Problem: #
create pair of of people with similar properties. Minimize difference between members of a pair
Solution #
Algorithm for optimal node pairing that minimizes the total distance between paired nodes. This is essentially a minimum-weight perfect matching problem.I’ve created a comprehensive implementation of optimal node pairing algorithms. Here’s what the code includes:
Key Components: #
- Node Class: Represents a point in 2D space with distance calculation
- Multiple Algorithm Approaches:
- Greedy: Fast O(n³) algorithm that repeatedly finds closest pairs
- Nearest Neighbor: O(n²) algorithm that pairs each node with its nearest unpaired neighbor
- Approximation with Local Search: Improves greedy solution using 2-opt style swaps
- Brute Force Optimal: Guaranteed optimal solution via backtracking (exponential time)
Algorithm Trade-offs: #
- Greedy: Fast but may get stuck in local optima
- Nearest Neighbor: Faster, good for large datasets, decent quality
- Approximation: Best balance of speed and quality for medium datasets
- Brute Force: Perfect solution but only practical for small instances (≤8-10 nodes)
Usage Recommendations: #
- Small datasets (≤8 nodes): Use brute force for guaranteed optimal
- Medium datasets (10-100 nodes): Use approximation algorithm
- Large datasets (>100 nodes): Use nearest neighbor or greedy
The code includes a test function that demonstrates all algorithms on a sample dataset, showing the total distance and individual pairs for each approach. You can easily adapt it for your specific coordinate system or distance metric.