problem(&self.problem).into(),
+            MaxflowAlgorithmEnum::GoldbergTarjan(_) => self.algorithm = GoldbergTarjan::from_problem(&self.problem).into(),
+        }
+    }
+
+    // display the current graph & apply display options from GUI
+    fn update_graph(&mut self) {
+        let graph = &self.current_graph;
+        let mut gui_graph_lock = self.gui_graph.lock().unwrap();
+        if self.display_active_flows {
+            *gui_graph_lock = graph.filter_empty_flows().to_gui_graph(self.problem.s, self.problem.t);
+        } else {
+            match &mut self.algorithm {
+                MaxflowAlgorithmEnum::GoldbergTarjan(g) => {
+                    if let Some(l) = g.distance_label.clone() {
+                        *gui_graph_lock = graph.to_gui_graph_distance(self.problem.s, self.problem.t, l);
+                    } else {
+                        *gui_graph_lock = graph.to_gui_graph(self.problem.s, self.problem.t);
+                    }
+                },
+                MaxflowAlgorithmEnum::Dinic(_) => {
+                    if self.display_layer_graph {
+                        *gui_graph_lock = graph.layer_graph(self.problem.s, self.problem.t).to_gui_graph(self.problem.s, self.problem.t);
+                    } else {
+                        *gui_graph_lock = graph.to_gui_graph(self.problem.s, self.problem.t);
+                    }
+                }
+                _ => *gui_graph_lock = graph.to_gui_graph(self.problem.s, self.problem.t)
+            }
+        }
+    }
+
+    fn run_algorithm(&mut self) {
+        match &mut self.algorithm {
+            MaxflowAlgorithmEnum::FordFulkerson(x) => {
+                self.current_graph = x.run();
+            },
+            MaxflowAlgorithmEnum::EdmondsKarp(x) => {
+                self.current_graph = x.run();
+            },
+            MaxflowAlgorithmEnum::Dinic(x) => {
+                self.current_graph = x.run();
+            },
+            MaxflowAlgorithmEnum::GoldbergTarjan(x) => {
+                self.current_graph = x.run();
+            }
+        }
+    }
+
+    fn step_algorithm(&mut self) -> bool {
+        match &mut self.algorithm {
+            MaxflowAlgorithmEnum::FordFulkerson(x) => {
+                let finished = x.step();
+                self.num_steps += 1;
+                self.current_graph = x.graph();
+                finished
+            },
+            MaxflowAlgorithmEnum::EdmondsKarp(x) => {
+                let finished = x.step();
+                self.num_steps += 1;
+                self.current_graph = x.graph();
+                finished
+            },
+            MaxflowAlgorithmEnum::Dinic(x) => {
+                let finished = x.step();
+                self.num_steps += 1;
+                self.current_graph = x.graph();
+                finished
+            },
+            MaxflowAlgorithmEnum::GoldbergTarjan(x) => {
+                let finished = x.step();
+                self.num_steps += 1;
+                self.current_graph = x.graph();
+                finished
+            }
+        }
     }
 }
 
 impl App for MaxflowApp {
     fn update(&mut self, ctx: &Context, _: &mut Frame) {
+        ctx.set_theme(egui::Theme::Light);
         CentralPanel::default().show(ctx, |ui| {
-            ui.add(&mut GraphView::<_, _, _, _, _, _, LayoutStateRandom, LayoutRandom>::new(&mut self.g).with_styles(&SettingsStyle::default().with_labels_always(true)));
+            ui.add(&mut GraphView::<_, _, _, _, _, CustomEdgeShape, LayoutStateRandom, LayoutRandom>::new(&mut self.gui_graph.lock().unwrap()).with_styles(&SettingsStyle::default().with_labels_always(true)));
         });
         SidePanel::right("right_panel")
             .min_width(200.)
             .show(ctx, |ui| {
-                ui.label("node count");
-                ui.add(egui::DragValue::new(&mut self.node_count).range(1..=1000));
-                ui.label("maximum capacity");
-                ui.add(egui::DragValue::new(&mut self.max_capacity).range(1..=10));
-                if ui.button("generate graph").clicked() {
-                    let problem = random_generator::MaxflowProblem::new(self.node_count, self.max_capacity);
-                    self.g = problem.g;
-                }
-                if ui.button("run algorithm").clicked() {
-                }
+                ScrollArea::vertical().show(ui, |ui| {
+                    CollapsingHeader::new("Graph generation")
+                        .default_open(true)
+                        .show(ui, |ui| {
+                            ui.label("node count");
+                            ui.add(egui::DragValue::new(&mut self.node_count).range(2..=50));
+                            ui.label("maximum capacity");
+                            ui.add(egui::DragValue::new(&mut self.max_capacity).range(1..=100));
+                            if ui.button("generate graph").clicked() {
+                                self.problem = random_generator::MaxflowProblem::new_planar_graph(self.node_count, self.max_capacity);
+                                self.reset_state();
+                                self.update_graph();
+                            }
+                        });
+
+                    CollapsingHeader::new("Max-flow algorithms")
+                        .default_open(true)
+                        .show(ui, |ui| {
+                            ComboBox::from_label("algorithm")
+                                .selected_text(self.algorithm.to_string())
+                                .show_ui(ui, |ui| {
+                                    let mut changed = ui.selectable_value(&mut self.algorithm, FordFulkerson::from_problem(&self.problem).into(), "Ford-Fulkerson").changed();
+                                    changed = changed || ui.selectable_value(&mut self.algorithm, EdmondsKarp::from_problem(&self.problem).into(), "Edmonds-Karp").changed();
+                                    changed = changed || ui.selectable_value(&mut self.algorithm, Dinic::from_problem(&self.problem).into(), "Dinic").changed();
+                                    changed = changed || ui.selectable_value(&mut self.algorithm, GoldbergTarjan::from_problem(&self.problem).into(), "Goldberg-Tarjan").changed();
+                                    //for algo in MaxflowAlgos::iter() {
+                                    //}
+                                    //ui.selectable_value(&mut self.algorithm, edmonds_karp, "Edmonds-Karp");
+                                    //ui.selectable_value(&mut self.algorithm, dinic, "Dinic");
+                                    if changed {
+                                        self.reset_state();
+                                        self.update_graph();
+                                    }
+                                });
+                            ui.add(Slider::new(&mut self.delay, 0..=1000).text("delay").suffix("ms"));
+                            ui.add_enabled_ui(!self.algorithm_finished, |ui| {
+                                if ui.button("step").clicked() {
+                                    // check if algo is initialized
+                                    // if not, initialize
+                                    // run step function
+                                    self.algorithm_finished = self.step_algorithm();
+                                    self.update_graph();
+                                }
+                                if ui.button("run").clicked() {
+                                    self.animation_runnning = true;
+                                }
+                            });
+                            if ui.button("reset").clicked() {
+                                self.reset_state();
+                                self.update_graph();
+                            }
+                            // step button (disable when finished)
+                            if self.animation_runnning {
+                                if self.last_update.elapsed().as_millis() > self.delay as u128 {
+                                    self.algorithm_finished = self.step_algorithm();
+                                    self.update_graph();
+                                    self.animation_runnning = !self.algorithm_finished;
+                                    self.last_update = Instant::now();
+                                }
+                            }
+                        });
+
+                    CollapsingHeader::new("Display options")
+                        .default_open(true)
+                        .show(ui, |ui| {
+                            if ui.checkbox(&mut self.display_active_flows, "show active flows only").changed() {
+                                self.update_graph();
+                            }
+                            ui.add_enabled_ui(matches!(self.algorithm, MaxflowAlgorithmEnum::Dinic(_)), |ui| {
+                                if ui.checkbox(&mut self.display_layer_graph, "show layer graph (Dinic)").changed() {
+                                    self.update_graph();
+                                }
+                            });
+                            
+                        });
+
+                    CollapsingHeader::new("Properties")
+                        .default_open(true)
+                        .show(ui, |ui| {
+                            ui.label(format!("is valid flow: {}", self.current_graph.valid_flow(self.problem.s, self.problem.t)));
+
+                            ui.label(format!("total flow: {}", self.current_graph.total_flow(self.problem.s, self.problem.t)));
+
+                            ui.label(format!("number of steps: {}", self.num_steps))
+                        });
+
+                    CollapsingHeader::new("Tests")
+                        .default_open(true)
+                        .show(ui, |ui| {
+                            if ui.button("run tests (small)").clicked() {
+                                // run tests
+                                match &mut self.test_thread {
+                                    // other thread currently running - ignore
+                                    Some(_) => {},
+                                    None => {
+                                        self.test_thread = Some(thread::spawn(move || { run_small_tests() }));
+                                    }
+                                };
+                            }
+
+                            if ui.button("run tests (large)").clicked() {
+                                // run tests
+                                match &mut self.test_thread {
+                                    // other thread currently running - ignore
+                                    Some(_) => {},
+                                    None => {
+                                        self.test_thread = Some(thread::spawn(|| { run_large_tests() }));
+                                    }
+                                };
+                            }
+                            match &mut self.test_thread {
+                                Some(t) => {
+                                    if t.is_finished() {
+                                        self.test_results = self.test_thread.take().map(JoinHandle::join).expect("No running thread found").expect("Could not join thread");
+                                        self.test_results_open = true;
+                                    }
+                                },
+                                None => {},
+                            }
+                        })
+                });
+
+
             });
+            if self.test_results_open {
+                Window::new("Test Results")
+                    .open(&mut self.test_results_open)
+                    .show(ctx, |ui| {
+                        ui.label(self.test_results.clone());
+                    });
+            }
     }
 }
 

src/random_generator.rs

@@ -1,66 +1,75 @@
 use petgraph::stable_graph::{StableGraph, NodeIndex};
-use petgraph::{Directed};
-use egui_graphs::{Graph};
-use egui::Pos2;
 use rand::thread_rng;
 use rand::Rng;
 use rand::seq::SliceRandom;
 use itertools::Itertools;
 use geo::{Line, coord, line_intersection::{line_intersection, LineIntersection}};
-use egui::Color32;
+use std::cmp::min;
 
 pub struct MaxflowProblem {
-    pub g: Graph<(), u64, Directed, u32, egui_graphs::DefaultNodeShape, egui_graphs::DefaultEdgeShape>,
+    pub g: StableGraph<(f32, f32), (u64, u64)>,
     pub s: NodeIndex,
     pub t: NodeIndex,
 }
 
 impl MaxflowProblem {
-    pub fn new(num_nodes: u64, max_capacity: u64) -> Self {
-        let mut graph: Graph<_, u64> = Graph::new(StableGraph::default());
+    // this function generates a maximally connected, planar graph with x/y coordinates which can be used for
+    // displaying a max-flow problem in a GUI. since the algorithm is rather inefficient, it only scales up to 50 nodes
+    pub fn new_planar_graph(num_nodes: u64, max_capacity: u64) -> Self {
+        // Node Type: (x,y) Edge Type: (current_flow, capacity)
+        let mut graph: StableGraph<(f32, f32), (u64, u64)> = StableGraph::default();
         let mut nodes: Vec<NodeIndex> = Vec::new();
         let mut rng = thread_rng();
 
         // generate nodes
         for _i in 0..num_nodes {
-            let x: f32 = rng.gen_range(0.0..=400.0);
-            let y: f32 = rng.gen_range(0.0..=300.0);
-            let pos = Pos2::new(x,y);
-            let n = graph.add_node_with_label_and_location((), String::new(), pos);
+            // check if node is too close to another node (distance < 40)
+            let mut too_close = true;
+            let (mut x, mut y) = (0.0, 0.0);
+            // this is a poor attempt at modeling a do..while loop in Rust
+            while too_close {
+                too_close = false;
+                x = rng.gen_range(0.0..=400.0);
+                y = rng.gen_range(0.0..=300.0);
+                for node in &nodes {
+                    if MaxflowProblem::distance(*graph.node_weight(*node).expect("node index not found"), (x,y)) < 40.0 {
+                        too_close = true;
+                    }
+                }
+            }
+            let n = graph.add_node((x,y));
             nodes.push(n);
         }
 
         // select source (s) and sink (t)
-        let s = *nodes.choose(&mut rng).expect("no nodes found");
-        let t = *nodes.choose(&mut rng).expect("no nodes found");
-        graph.node_mut(s).expect("node index not found").set_label(String::from("s"));
-        graph.node_mut(t).expect("node index not found").set_label(String::from("t"));
-        graph.node_mut(s).expect("node index not found").set_color(Color32::RED);
-        graph.node_mut(t).expect("node index not found").set_color(Color32::GREEN);
+        let (s,t) = nodes.choose_multiple(&mut rng, 2).copied().collect_tuple::<(NodeIndex, NodeIndex)>().expect("not enough nodes");
 
         // iterate over all possible edges
         let mut possible_edges: Vec<(NodeIndex, NodeIndex, f32)> = Vec::new();
         for pair in nodes.clone().into_iter().combinations(2) {
             // calculate distance & append tuple (node_a, node_b, distance) to possible_edges
-            let distance = Self::distance(graph.node(pair[0]).expect("node index not found").location(), graph.node(pair[1]).expect("node index not found").location());
+            let distance = Self::distance(
+                *graph.node_weight(pair[0]).expect("node index not found"),
+                *graph.node_weight(pair[1]).expect("node index not found")
+            );
+            //let distance = Self::distance(graph.node(pair[0]).expect("node index not found").location(), graph.node(pair[1]).expect("node index not found").location());
             possible_edges.push((pair[0], pair[1], distance));
         }
 
         // sort mapping by distance
         possible_edges.sort_by(|a, b| a.2.partial_cmp(&b.2).unwrap());
-        println!("possible_edges len: {}", possible_edges.len());
 
         // insert the edge if possible
         let mut inserted_edges: Vec<(NodeIndex, NodeIndex)> = Vec::new();
-        for (node1, node2, distance) in possible_edges {
+        for (node1, node2, _) in possible_edges {
             // check for collision with already inserted edges
             let mut intersects = false;
             for (node3, node4) in &inserted_edges {
                 if Self::intersects(
-                    graph.node(node1).expect("node index not found").location(),
-                    graph.node(node2).expect("node index not found").location(),
-                    graph.node(*node3).expect("node index not found").location(),
-                    graph.node(*node4).expect("node index not found").location(),
+                    *graph.node_weight(node1).expect("node index not found"),
+                    *graph.node_weight(node2).expect("node index not found"),
+                    *graph.node_weight(*node3).expect("node index not found"),
+                    *graph.node_weight(*node4).expect("node index not found"),
                 ) {
                     intersects = true;
                     break;
@@ -70,26 +79,61 @@ impl MaxflowProblem {
                 // otherwise insert the edge and its residual edge
                 inserted_edges.push((node1, node2));
                 inserted_edges.push((node2, node1));
-                let capacity: u64 = rng.gen_range(1..=max_capacity);
-                graph.add_edge_with_label(node1, node2, capacity, capacity.to_string());
-                graph.add_edge_with_label(node2, node1, capacity, capacity.to_string());
+                let capacity1: u64 = rng.gen_range(1..=max_capacity);
+                let capacity2: u64 = rng.gen_range(1..=max_capacity);
+                graph.add_edge(node1, node2, (0, capacity1));
+                graph.add_edge(node2, node1, (0, capacity2));
             }
         }
 
         Self { g: graph, s: s, t: t }
     }
 
+    // this function generates a fully connected random graph which can be used for solving max-flow problems
+    pub fn new_random_graph(num_nodes: u64, max_capacity: u64) -> Self {
+        let mut graph: StableGraph<(f32, f32), (u64, u64)> = StableGraph::default();
+        let mut nodes: Vec<NodeIndex> = Vec::new();
+        let mut rng = thread_rng();
+
+        for _i in 0..num_nodes {
+            let x = rng.gen_range(0.0..=400.0);
+            let y = rng.gen_range(0.0..=300.0);
+            let n = graph.add_node((x,y));
+
+            // choose a random number of nodes between 1 and 5 to connect to
+            let num_neighbors = rng.gen_range(min(nodes.len(), 1)..=min(nodes.len(), 5));
+            let neighbors = nodes.choose_multiple(&mut rng, num_neighbors);
+            for neighbor in neighbors {
+                // insert edges for each neighbor
+                let capacity1: u64 = rng.gen_range(1..=max_capacity);
+                let capacity2: u64 = rng.gen_range(1..=max_capacity);
+                graph.add_edge(n, *neighbor, (0, capacity1));
+                graph.add_edge(*neighbor, n, (0, capacity2));
+            }
+            nodes.push(n);
+        }
+
+        // choose source & sink nodes
+        let (s,t) = nodes.choose_multiple(&mut rng, 2).copied().collect_tuple::<(NodeIndex, NodeIndex)>().expect("not enough nodes");
+
+        Self { g: graph, s: s, t: t }
+    }
+
+    pub fn from(g: StableGraph<(f32, f32), (u64, u64)>, s: NodeIndex, t: NodeIndex) -> Self{
+        Self {g: g, s: s, t: t}
+    }
+
     // returns the eudclidean distance between two points
-    fn distance(a: Pos2, b: Pos2) -> f32 {
-        let delta_x = a.x - b.x;
-        let delta_y = a.y - b.y;
+    fn distance(a: (f32, f32), b: (f32, f32)) -> f32 {
+        let delta_x = a.0 - b.0;
+        let delta_y = a.1 - b.1;
         return f32::sqrt(delta_x.powf(2.) + delta_y.powf(2.));
     }
 
     // checks if the lines between a-b and c-d intersect
-    fn intersects(a: Pos2, b: Pos2, c: Pos2, d: Pos2) -> bool {
-        let line1 = Line::new(coord! {x: a.x, y: a.y }, coord! {x: b.x, y: b.y  } );
-        let line2 = Line::new(coord! {x: c.x, y: c.y }, coord! {x: d.x, y: d.y  } );
+    fn intersects(a: (f32, f32), b: (f32, f32), c: (f32, f32), d: (f32, f32)) -> bool {
+        let line1 = Line::new(coord! {x: a.0, y: a.1 }, coord! {x: b.0, y: b.1  } );
+        let line2 = Line::new(coord! {x: c.0, y: c.1 }, coord! {x: d.0, y: d.1  } );
         match line_intersection(line1, line2) {
             // only return true for 'proper' intersections which are not at the end of a line
             Some(LineIntersection::SinglePoint { is_proper: true, .. }) => true,

src/testing.rs

@@ -0,0 +1,81 @@
+use itertools::Itertools;
+use crate::{algorithms::{Dinic, EdmondsKarp, FordFulkerson, GoldbergTarjan, MaxflowAlgorithm, MaxflowAlgorithmEnum}, random_generator::MaxflowProblem, graph::FlowGraph};
+
+use std::time::{Instant};
+
+fn solve_problem_all_algos(problem: &MaxflowProblem) -> (f64, f64, f64, f64) {
+    let ff = FordFulkerson::from_problem(&problem);
+    let ek = EdmondsKarp::from_problem(&problem);
+    let di = Dinic::from_problem(&problem);
+    let gt = GoldbergTarjan::from_problem(&problem);
+    let mut instances:Vec<MaxflowAlgorithmEnum> = vec![ff.into(), ek.into(), di.into(), gt.into()];
+    let mut durations = vec![0.0; 4];
+    for (i,a) in instances.iter_mut().enumerate() {
+        let now = Instant::now();
+        a.run();
+        durations[i] = now.elapsed().as_secs_f64();
+
+        // check if the flow is valid
+        assert!(a.graph().valid_flow(problem.s, problem.t), "invalid flow");
+    }
+
+    // check if all algorithms return the same total flow
+    let total_flows: Vec<u64> = instances.iter_mut().map(|x| x.graph().total_flow(problem.s, problem.t)).collect();
+    assert!(total_flows.iter().all(|&x| x == total_flows[0]), "algorithms return different total flows");
+
+    return durations.into_iter().collect_tuple().unwrap();
+}
+
+fn run_tests(test_tuples: Vec<(u64, u64, u64)>) -> String {
+    let mut response = String::new();
+    
+    for (problem_count, nodes, capacity) in test_tuples {
+        println!("Running test: {} times, {} nodes, {} capacity", problem_count, nodes, capacity);
+        response += format!("=== Testing with problem_count={}, nodes={}, capacity={}\n", problem_count, nodes, capacity).as_str();
+        let mut problems: Vec<_> = Vec::new();
+        for _ in 0..problem_count {
+            problems.push(MaxflowProblem::new_random_graph(nodes, capacity));
+        }
+        let mut durations = Vec::new();
+        for (_, problem) in problems.iter_mut().enumerate() {
+            durations.push(solve_problem_all_algos(problem));
+        }
+
+        let d0 = durations.iter().map(|x| x.0).sum::<f64>() / problem_count as f64;
+        let d1 = durations.iter().map(|x| x.1).sum::<f64>() / problem_count as f64;
+        let d2 = durations.iter().map(|x| x.2).sum::<f64>() / problem_count as f64;
+        let d3 = durations.iter().map(|x| x.3).sum::<f64>() / problem_count as f64;
+        response += format!("Ford-Fulkerson:\t{:02.8}s\nEdmonds-Karp:\t{:02.8}s\nDinic:\t\t\t\t\t\t{:02.8}s\nGoldberg-Tarjan:\t{:02.8}s\n\n", d0, d1, d2, d3).as_str();
+    }
+
+    return response
+}
+
+pub fn run_small_tests() -> String {
+    let test_tuples = [
+        // (number of problems, number of nodes, max. capacity)
+        (10, 10, 10),
+        (10, 10, 100),
+        (10, 50, 10),
+        (10, 50, 100),
+        (10, 100, 10),
+        (10, 100, 100)
+    ];
+    return run_tests(test_tuples.into());
+}
+
+pub fn run_large_tests() -> String {
+    let test_tuples = [
+        // (number of problems, number of nodes, max. capacity)
+        (10, 100, 10),
+        (10, 100, 100),
+        (10, 100, 1000),
+        (10, 200, 10),
+        (10, 200, 100),
+        (10, 200, 1000),
+        (10, 300, 10),
+        (10, 300, 100),
+        (10, 300, 1000)
+    ];
+    return run_tests(test_tuples.into());
+}

tests.txt

@@ -0,0 +1,54 @@
+=== Testing with problem_count=10, nodes=100, capacity=10
+Ford-Fulkerson:	    0.00019723s
+Edmonds-Karp:	    0.00017104s
+Dinic:				0.00114540s
+Goldberg-Tarjan:	0.11118784s
+
+=== Testing with problem_count=10, nodes=100, capacity=100
+Ford-Fulkerson:	    0.00044646s
+Edmonds-Karp:	    0.00030087s
+Dinic:				0.00212037s
+Goldberg-Tarjan:	0.15394399s
+
+=== Testing with problem_count=10, nodes=100, capacity=1000
+Ford-Fulkerson:	    0.00028169s
+Edmonds-Karp:	    0.00017956s
+Dinic:				0.00128019s
+Goldberg-Tarjan:	0.11455003s
+
+=== Testing with problem_count=10, nodes=200, capacity=10
+Ford-Fulkerson:	    0.00057035s
+Edmonds-Karp:	    0.00042638s
+Dinic:				0.00270890s
+Goldberg-Tarjan:	1.70483265s
+
+=== Testing with problem_count=10, nodes=200, capacity=100
+Ford-Fulkerson:	    0.00121046s
+Edmonds-Karp:	    0.00045426s
+Dinic:				0.00301752s
+Goldberg-Tarjan:	1.48397911s
+
+=== Testing with problem_count=10, nodes=200, capacity=1000
+Ford-Fulkerson:	    0.00183244s
+Edmonds-Karp:	    0.00062984s
+Dinic:				0.00411386s
+Goldberg-Tarjan:	1.49089764s
+
+=== Testing with problem_count=10, nodes=300, capacity=10
+Ford-Fulkerson:	    0.00086230s
+Edmonds-Karp:	    0.00071712s
+Dinic:				0.00423448s
+Goldberg-Tarjan:	5.84010118s
+
+=== Testing with problem_count=10, nodes=300, capacity=100
+Ford-Fulkerson:	    0.00164213s
+Edmonds-Karp:	    0.00040957s
+Dinic:				0.00322493s
+Goldberg-Tarjan:	1.97116912s
+
+=== Testing with problem_count=10, nodes=300, capacity=1000
+Ford-Fulkerson:	    0.00362413s
+Edmonds-Karp:	    0.00094858s
+Dinic:				0.00600265s
+Goldberg-Tarjan:	5.16341617s
+

tests/example_flows.rs

@@ -0,0 +1,108 @@
+use maxflow_rs::graph::FlowGraph;
+use petgraph::prelude::StableGraph;
+use petgraph::stable_graph::NodeIndex;
+use maxflow_rs::random_generator::MaxflowProblem;
+use maxflow_rs::algorithms::{MaxflowAlgorithm, FordFulkerson, EdmondsKarp, Dinic, GoldbergTarjan};
+
+// Example taken from: https://en.wikipedia.org/wiki/Dinic%27s_algorithm#Example
+fn generate_small_maxflow_example() -> (StableGraph<(f32, f32), (u64, u64)>, StableGraph<(f32, f32), (u64, u64)>, NodeIndex, NodeIndex) {
+    let mut g: StableGraph<(f32, f32), (u64, u64)> = StableGraph::new();
+    let s = g.add_node((0., 5.));
+    let one = g.add_node((10., 0.));
+    let two = g.add_node((10., 10.));
+    let three = g.add_node((20., 0.));
+    let four = g.add_node((20., 10.));
+    let t = g.add_node((30., 5.));
+    g.add_edge(s, one, (0, 10));
+    g.add_edge(s, two, (0, 10));
+    g.add_edge(one, three, (0, 4));
+    g.add_edge(one, four, (0, 8));
+    g.add_edge(one, two, (0,2));
+    g.add_edge(two, four, (0,9));
+    g.add_edge(three, t, (0,10));
+    g.add_edge(four, three, (0,5)); // changed capacity to 5 to enforce a single optimal solution
+    g.add_edge(four, t, (0,10));
+
+    let mut m = g.clone();
+    m.update_edge(s, one, (10, 10));
+    m.update_edge(s, two, (9, 10));
+    m.update_edge(one, three, (4, 4));
+    m.update_edge(one, four, (6, 8));
+    m.update_edge(one, two, (0,2));
+    m.update_edge(two, four, (9,9));
+    m.update_edge(three, t, (9,10));
+    m.update_edge(four, three, (5,5)); // changed capacity to 5 to enforce a single optimal solution
+    m.update_edge(four, t, (10,10));
+
+    return (g, m, s, t);
+}
+
+fn graph_equal(one: StableGraph<(f32, f32), (u64, u64)>, other: StableGraph<(f32, f32), (u64, u64)>) -> bool {
+    // ensure all edges have the same weights
+    let edges = one.edge_indices().map(|e| e).collect::<Vec<_>>();
+    for edge in edges {
+        if one.edge_weight(edge).expect("edge index not found") != other.edge_weight(edge).expect("edge index not found") {
+            println!("Edge weights don't match");
+            println!("Graph 1: {:?}", one);
+            println!("Graph 2: {:?}", other);
+            return false;
+        }
+    }
+
+    // ensure all nodes have the same weights
+    let nodes = one.node_indices().map(|n| n).collect::<Vec<_>>();
+    for node in nodes {
+        if one.node_weight(node).expect("node index not found") != other.node_weight(node).expect("node index not found") {
+            println!("Node weights don't match");
+            println!("Graph 1: {:?}", one);
+            println!("Graph 2: {:?}", other);
+            return false;
+        }
+    }
+
+    true
+}
+
+#[test]
+fn test_ford_fulkerson() {
+    let (g, m, s, t) = generate_small_maxflow_example();
+
+    let problem = MaxflowProblem::from(g, s, t);
+    let mut  algo = FordFulkerson::from_problem(&problem);
+    let solution = algo.run();
+
+    assert!(graph_equal(solution.prune_zero(), m.residual().prune_zero()));
+}
+
+#[test]
+fn test_edmonds_karp() {
+    let (g, m, s, t) = generate_small_maxflow_example();
+
+    let problem = MaxflowProblem::from(g, s, t);
+    let mut  algo = EdmondsKarp::from_problem(&problem);
+    let solution = algo.run();
+
+    assert!(graph_equal(solution.prune_zero(), m.residual().prune_zero()));
+}
+
+#[test]
+fn test_dinic() {
+    let (g, m, s, t) = generate_small_maxflow_example();
+
+    let problem = MaxflowProblem::from(g, s, t);
+    let mut  algo = Dinic::from_problem(&problem);
+    let solution = algo.run();
+
+    assert!(graph_equal(solution.prune_zero(), m.residual().prune_zero()));
+}
+
+#[test]
+fn test_goldberg_tarjan() {
+    let (g, m, s, t) = generate_small_maxflow_example();
+
+    let problem = MaxflowProblem::from(g, s, t);
+    let mut  algo = GoldbergTarjan::from_problem(&problem);
+    let solution = algo.run();
+
+    assert!(graph_equal(solution.prune_zero(), m.residual().prune_zero()));
+}

tests/valid_flow.rs

@@ -0,0 +1,2 @@
+// check capacity at each edge (incoming flows = outgoing flows)
+// check capacity isn't violated (flow <= capacity)