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https://github.com/klus3kk/graph-isomorphism-aco
Solving the Graph Isomorphism problem using Ant Colony Optimization.
https://github.com/klus3kk/graph-isomorphism-aco
ant-colony-optimization isomorphism metaheuristic-optimisation python
Last synced: about 13 hours ago
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Solving the Graph Isomorphism problem using Ant Colony Optimization.
- Host: GitHub
- URL: https://github.com/klus3kk/graph-isomorphism-aco
- Owner: Klus3kk
- Created: 2024-10-20T20:23:22.000Z (3 months ago)
- Default Branch: main
- Last Pushed: 2024-12-18T14:15:23.000Z (23 days ago)
- Last Synced: 2024-12-18T15:26:27.947Z (23 days ago)
- Topics: ant-colony-optimization, isomorphism, metaheuristic-optimisation, python
- Language: Python
- Homepage:
- Size: 746 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Graph-Isomorphism-ACO
This project addresses the **Graph Isomorphism Problem**, which involves determining whether two graphs are structurally identical (isomorphic). The project implements three different algorithms to solve the problem:
1. **Greedy Algorithm** - A heuristic-based approach that attempts to find isomorphisms quickly.
2. **Brute Force Algorithm** - Exhaustively explores all possible vertex permutations for exact solutions.
3. **Ant Colony Optimization (ACO)** - A metaheuristic inspired by the behavior of ants to find approximate solutions efficiently.
## Features
- Generate random graphs for testing with customizable parameters (number of vertices, edge probabilities, and weights).
- Load graphs from JSON files for reproducibility and external data.
- Benchmark and compare the performance of the algorithms in terms of runtime and solution quality.
- Visualize graph mappings and connections using **NetworkX**.
## Usage
The project supports two modes: **graph generation** and **loading graphs from JSON files**.
### Running the Benchmark
To run benchmarks for graphs with vertex counts ranging from 5 to 10 (by default):
```bash
python benchmark.py
```
This will:
- Generate random graphs dynamically.
- Compare the execution time and quality of all three algorithms.
- Save plots for runtime (`algorithm_time_comparison_log.png`) and solution quality (`algorithm_quality_comparison.png`) in the `results/` folder.
### Running the Main Program
The main program supports custom configurations for graph input:
#### 1. Generate Random Graphs
To generate random graphs and test the algorithms:
```bash
python main.py --generate --vertices --edge_probability --max_weight
```
##### Example of usage with random graphs
```bash
python main.py --generate --vertices 5 --edge_probability 0.5 --max_weight 10
```
#### 2. Load Graphs from JSON
To load graphs from JSON files for testing:
```bash
python main.py --file1 --file2
```
##### Example of usage with files
```bash
python main.py --file1 data/graph1.json --file2 data/graph2.json
```
## Output Files
- **Results**:
- `results/results.json`: Contains mappings, scores, and execution times for all three algorithms.
- Individual mapping files:
- `results/greedy_mapping.json`
- `results/brute_force_mapping.json`
- `results/aco_mapping.json`
- **Plots**:
- `results/algorithm_time_comparison_log.png`: Runtime comparison of algorithms.
- `results/algorithm_quality_comparison.png`: Quality comparison of solutions.
## How It Works
### Algorithms
1. **Greedy Algorithm**:
- Matches vertices in one graph to another based on the highest connectivity.
- Fast but not guaranteed to find the optimal solution.
2. **Brute Force**:
- Tests all permutations of vertex mappings to find the exact isomorphism.
- Guarantees correctness but scales poorly with larger graphs.
3. **Ant Colony Optimization (ACO)**:
- Uses pheromones to guide a population of ants to explore promising mappings.
- Balances exploration and exploitation to approximate solutions effectively.
### Graph Representation
- Adjacency matrices represent the graphs.
- Weights on edges indicate connections between vertices.
## Examples
### Benchmark Output Example
When running `benchmark.py`, you will see console outputs like:
```bash
=== Testowanie dla 5 wierzchołków ===
Uruchamianie algorytmu zachłannego (Greedy)...
Greedy: czas = 0.000002s, jakość = 0.900000
Uruchamianie algorytmu brute-force...
BruteForce: czas = 0.012048s, jakość = 1.000000
Uruchamianie algorytmu mrówkowego (ACO)...
ACO: czas = 0.004231s, jakość = 0.950000
```
## Install Dependencies
Before running the project, ensure you have the necessary Python dependencies installed. You can install them using:
```bash
pip install -r requirements.txt
```