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Fix #167: Add TravelingSalesman to QUBO reduction (#605)
* Add plan for #167: TravelingSalesman to QUBO reduction Co-authored-by: Claude <noreply@anthropic.com> * Implement TravelingSalesman to QUBO reduction (#167) Position-based encoding (Lucas 2014): n² binary variables x_{v,p} with one-hot row/column constraints and distance objective. Handles non-complete graphs by penalizing non-edge consecutive pairs. Co-authored-by: Claude <noreply@anthropic.com> * chore: remove plan file after implementation Co-authored-by: Claude <noreply@anthropic.com> * style: rustfmt after upstream merge Co-authored-by: Claude <noreply@anthropic.com> * fix: address Copilot review — store num_edges instead of edges Vec, call self.edges() once Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude <noreply@anthropic.com> Co-authored-by: GiggleLiu <cacate0129@gmail.com>
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‎docs/paper/examples/travelingsalesman_to_qubo.json‎

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{
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"source": {
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"problem": "TravelingSalesman",
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"variant": {
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"weight": "i32",
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"graph": "SimpleGraph"
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},
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"instance": {
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"num_edges": 3,
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"num_vertices": 3
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}
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},
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"target": {
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"problem": "QUBO",
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"variant": {
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"weight": "f64"
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},
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"instance": {
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"matrix": [
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},
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"formula": "num_vertices^2"
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}
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]
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}

‎docs/paper/examples/travelingsalesman_to_qubo.result.json‎

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{
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"solutions": [
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}

‎examples/reduction_travelingsalesman_to_qubo.rs‎

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// # Traveling Salesman to QUBO Reduction (Penalty Method)
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//
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// ## Mathematical Relationship
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// The TSP on a graph G = (V, E) with edge weights is mapped to QUBO using
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// position-based encoding. Each vertex v and position k has a binary variable
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// x_{v,k}, with penalties enforcing:
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//
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// 1. Assignment constraint: each vertex appears exactly once in the tour
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// 2. Position constraint: each position has exactly one vertex
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// 3. Edge constraint: consecutive positions use valid edges
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// 4. Objective: total edge weight of the tour
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//
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// The QUBO has n^2 variables (n vertices x n positions).
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//
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// ## This Example
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// - Instance: K3 complete graph with edge weights [1, 2, 3]
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// (w01=1, w02=2, w12=3)
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// - Source: TravelingSalesman on 3 vertices, 3 edges
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// - QUBO variables: 9 (3^2 = 9, position encoding)
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// - Optimal tour cost = 6 (all edges used: 1 + 2 + 3)
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//
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// ## Outputs
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// - `docs/paper/examples/travelingsalesman_to_qubo.json` — reduction structure
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// - `docs/paper/examples/travelingsalesman_to_qubo.result.json` — solutions
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//
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// ## Usage
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// ```bash
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// cargo run --example reduction_travelingsalesman_to_qubo
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// ```
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use problemreductions::export::*;
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use problemreductions::prelude::*;
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use problemreductions::topology::{Graph, SimpleGraph};
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pub fn run() {
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println!("=== TravelingSalesman -> QUBO Reduction ===\n");
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// K3 complete graph with edge weights: w01=1, w02=2, w12=3
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let graph = SimpleGraph::new(3, vec![(0, 1), (0, 2), (1, 2)]);
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let tsp = TravelingSalesman::new(graph, vec![1i32, 2, 3]);
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// Reduce to QUBO
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let reduction = ReduceTo::<QUBO>::reduce_to(&tsp);
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let qubo = reduction.target_problem();
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println!(
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"Source: TravelingSalesman on K3 ({} vertices, {} edges)",
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tsp.graph().num_vertices(),
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tsp.graph().num_edges()
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);
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println!(
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"Target: QUBO with {} variables (position encoding: 3 vertices x 3 positions)",
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qubo.num_variables()
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);
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println!("Q matrix:");
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for row in qubo.matrix() {
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let formatted: Vec<String> = row.iter().map(|v| format!("{:8.1}", v)).collect();
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println!(" [{}]", formatted.join(", "));
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}
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// Solve QUBO with brute force
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let solver = BruteForce::new();
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let qubo_solutions = solver.find_all_best(qubo);
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// Extract and verify solutions
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println!("\nOptimal QUBO solutions: {}", qubo_solutions.len());
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let mut solutions = Vec::new();
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for sol in &qubo_solutions {
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let extracted = reduction.extract_solution(sol);
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let edge_names = ["(0,1)", "(0,2)", "(1,2)"];
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let selected: Vec<&str> = extracted
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.iter()
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.enumerate()
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.filter(|(_, &v)| v == 1)
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.map(|(i, _)| edge_names[i])
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.collect();
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println!(" Edges: {}", selected.join(", "));
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// Closed-loop verification: check solution is valid in original problem
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let metric = tsp.evaluate(&extracted);
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assert!(metric.is_valid(), "Tour must be valid in source problem");
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println!(" Cost: {:?}", metric);
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solutions.push(SolutionPair {
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source_config: extracted,
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target_config: sol.clone(),
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});
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}
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// Cross-check with brute force on original problem
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let bf_solutions = solver.find_all_best(&tsp);
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let bf_metric = tsp.evaluate(&bf_solutions[0]);
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let qubo_metric = tsp.evaluate(&reduction.extract_solution(&qubo_solutions[0]));
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assert_eq!(
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bf_metric, qubo_metric,
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"QUBO reduction must match brute force optimum"
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);
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println!(
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"\nVerification passed: optimal tour cost matches brute force ({:?})",
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bf_metric
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);
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// Export JSON
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let source_variant = variant_to_map(TravelingSalesman::<SimpleGraph, i32>::variant());
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let target_variant = variant_to_map(QUBO::<f64>::variant());
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let overhead = lookup_overhead(
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"TravelingSalesman",
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&source_variant,
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"QUBO",
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&target_variant,
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)
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.expect("TravelingSalesman -> QUBO overhead not found");
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let data = ReductionData {
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source: ProblemSide {
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problem: TravelingSalesman::<SimpleGraph, i32>::NAME.to_string(),
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variant: source_variant,
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instance: serde_json::json!({
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"num_vertices": tsp.graph().num_vertices(),
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"num_edges": tsp.graph().num_edges(),
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}),
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},
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target: ProblemSide {
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problem: QUBO::<f64>::NAME.to_string(),
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variant: target_variant,
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instance: serde_json::json!({
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"num_vars": qubo.num_vars(),
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"matrix": qubo.matrix(),
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}),
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},
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overhead: overhead_to_json(&overhead),
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};
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let results = ResultData { solutions };
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let name = "travelingsalesman_to_qubo";
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write_example(name, &data, &results);
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}
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fn main() {
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run()
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}

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