diff --git a/docs/paper/reductions.typ b/docs/paper/reductions.typ index 50adefd1d..4f3cb6ad2 100644 --- a/docs/paper/reductions.typ +++ b/docs/paper/reductions.typ @@ -3806,6 +3806,22 @@ The following reductions to Integer Linear Programming are straightforward formu _Solution extraction._ For each witness position $p$, read the unique symbol $a$ with $x_(p, a) = 1$ and output the resulting length-$K$ string. ] +#reduction-rule("MinimumMultiwayCut", "ILP")[ + The vertex-assignment + edge-cut indicator formulation @chopra1996 introduces binary variables for vertex-to-component membership and edge-cut indicators. Terminal vertices are fixed to their own components, partition constraints ensure every vertex belongs to exactly one component, and linking inequalities force the cut indicator on whenever an edge's endpoints are in different components. +][ + _Construction._ Given graph $G = (V, E, w)$ with $n = |V|$ vertices, $m = |E|$ edges, edge weights $w_e > 0$, and $k$ terminals $T = {t_0, dots, t_(k-1)}$: + + _Variables:_ (1) $y_(i v) in {0, 1}$ for $i in {0, dots, k-1}$, $v in V$: vertex $v$ belongs to the component of terminal $t_i$. (2) $x_e in {0, 1}$ for $e in E$: edge $e$ is in the cut. Total: $k n + m$ variables. + + _Constraints:_ (1) Terminal fixing: $y_(i, t_i) = 1$ for each $i$ (terminal $t_i$ is in its own component); $y_(j, t_i) = 0$ for $j eq.not i$ (each terminal excluded from other components). (2) Partition: $sum_(i=0)^(k-1) y_(i v) = 1$ for each $v in V$ (each vertex in exactly one component). (3) Edge-cut linking: for each edge $e = (u, v)$ and each terminal $i$: $x_e gt.eq y_(i u) - y_(i v)$ and $x_e gt.eq y_(i v) - y_(i u)$ (force $x_e = 1$ when endpoints are in different components). Total: $k^2 + n + 2 k m$ constraints. + + _Objective:_ Minimize $sum_(e in E) w_e dot x_e$. + + _Correctness._ ($arrow.r.double$) A multiway cut $C$ partitions $V$ into $k$ components, one per terminal. Setting $y_(i v) = 1$ iff $v$ is in $t_i$'s component and $x_e = 1$ iff $e in C$ satisfies all constraints: partition by construction, terminal fixing by definition, and linking because any edge with endpoints in different components is in $C$. The objective equals the cut weight. ($arrow.l.double$) Any feasible ILP solution defines a valid partition (by constraint (2)) separating all terminals (by constraint (1)). The linking constraints (3) force $x_e = 1$ for all cross-component edges, so the objective is at least the multiway cut weight; minimization ensures optimality. + + _Solution extraction._ For each edge $e$ at index $"idx"$, read $x_e = x^*_(k n + "idx")$. The source configuration is $"config"[e] = x_e$ (1 = cut, 0 = keep). +] + == Unit Disk Mapping #reduction-rule("MaximumIndependentSet", "KingsSubgraph")[ diff --git a/docs/paper/references.bib b/docs/paper/references.bib index db270576b..5a949127a 100644 --- a/docs/paper/references.bib +++ b/docs/paper/references.bib @@ -798,6 +798,16 @@ @article{papadimitriou1982 doi = {10.1145/322307.322309} } +@article{chopra1996, + author = {Sunil Chopra and Jonathan H. Owen}, + title = {Extended formulations for the A-cut problem}, + journal = {Mathematical Programming}, + volume = {73}, + pages = {7--30}, + year = {1996}, + doi = {10.1007/BF02592096} +} + @article{kou1977, author = {Lawrence T. Kou}, title = {Polynomial Complete Consecutive Information Retrieval Problems}, diff --git a/src/example_db/fixtures/examples.json b/src/example_db/fixtures/examples.json index dee92309f..d5007656f 100644 --- a/src/example_db/fixtures/examples.json +++ b/src/example_db/fixtures/examples.json @@ -64,18 +64,18 @@ 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{"source":{"problem":"TravelingSalesman","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[10,15,20,35,25,30],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[0,3,null],[1,2,null],[1,3,null],[2,3,null]],"node_holes":[],"nodes":[null,null,null,null]}}}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Eq","rhs":1.0,"terms":[[0,1.0],[1,1.0],[2,1.0],[3,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[4,1.0],[5,1.0],[6,1.0],[7,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[8,1.0],[9,1.0],[10,1.0],[11,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[12,1.0],[13,1.0],[14,1.0],[15,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[0,1.0],[4,1.0],[8,1.0],[12,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[1,1.0],[5,1.0],[9,1.0],[13,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[2,1.0],[6,1.0],[10,1.0],[14,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[3,1.0],[7,1.0],[11,1.0],[15,1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[16,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[16,1.0],[5,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[16,1.0],[0,-1.0],[5,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[17,1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[17,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[17,1.0],[4,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[18,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[18,1.0],[6,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[18,1.0],[1,-1.0],[6,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[19,1.0],[5,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[19,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[19,1.0],[5,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[20,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[20,1.0],[7,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[20,1.0],[2,-1.0],[7,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[21,1.0],[6,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[21,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[21,1.0],[6,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[22,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[22,1.0],[4,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[22,1.0],[3,-1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[23,1.0],[7,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[23,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[23,1.0],[7,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[24,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[24,1.0],[9,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[24,1.0],[0,-1.0],[9,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[25,1.0],[8,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[25,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[25,1.0],[8,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[26,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[26,1.0],[10,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[26,1.0],[1,-1.0],[10,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[27,1.0],[9,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[27,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[27,1.0],[9,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[28,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[28,1.0],[11,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[28,1.0],[2,-1.0],[11,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[29,1.0],[10,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[29,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[29,1.0],[10,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[30,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[30,1.0],[8,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[30,1.0],[3,-1.0],[8,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[31,1.0],[11,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[31,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[31,1.0],[11,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[32,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[32,1.0],[13,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[32,1.0],[0,-1.0],[13,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[33,1.0],[12,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[33,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[33,1.0],[12,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[34,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[34,1.0],[14,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[34,1.0],[1,-1.0],[14,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[35,1.0],[13,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[35,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[35,1.0],[13,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[36,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[36,1.0],[15,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[36,1.0],[2,-1.0],[15,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[37,1.0],[14,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[37,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[37,1.0],[14,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[38,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[38,1.0],[12,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[38,1.0],[3,-1.0],[12,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[39,1.0],[15,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[39,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[39,1.0],[15,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[40,1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[40,1.0],[9,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[40,1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+ {"source":{"problem":"TravelingSalesman","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,2,3],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[1,2,null]],"node_holes":[],"nodes":[null,null,null]}}}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[-14.0,14.0,14.0,14.0,1.0,1.0,14.0,2.0,2.0],[0.0,-14.0,14.0,1.0,14.0,1.0,2.0,14.0,2.0],[0.0,0.0,-14.0,1.0,1.0,14.0,2.0,2.0,14.0],[0.0,0.0,0.0,-14.0,14.0,14.0,14.0,3.0,3.0],[0.0,0.0,0.0,0.0,-14.0,14.0,3.0,14.0,3.0],[0.0,0.0,0.0,0.0,0.0,-14.0,3.0,3.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,-14.0,14.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-14.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-14.0]],"num_vars":9}},"solutions":[{"source_config":[1,1,1],"target_config":[0,0,1,1,0,0,0,1,0]}]} ] } diff --git a/src/rules/minimummultiwaycut_ilp.rs b/src/rules/minimummultiwaycut_ilp.rs new file mode 100644 index 000000000..211ce2344 --- /dev/null +++ b/src/rules/minimummultiwaycut_ilp.rs @@ -0,0 +1,144 @@ +//! Reduction from MinimumMultiwayCut to ILP (Integer Linear Programming). +//! +//! Uses the standard vertex-assignment + edge-cut indicator formulation +//! (Chopra & Owen, 1996): +//! - Variables: `y_{iv}` (vertex v in component i) + `x_e` (edge e in cut), all binary +//! - Constraints: partition (each vertex in exactly one component) + edge-cut linking +//! - Objective: minimize total weight of cut edges + +use crate::models::algebraic::{LinearConstraint, ObjectiveSense, ILP}; +use crate::models::graph::MinimumMultiwayCut; +use crate::reduction; +use crate::rules::traits::{ReduceTo, ReductionResult}; +use crate::topology::{Graph, SimpleGraph}; + +/// Result of reducing MinimumMultiwayCut to ILP. +/// +/// Variable layout (all binary): +/// - `y_{iv}` for i=0..k-1, v=0..n-1: vertex v assigned to component of terminal t_i +/// (index: i*n + v) +/// - `x_e` for e=0..m-1: edge e is in the cut (index: k*n + e) +/// +/// Total: kn + m variables. +#[derive(Debug, Clone)] +pub struct ReductionMMCToILP { + target: ILP, + /// Number of vertices in the source graph. + n: usize, + /// Number of edges in the source graph. + m: usize, + /// Number of terminals. + k: usize, +} + +impl ReductionResult for ReductionMMCToILP { + type Source = MinimumMultiwayCut; + type Target = ILP; + + fn target_problem(&self) -> &ILP { + &self.target + } + + /// Extract solution from ILP back to MinimumMultiwayCut. + /// + /// For each edge e, source config[e] = target_solution[k*n + e] (the x_e variable). + fn extract_solution(&self, target_solution: &[usize]) -> Vec { + let offset = self.k * self.n; + (0..self.m).map(|e| target_solution[offset + e]).collect() + } +} + +#[reduction( + overhead = { + num_vars = "num_terminals * num_vertices + num_edges", + num_constraints = "num_vertices + 2 * num_terminals * num_edges + num_terminals * num_terminals", + } +)] +impl ReduceTo> for MinimumMultiwayCut { + type Result = ReductionMMCToILP; + + fn reduce_to(&self) -> Self::Result { + let n = self.num_vertices(); + let m = self.num_edges(); + let k = self.num_terminals(); + let terminals = self.terminals(); + let edges = self.graph().edges(); + let weights = self.edge_weights(); + let num_vars = k * n + m; + + // Terminal fixing constraints: k constraints for y_{i,t_i} = 1, + // and k*(k-1) constraints for y_{j,t_i} = 0 where j != i. + // Total terminal fixes: k + k*(k-1) = k^2. + let num_terminal_fixes = k * k; + let num_constraints = n + 2 * k * m + num_terminal_fixes; + let mut constraints = Vec::with_capacity(num_constraints); + + // Terminal fixing: y_{i, t_i} = 1 for each terminal i + for (i, &t) in terminals.iter().enumerate() { + constraints.push(LinearConstraint::eq(vec![(i * n + t, 1.0)], 1.0)); + } + + // Terminal fixing: y_{j, t_i} = 0 for j != i + for (i, &t) in terminals.iter().enumerate() { + for j in 0..k { + if j != i { + constraints.push(LinearConstraint::eq(vec![(j * n + t, 1.0)], 0.0)); + } + } + } + + // Partition constraints: sum_i y_{iv} = 1 for each vertex v + for v in 0..n { + let terms: Vec<(usize, f64)> = (0..k).map(|i| (i * n + v, 1.0)).collect(); + constraints.push(LinearConstraint::eq(terms, 1.0)); + } + + // Edge-cut linking constraints: for each edge e=(u,v) and each terminal i: + // x_e >= y_{iu} - y_{iv} => x_e - y_{iu} + y_{iv} >= 0 + // x_e >= y_{iv} - y_{iu} => x_e + y_{iu} - y_{iv} >= 0 + for (e_idx, (u, v)) in edges.iter().enumerate() { + let x_var = k * n + e_idx; + for i in 0..k { + let y_iu = i * n + u; + let y_iv = i * n + v; + // x_e - y_{iu} + y_{iv} >= 0 + constraints.push(LinearConstraint::ge( + vec![(x_var, 1.0), (y_iu, -1.0), (y_iv, 1.0)], + 0.0, + )); + // x_e + y_{iu} - y_{iv} >= 0 + constraints.push(LinearConstraint::ge( + vec![(x_var, 1.0), (y_iu, 1.0), (y_iv, -1.0)], + 0.0, + )); + } + } + + // Objective: minimize sum_e w_e * x_e + let objective: Vec<(usize, f64)> = weights + .iter() + .enumerate() + .map(|(e_idx, w)| (k * n + e_idx, *w as f64)) + .collect(); + + let target = ILP::new(num_vars, constraints, objective, ObjectiveSense::Minimize); + + ReductionMMCToILP { target, n, m, k } + } +} + +#[cfg(feature = "example-db")] +pub(crate) fn canonical_rule_example_specs() -> Vec { + vec![crate::example_db::specs::RuleExampleSpec { + id: "minimummultiwaycut_to_ilp", + build: || { + let graph = SimpleGraph::new(5, vec![(0, 1), (1, 2), (2, 3), (3, 4), (0, 4), (1, 3)]); + let problem = MinimumMultiwayCut::new(graph, vec![0, 2, 4], vec![2, 3, 1, 2, 4, 5]); + crate::example_db::specs::direct_ilp_example::<_, bool, _>(problem, |_, _| true) + }, + }] +} + +#[cfg(test)] +#[path = "../unit_tests/rules/minimummultiwaycut_ilp.rs"] +mod tests; diff --git a/src/rules/mod.rs b/src/rules/mod.rs index 7a2feab15..135b34c38 100644 --- a/src/rules/mod.rs +++ b/src/rules/mod.rs @@ -66,6 +66,8 @@ pub(crate) mod minimumdominatingset_ilp; #[cfg(feature = "ilp-solver")] pub(crate) mod minimumfeedbackvertexset_ilp; #[cfg(feature = "ilp-solver")] +pub(crate) mod minimummultiwaycut_ilp; +#[cfg(feature = "ilp-solver")] pub(crate) mod minimumsetcovering_ilp; #[cfg(feature = "ilp-solver")] pub(crate) mod qubo_ilp; @@ -112,6 +114,7 @@ pub(crate) fn canonical_rule_example_specs() -> Vec MinimumMultiwayCut { + let graph = SimpleGraph::new(5, vec![(0, 1), (1, 2), (2, 3), (3, 4), (0, 4), (1, 3)]); + MinimumMultiwayCut::new(graph, vec![0, 2, 4], vec![2, 3, 1, 2, 4, 5]) +} + +#[test] +fn test_reduction_creates_valid_ilp() { + let problem = canonical_instance(); + let reduction: ReductionMMCToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + let k = 3; + let n = 5; + let m = 6; + // kn + m = 21 variables + assert_eq!(ilp.num_vars, k * n + m); + // n + 2km + k^2 = 5 + 36 + 9 = 50 constraints + assert_eq!(ilp.constraints.len(), n + 2 * k * m + k * k); + assert_eq!(ilp.sense, ObjectiveSense::Minimize); +} + +#[test] +fn test_minimummultiwaycut_to_ilp_closed_loop() { + let problem = canonical_instance(); + let reduction: ReductionMMCToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + let bf = BruteForce::new(); + let ilp_solver = ILPSolver::new(); + + // Solve original with brute force + let bf_solutions = bf.find_all_best(&problem); + let bf_obj = problem.evaluate(&bf_solutions[0]); + + // Solve via ILP + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + let ilp_obj = problem.evaluate(&extracted); + + // Optimal cut cost is 8 + assert_eq!(bf_obj, SolutionSize::Valid(8)); + assert_eq!(ilp_obj, SolutionSize::Valid(8)); +} + +#[test] +fn test_triangle_with_3_terminals() { + // Triangle: 3 vertices, all terminals, edges: (0,1)=1, (1,2)=2, (0,2)=3 + // All 3 edges must be cut to separate every terminal pair (complete graph). + // Optimal cost = 1 + 2 + 3 = 6 + let graph = SimpleGraph::new(3, vec![(0, 1), (1, 2), (0, 2)]); + let problem = MinimumMultiwayCut::new(graph, vec![0, 1, 2], vec![1, 2, 3]); + + let reduction: ReductionMMCToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + let ilp_solver = ILPSolver::new(); + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + + let obj = problem.evaluate(&extracted); + assert_eq!(obj, SolutionSize::Valid(6)); +} + +#[test] +fn test_two_terminals() { + // Path: 0--1--2, terminals {0, 2}, weights [1, 2] + // Optimal min s-t cut: cut edge (0,1) with cost 1 + let graph = SimpleGraph::new(3, vec![(0, 1), (1, 2)]); + let problem = MinimumMultiwayCut::new(graph, vec![0, 2], vec![1, 2]); + + let reduction: ReductionMMCToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + let ilp_solver = ILPSolver::new(); + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + + let obj = problem.evaluate(&extracted); + assert_eq!(obj, SolutionSize::Valid(1)); +} + +#[test] +fn test_solution_extraction() { + let problem = canonical_instance(); + let reduction: ReductionMMCToILP = ReduceTo::>::reduce_to(&problem); + + let k = 3; + let n = 5; + let m = 6; + let num_vars = k * n + m; + + // Manually construct an ILP solution representing the optimal partition: + // V_0 = {0}, V_1 = {1, 2, 3}, V_2 = {4} + // Cut edges: (0,1)=idx 0, (3,4)=idx 3, (0,4)=idx 4 + let mut ilp_solution = vec![0usize; num_vars]; + + // y_{0,v}: component 0 assignments (indices 0..5) + ilp_solution[0] = 1; // y_{0,0} = 1 (vertex 0 in component 0) + + // y_{1,v}: component 1 assignments (indices 5..10) + ilp_solution[5 + 1] = 1; // y_{1,1} = 1 + ilp_solution[5 + 2] = 1; // y_{1,2} = 1 + ilp_solution[5 + 3] = 1; // y_{1,3} = 1 + + // y_{2,v}: component 2 assignments (indices 10..15) + ilp_solution[10 + 4] = 1; // y_{2,4} = 1 + + // x_e: cut indicators (indices 15..21) + ilp_solution[15] = 1; // edge (0,1) cut + ilp_solution[15 + 3] = 1; // edge (3,4) cut + ilp_solution[15 + 4] = 1; // edge (0,4) cut + + let extracted = reduction.extract_solution(&ilp_solution); + assert_eq!(extracted, vec![1, 0, 0, 1, 1, 0]); + + let obj = problem.evaluate(&extracted); + assert_eq!(obj, SolutionSize::Valid(8)); +} + +#[test] +fn test_solve_reduced() { + let problem = canonical_instance(); + + let ilp_solver = ILPSolver::new(); + let solution = ilp_solver + .solve_reduced(&problem) + .expect("solve_reduced should work"); + + assert!(problem.evaluate(&solution).is_valid()); + assert_eq!(problem.evaluate(&solution), SolutionSize::Valid(8)); +}