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ruv
327
crates/ruvector-mincut/examples/localkcut_demo.rs
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crates/ruvector-mincut/examples/localkcut_demo.rs
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//! LocalKCut Algorithm Demonstration
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//!
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//! This example demonstrates the deterministic LocalKCut algorithm from the
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//! December 2024 paper. It shows how to:
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//!
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//! 1. Find local minimum cuts near specific vertices
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//! 2. Use deterministic edge colorings for reproducibility
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//! 3. Apply forest packing for witness guarantees
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//! 4. Compare with global minimum cut algorithms
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use ruvector_mincut::prelude::*;
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use std::sync::Arc;
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fn main() {
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println!("=== LocalKCut Algorithm Demonstration ===\n");
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// Example 1: Simple graph with bridge
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println!("Example 1: Bridge Detection");
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demo_bridge_detection();
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println!();
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// Example 2: Deterministic behavior
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println!("Example 2: Deterministic Coloring");
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demo_deterministic_coloring();
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println!();
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// Example 3: Forest packing
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println!("Example 3: Forest Packing Witnesses");
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demo_forest_packing();
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println!();
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// Example 4: Comparison with global mincut
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println!("Example 4: Local vs Global Minimum Cut");
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demo_local_vs_global();
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println!();
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// Example 5: Complex graph
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println!("Example 5: Complex Graph Analysis");
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demo_complex_graph();
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}
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/// Demonstrates finding a bridge using LocalKCut
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fn demo_bridge_detection() {
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let graph = Arc::new(DynamicGraph::new());
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// Create two components connected by a bridge
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// Component 1: triangle {1, 2, 3}
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graph.insert_edge(1, 2, 1.0).unwrap();
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graph.insert_edge(2, 3, 1.0).unwrap();
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graph.insert_edge(3, 1, 1.0).unwrap();
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// Bridge: 3 -> 4 (the minimum cut!)
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graph.insert_edge(3, 4, 1.0).unwrap();
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// Component 2: triangle {4, 5, 6}
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graph.insert_edge(4, 5, 1.0).unwrap();
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graph.insert_edge(5, 6, 1.0).unwrap();
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graph.insert_edge(6, 4, 1.0).unwrap();
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println!("Graph: Two triangles connected by a bridge");
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println!(
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"Vertices: {}, Edges: {}",
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graph.num_vertices(),
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graph.num_edges()
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);
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// Find local cut from vertex 1
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let local_kcut = LocalKCut::new(graph.clone(), 5);
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println!("\nSearching for local cut from vertex 1 with k=5...");
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if let Some(result) = local_kcut.find_cut(1) {
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println!("✓ Found local cut!");
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println!(" Cut value: {}", result.cut_value);
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println!(" Cut set size: {}", result.cut_set.len());
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println!(" Cut edges: {:?}", result.cut_edges);
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println!(" Iterations: {}", result.iterations);
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// The bridge should be found
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if result.cut_value == 1.0 {
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println!(" → Successfully detected the bridge!");
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}
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} else {
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println!("✗ No cut found within bound k=5");
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}
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}
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/// Demonstrates deterministic coloring behavior
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fn demo_deterministic_coloring() {
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let graph = Arc::new(DynamicGraph::new());
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// Create a simple path graph: 1-2-3-4-5
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for i in 1..=4 {
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graph.insert_edge(i, i + 1, 1.0).unwrap();
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}
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println!("Graph: Path of 5 vertices");
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// Create two LocalKCut instances
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let lk1 = LocalKCut::new(graph.clone(), 3);
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let lk2 = LocalKCut::new(graph.clone(), 3);
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println!("\nEdge colorings (deterministic):");
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for edge in graph.edges() {
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let color1 = lk1.edge_color(edge.id).unwrap();
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let color2 = lk2.edge_color(edge.id).unwrap();
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println!(" Edge ({}, {}): {:?}", edge.source, edge.target, color1);
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// Verify determinism
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assert_eq!(color1, color2, "Colors should be deterministic!");
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}
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println!("\n✓ All edge colorings are deterministic!");
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// Find cuts from different vertices
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println!("\nFinding cuts from different starting vertices:");
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for start_vertex in 1..=5 {
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if let Some(result) = lk1.find_cut(start_vertex) {
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println!(
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" Vertex {}: cut value = {}, set size = {}",
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start_vertex,
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result.cut_value,
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result.cut_set.len()
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);
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}
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}
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}
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/// Demonstrates forest packing and witness properties
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fn demo_forest_packing() {
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let graph = Arc::new(DynamicGraph::new());
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// Create a more complex graph
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// 1 - 2
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// | |
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// 3 - 4 - 5
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// | |
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// 6 - 7
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graph.insert_edge(1, 2, 1.0).unwrap();
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graph.insert_edge(1, 3, 1.0).unwrap();
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graph.insert_edge(2, 4, 1.0).unwrap();
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graph.insert_edge(3, 4, 1.0).unwrap();
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graph.insert_edge(4, 5, 1.0).unwrap();
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graph.insert_edge(4, 6, 1.0).unwrap();
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graph.insert_edge(5, 7, 1.0).unwrap();
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graph.insert_edge(6, 7, 1.0).unwrap();
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println!("Graph: Complex grid-like structure");
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println!(
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"Vertices: {}, Edges: {}",
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graph.num_vertices(),
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graph.num_edges()
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);
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// Create forest packing
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let lambda_max = 3; // Upper bound on min cut
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let epsilon = 0.1; // Approximation parameter
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println!(
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"\nCreating forest packing with λ_max={}, ε={}...",
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lambda_max, epsilon
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);
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let packing = ForestPacking::greedy_packing(&*graph, lambda_max, epsilon);
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println!("✓ Created {} forests", packing.num_forests());
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// Show forest structures
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for i in 0..packing.num_forests().min(3) {
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if let Some(forest) = packing.forest(i) {
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println!(" Forest {}: {} edges", i, forest.len());
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}
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}
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// Find a cut and check witness property
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let local_kcut = LocalKCut::new(graph.clone(), 5);
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if let Some(result) = local_kcut.find_cut(1) {
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println!("\nFound cut with value {}", result.cut_value);
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let is_witnessed = packing.witnesses_cut(&result.cut_edges);
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println!(" Witnessed by all forests: {}", is_witnessed);
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if is_witnessed {
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println!(" ✓ Cut satisfies witness property!");
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}
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}
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}
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/// Compare local and global minimum cuts
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fn demo_local_vs_global() {
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let graph = Arc::new(DynamicGraph::new());
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// Create a graph where local and global cuts differ
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// 1 - 2 - 3
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// | | |
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// 4 - 5 - 6
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// | | |
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// 7 - 8 - 9
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// Top row
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graph.insert_edge(1, 2, 2.0).unwrap();
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graph.insert_edge(2, 3, 2.0).unwrap();
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// Middle row
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graph.insert_edge(4, 5, 2.0).unwrap();
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graph.insert_edge(5, 6, 2.0).unwrap();
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// Bottom row
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graph.insert_edge(7, 8, 2.0).unwrap();
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graph.insert_edge(8, 9, 2.0).unwrap();
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// Vertical connections (weaker)
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graph.insert_edge(1, 4, 1.0).unwrap();
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graph.insert_edge(2, 5, 1.0).unwrap();
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graph.insert_edge(3, 6, 1.0).unwrap();
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graph.insert_edge(4, 7, 1.0).unwrap();
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graph.insert_edge(5, 8, 1.0).unwrap();
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graph.insert_edge(6, 9, 1.0).unwrap();
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println!("Graph: 3x3 grid with different edge weights");
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println!(
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"Vertices: {}, Edges: {}",
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graph.num_vertices(),
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graph.num_edges()
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);
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// Find local cuts from different vertices
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let local_kcut = LocalKCut::new(graph.clone(), 10);
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println!("\nLocal cuts from different vertices:");
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for vertex in &[1, 5, 9] {
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if let Some(result) = local_kcut.find_cut(*vertex) {
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println!(
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" Vertex {}: cut value = {}, iterations = {}",
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vertex, result.cut_value, result.iterations
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);
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}
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}
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// Build global minimum cut (using the algorithm)
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let mut mincut = MinCutBuilder::new().exact().build().unwrap();
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// Add edges to global mincut
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for edge in graph.edges() {
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let _ = mincut.insert_edge(edge.source, edge.target, edge.weight);
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}
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let global_value = mincut.min_cut_value();
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println!("\nGlobal minimum cut value: {}", global_value);
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println!("\n✓ Local cuts provide fast approximations to global minimum cut");
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}
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/// Analyze a complex graph with multiple cut candidates
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fn demo_complex_graph() {
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let graph = Arc::new(DynamicGraph::new());
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// Create a graph with multiple communities
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// Community 1: clique {1,2,3,4}
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for i in 1..=4 {
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for j in i + 1..=4 {
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graph.insert_edge(i, j, 2.0).unwrap();
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}
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}
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// Community 2: clique {5,6,7,8}
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for i in 5..=8 {
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for j in i + 1..=8 {
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graph.insert_edge(i, j, 2.0).unwrap();
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}
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}
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// Weak connections between communities
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graph.insert_edge(4, 5, 0.5).unwrap();
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graph.insert_edge(3, 6, 0.5).unwrap();
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println!("Graph: Two dense communities with weak connections");
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println!(
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"Vertices: {}, Edges: {}",
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graph.num_vertices(),
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graph.num_edges()
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);
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let stats = graph.stats();
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println!("Average degree: {:.2}", stats.avg_degree);
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println!("Total weight: {:.2}", stats.total_weight);
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// Find local cuts
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let local_kcut = LocalKCut::new(graph.clone(), 5);
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println!("\nSearching for cuts with k=5...");
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// Try from community 1
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if let Some(result) = local_kcut.find_cut(1) {
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println!(" From community 1:");
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println!(" Cut value: {}", result.cut_value);
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println!(
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" Separates {} vertices from {}",
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result.cut_set.len(),
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graph.num_vertices() - result.cut_set.len()
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);
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}
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// Try from community 2
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if let Some(result) = local_kcut.find_cut(5) {
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println!(" From community 2:");
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println!(" Cut value: {}", result.cut_value);
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println!(
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" Separates {} vertices from {}",
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result.cut_set.len(),
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graph.num_vertices() - result.cut_set.len()
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);
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}
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// Enumerate paths to understand graph structure
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println!("\nPath enumeration from vertex 1:");
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let paths = local_kcut.enumerate_paths(1, 2);
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println!(" Found {} distinct reachable sets at depth 2", paths.len());
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// Show diversity of reachable sets
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let mut sizes: Vec<_> = paths.iter().map(|p| p.len()).collect();
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sizes.sort_unstable();
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sizes.dedup();
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println!(" Reachable set sizes: {:?}", sizes);
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println!("\n✓ LocalKCut successfully analyzes community structure");
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}
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