From 39fa0d48fcaf12c0d89629c20f36b3bab3c8fdc3 Mon Sep 17 00:00:00 2001 From: zazabap Date: Fri, 13 Mar 2026 07:28:47 +0000 Subject: [PATCH 1/7] Add plan for #141: MinimumFeedbackVertexSet to ILP reduction --- ...6-03-13-minimumfeedbackvertexset-to-ilp.md | 49 +++++++++++++++++++ 1 file changed, 49 insertions(+) create mode 100644 docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md diff --git a/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md b/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md new file mode 100644 index 000000000..6cc57643d --- /dev/null +++ b/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md @@ -0,0 +1,49 @@ +# Plan: MinimumFeedbackVertexSet to ILP Reduction + +**Issue:** #141 +**Type:** Rule +**Source:** `MinimumFeedbackVertexSet` +**Target:** `ILP` (mixed binary + integer variables) + +## Reduction Algorithm + +MTZ-style topological ordering formulation: +- **Variables:** n binary x_i (vertex removal) + n integer o_i in {0,...,n-1} (topological order) = 2n total +- **Constraints:** For each arc (u->v): o_v - o_u >= 1 - n*(x_u + x_v). Plus binary bounds (x_i <= 1) and order bounds (o_i <= n-1) = m + 2n total +- **Objective:** minimize sum w_i * x_i +- **Solution extraction:** first n variables of ILP solution are the x_i values + +## Steps + +### Step 1: Implement the reduction rule +- Create `src/rules/minimumfeedbackvertexset_ilp.rs` +- ReductionResult struct: `ReductionMFVSToILP` with target `ILP` and `num_vertices: usize` +- `reduce_to()`: construct 2n variables, m arc constraints + n binary constraints + n order bound constraints +- `extract_solution()`: take first n values from ILP solution +- Overhead: `num_vars = "2 * num_vertices"`, `num_constraints = "num_arcs + 2 * num_vertices"` +- Feature-gate under `#[cfg(feature = "ilp-solver")]` + +### Step 2: Register in mod.rs +- Add `#[cfg(feature = "ilp-solver")] mod minimumfeedbackvertexset_ilp;` to `src/rules/mod.rs` + +### Step 3: Write unit tests +- Create `src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs` +- `test_minimumfeedbackvertexset_to_ilp_closed_loop`: 3-cycle, verify BF vs ILP +- `test_reduction_structure`: verify num_vars = 2n, num_constraints = m + 2n +- `test_cycle_of_triangles`: the example from the issue (n=9, m=15, FVS=3) +- `test_dag_no_removal`: DAG input requires FVS=0 +- `test_single_vertex`: trivial case +- `test_weighted`: verify weight transfer to objective + +### Step 4: Write example program +- Create `examples/reduction_minimumfeedbackvertexset_to_ilp.rs` +- Use the cycle-of-triangles instance from the issue +- Register in `tests/suites/examples.rs` + +### Step 5: Document in paper +- Add `reduction-rule` entry in `docs/paper/reductions.typ` + +### Step 6: Regenerate exports and verify +- `cargo run --example export_graph` +- `cargo run --example export_schemas` +- `make test clippy` From a197c3cf1fd6d0274fef2ab070a71654ada09330 Mon Sep 17 00:00:00 2001 From: zazabap Date: Fri, 13 Mar 2026 07:36:03 +0000 Subject: [PATCH 2/7] Implement #141: MinimumFeedbackVertexSet to ILP reduction Add MTZ-style topological ordering reduction from MinimumFeedbackVertexSet to ILP. Uses 2n variables (n binary + n integer ordering) and m + 2n constraints. Includes unit tests, example program, and paper documentation. Co-Authored-By: Claude Opus 4.6 --- docs/paper/reductions.typ | 16 ++ docs/src/reductions/reduction_graph.json | 30 +++ ...duction_minimumfeedbackvertexset_to_ilp.rs | 126 +++++++++++ src/rules/minimumfeedbackvertexset_ilp.rs | 109 ++++++++++ src/rules/mod.rs | 2 + .../rules/minimumfeedbackvertexset_ilp.rs | 195 ++++++++++++++++++ tests/suites/examples.rs | 5 + 7 files changed, 483 insertions(+) create mode 100644 examples/reduction_minimumfeedbackvertexset_to_ilp.rs create mode 100644 src/rules/minimumfeedbackvertexset_ilp.rs create mode 100644 src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs diff --git a/docs/paper/reductions.typ b/docs/paper/reductions.typ index 565abdb14..2e0b329d1 100644 --- a/docs/paper/reductions.typ +++ b/docs/paper/reductions.typ @@ -1655,6 +1655,22 @@ The following reductions to Integer Linear Programming are straightforward formu _Solution extraction._ $D = {v : x_v = 1}$. ] +#reduction-rule("MinimumFeedbackVertexSet", "ILP")[ + A directed graph is a DAG iff it admits a topological ordering. MTZ-style ordering variables enforce this: for each kept vertex, an integer position variable must increase strictly along every arc. Removed vertices relax the ordering constraints via big-$M$ terms. +][ + _Construction._ Given directed graph $G = (V, A)$ with $n = |V|$, $m = |A|$, and weights $w_v$: + + _Variables:_ Binary $x_v in {0, 1}$ for each $v in V$: $x_v = 1$ iff $v$ is removed. Integer $o_v in {0, dots, n-1}$ for each $v in V$: topological order position. Total: $2n$ variables. + + _Constraints:_ (1) For each arc $(u -> v) in A$: $o_v - o_u >= 1 - n(x_u + x_v)$. When both endpoints are kept ($x_u = x_v = 0$), this forces $o_v > o_u$ (strict topological order). When either is removed, the constraint relaxes to $o_v - o_u >= 1 - n$ (trivially satisfied). (2) Binary bounds: $x_v <= 1$. (3) Order bounds: $o_v <= n - 1$. Total: $m + 2n$ constraints. + + _Objective:_ Minimize $sum_v w_v x_v$. + + _Correctness._ ($arrow.r.double$) If $S$ is a feedback vertex set, then $G[V backslash S]$ is a DAG with a topological ordering. Set $x_v = 1$ for $v in S$, $o_v$ to the topological position for kept vertices, and $o_v = 0$ for removed vertices. All constraints are satisfied. ($arrow.l.double$) If the ILP is feasible with all arc constraints satisfied, no directed cycle can exist among kept vertices: a cycle $v_1 -> dots -> v_k -> v_1$ would require $o_(v_1) < o_(v_2) < dots < o_(v_k) < o_(v_1)$, a contradiction. + + _Solution extraction._ $S = {v : x_v = 1}$. +] + #reduction-rule("MaximumClique", "ILP")[ A clique requires every pair of selected vertices to be adjacent; equivalently, no two selected vertices may share a _non_-edge. This is the independent set formulation on the complement graph $overline(G)$. ][ diff --git a/docs/src/reductions/reduction_graph.json b/docs/src/reductions/reduction_graph.json index 0b3bf3b6f..aab886f2e 100644 --- a/docs/src/reductions/reduction_graph.json +++ b/docs/src/reductions/reduction_graph.json @@ -412,6 +412,21 @@ } ], "edges": [ + { + "source": 3, + "target": 9, + "overhead": [ + { + "field": "num_vars", + "formula": "num_items * num_items + num_items" + }, + { + "field": "num_constraints", + "formula": "2 * num_items" + } + ], + "doc_path": "rules/binpacking_ilp/index.html" + }, { "source": 4, "target": 9, @@ -992,6 +1007,21 @@ ], "doc_path": "rules/minimumdominatingset_ilp/index.html" }, + { + "source": 35, + "target": 10, + "overhead": [ + { + "field": "num_vars", + "formula": "2 * num_vertices" + }, + { + "field": "num_constraints", + "formula": "num_arcs + 2 * num_vertices" + } + ], + "doc_path": "rules/minimumfeedbackvertexset_ilp/index.html" + }, { "source": 36, "target": 9, diff --git a/examples/reduction_minimumfeedbackvertexset_to_ilp.rs b/examples/reduction_minimumfeedbackvertexset_to_ilp.rs new file mode 100644 index 000000000..a41b47cdc --- /dev/null +++ b/examples/reduction_minimumfeedbackvertexset_to_ilp.rs @@ -0,0 +1,126 @@ +// # Feedback Vertex Set to ILP Reduction +// +// ## Mathematical Formulation +// Uses MTZ-style topological ordering constraints: +// Variables: n binary x_i (vertex removal) + n integer o_i (topological order) +// Constraints: For each arc (u->v): o_v - o_u >= 1 - n*(x_u + x_v) +// Plus binary bounds (x_i <= 1) and order bounds (o_i <= n-1) +// Objective: minimize sum w_i * x_i +// +// ## This Example +// - Instance: "Cycle of triangles" (9 vertices, 15 arcs), FVS = 3 +// - Source MinimumFeedbackVertexSet: 9 vertices, unit weights +// - Target ILP: 18 variables (9 binary + 9 integer), 33 constraints +// +// ## Output +// Exports `docs/paper/examples/minimumfeedbackvertexset_to_ilp.json` and +// `minimumfeedbackvertexset_to_ilp.result.json`. + +use problemreductions::export::*; +use problemreductions::models::algebraic::ILP; +use problemreductions::models::graph::MinimumFeedbackVertexSet; +use problemreductions::prelude::*; +use problemreductions::solvers::ILPSolver; +use problemreductions::topology::DirectedGraph; + +pub fn run() { + // 1. Create MinimumFeedbackVertexSet instance: cycle of triangles + // Three directed triangles (0-1-2, 3-4-5, 6-7-8) connected in a cycle + let arcs = vec![ + (0, 1), + (1, 2), + (2, 0), // triangle 0-1-2 + (3, 4), + (4, 5), + (5, 3), // triangle 3-4-5 + (6, 7), + (7, 8), + (8, 6), // triangle 6-7-8 + (1, 3), + (4, 6), + (7, 0), // inter-triangle forward arcs + (2, 5), + (5, 8), + (8, 2), // inter-triangle cross arcs + ]; + let graph = DirectedGraph::new(9, arcs.clone()); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 9]); + + // 2. Reduce to ILP + let reduction = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + // 3. Print transformation + println!("\n=== Problem Transformation ==="); + println!( + "Source: MinimumFeedbackVertexSet with {} vertices, {} arcs", + problem.num_variables(), + arcs.len() + ); + println!( + "Target: ILP with {} variables, {} constraints", + ilp.num_vars, + ilp.constraints.len() + ); + + // 4. Solve target ILP using ILP solver (BruteForce can't handle ILP) + let ilp_solver = ILPSolver::new(); + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + println!("\n=== Solution ==="); + println!("ILP solution: {:?}", &ilp_solution[..9]); + + // 5. Extract source solution + let fvs_solution = reduction.extract_solution(&ilp_solution); + println!("Source FVS solution: {:?}", fvs_solution); + + // 6. Verify + let size = problem.evaluate(&fvs_solution); + println!("Solution size: {:?}", size); + assert!(size.is_valid()); + println!("\nReduction verified successfully"); + + // 7. Collect solutions and export JSON + let solutions = vec![SolutionPair { + source_config: fvs_solution.clone(), + target_config: ilp_solution.clone(), + }]; + + let source_variant = variant_to_map(MinimumFeedbackVertexSet::::variant()); + let target_variant = variant_to_map(ILP::::variant()); + let overhead = lookup_overhead( + "MinimumFeedbackVertexSet", + &source_variant, + "ILP", + &target_variant, + ) + .unwrap_or_default(); + + let data = ReductionData { + source: ProblemSide { + problem: MinimumFeedbackVertexSet::::NAME.to_string(), + variant: source_variant, + instance: serde_json::json!({ + "num_vertices": 9, + "num_arcs": 15, + "arcs": arcs, + }), + }, + target: ProblemSide { + problem: ILP::::NAME.to_string(), + variant: target_variant, + instance: serde_json::json!({ + "num_vars": ilp.num_vars, + "num_constraints": ilp.constraints.len(), + }), + }, + overhead: overhead_to_json(&overhead), + }; + + let results = ResultData { solutions }; + let name = "minimumfeedbackvertexset_to_ilp"; + write_example(name, &data, &results); +} + +fn main() { + run() +} diff --git a/src/rules/minimumfeedbackvertexset_ilp.rs b/src/rules/minimumfeedbackvertexset_ilp.rs new file mode 100644 index 000000000..9e11c8d30 --- /dev/null +++ b/src/rules/minimumfeedbackvertexset_ilp.rs @@ -0,0 +1,109 @@ +//! Reduction from MinimumFeedbackVertexSet to ILP (Integer Linear Programming). +//! +//! Uses MTZ-style topological ordering constraints: +//! - Variables: n binary x_i (vertex removal) + n integer o_i (topological order) = 2n total +//! - Constraints: For each arc (u->v): o_v - o_u >= 1 - n*(x_u + x_v) +//! Plus binary bounds (x_i <= 1) and order bounds (o_i <= n-1) +//! - Objective: Minimize the weighted sum of removed vertices + +use crate::models::algebraic::{LinearConstraint, ObjectiveSense, ILP}; +use crate::models::graph::MinimumFeedbackVertexSet; +use crate::reduction; +use crate::rules::traits::{ReduceTo, ReductionResult}; + +/// Result of reducing MinimumFeedbackVertexSet to ILP. +/// +/// The ILP uses integer variables (`ILP`) because it needs both +/// binary selection variables (x_i) and integer ordering variables (o_i). +/// +/// Variable layout: +/// - `x_i` at index `i` for `i in 0..n`: binary (0 or 1), vertex removal indicator +/// - `o_i` at index `n + i` for `i in 0..n`: integer in {0, ..., n-1}, topological order +#[derive(Debug, Clone)] +pub struct ReductionMFVSToILP { + target: ILP, + /// Number of vertices in the source graph (needed for solution extraction). + num_vertices: usize, +} + +impl ReductionResult for ReductionMFVSToILP { + type Source = MinimumFeedbackVertexSet; + type Target = ILP; + + fn target_problem(&self) -> &ILP { + &self.target + } + + /// Extract solution from ILP back to MinimumFeedbackVertexSet. + /// + /// The first n variables of the ILP solution are the binary x_i values, + /// which directly correspond to the FVS configuration (1 = removed). + fn extract_solution(&self, target_solution: &[usize]) -> Vec { + target_solution[..self.num_vertices].to_vec() + } +} + +#[reduction( + overhead = { + num_vars = "2 * num_vertices", + num_constraints = "num_arcs + 2 * num_vertices", + } +)] +impl ReduceTo> for MinimumFeedbackVertexSet { + type Result = ReductionMFVSToILP; + + fn reduce_to(&self) -> Self::Result { + let n = self.graph().num_vertices(); + let arcs = self.graph().arcs(); + let num_vars = 2 * n; + + // Variable indices: + // x_i = i (binary: vertex i removed?) + // o_i = n + i (integer: topological order of vertex i) + + let mut constraints = Vec::new(); + + // Binary bounds: x_i <= 1 for i in 0..n + for i in 0..n { + constraints.push(LinearConstraint::le(vec![(i, 1.0)], 1.0)); + } + + // Order bounds: o_i <= n - 1 for i in 0..n + for i in 0..n { + constraints.push(LinearConstraint::le(vec![(n + i, 1.0)], (n - 1) as f64)); + } + + // Arc constraints: for each arc (u -> v): + // o_v - o_u >= 1 - n * (x_u + x_v) + // Rearranged: o_v - o_u + n*x_u + n*x_v >= 1 + let n_f64 = n as f64; + for &(u, v) in &arcs { + let terms = vec![ + (n + v, 1.0), // o_v + (n + u, -1.0), // -o_u + (u, n_f64), // n * x_u + (v, n_f64), // n * x_v + ]; + constraints.push(LinearConstraint::ge(terms, 1.0)); + } + + // Objective: minimize sum w_i * x_i + let objective: Vec<(usize, f64)> = self + .weights() + .iter() + .enumerate() + .map(|(i, &w)| (i, w as f64)) + .collect(); + + let target = ILP::new(num_vars, constraints, objective, ObjectiveSense::Minimize); + + ReductionMFVSToILP { + target, + num_vertices: n, + } + } +} + +#[cfg(test)] +#[path = "../unit_tests/rules/minimumfeedbackvertexset_ilp.rs"] +mod tests; diff --git a/src/rules/mod.rs b/src/rules/mod.rs index fa77a18dc..648f6d2c3 100644 --- a/src/rules/mod.rs +++ b/src/rules/mod.rs @@ -57,6 +57,8 @@ mod maximumsetpacking_ilp; #[cfg(feature = "ilp-solver")] mod minimumdominatingset_ilp; #[cfg(feature = "ilp-solver")] +mod minimumfeedbackvertexset_ilp; +#[cfg(feature = "ilp-solver")] mod minimumsetcovering_ilp; #[cfg(feature = "ilp-solver")] mod qubo_ilp; diff --git a/src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs b/src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs new file mode 100644 index 000000000..66be3cbff --- /dev/null +++ b/src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs @@ -0,0 +1,195 @@ +use super::*; +use crate::solvers::{BruteForce, ILPSolver}; +use crate::topology::DirectedGraph; +use crate::traits::Problem; +use crate::types::SolutionSize; + +#[test] +fn test_reduction_creates_valid_ilp() { + // Simple 3-cycle: 0 -> 1 -> 2 -> 0 + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2), (2, 0)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 3]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + // 2n = 6 variables (3 binary x_i + 3 integer o_i) + assert_eq!(ilp.num_vars, 6, "Should have 2n variables"); + // m + 2n = 3 + 6 = 9 constraints + assert_eq!(ilp.constraints.len(), 9, "Should have m + 2n constraints"); + assert_eq!(ilp.sense, ObjectiveSense::Minimize, "Should minimize"); +} + +#[test] +fn test_minimumfeedbackvertexset_to_ilp_closed_loop() { + // Simple 3-cycle: 0 -> 1 -> 2 -> 0 + // FVS = 1 (remove any single vertex) + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2), (2, 0)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 3]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + let bf = BruteForce::new(); + let ilp_solver = ILPSolver::new(); + + // Solve with brute force on original problem + let bf_solutions = bf.find_all_best(&problem); + let bf_size = problem.evaluate(&bf_solutions[0]); + + // Solve via ILP reduction + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + let ilp_size = problem.evaluate(&extracted); + + // Both should find optimal size = 1 + assert_eq!(bf_size, SolutionSize::Valid(1)); + assert_eq!(ilp_size, SolutionSize::Valid(1)); + + // Verify the ILP solution is valid for the original problem + assert!( + problem.evaluate(&extracted).is_valid(), + "Extracted solution should be valid" + ); +} + +#[test] +fn test_cycle_of_triangles() { + // The example from issue #141: n=9, m=15, FVS=3 + let arcs = vec![ + (0, 1), + (1, 2), + (2, 0), // triangle 0-1-2 + (3, 4), + (4, 5), + (5, 3), // triangle 3-4-5 + (6, 7), + (7, 8), + (8, 6), // triangle 6-7-8 + (1, 3), + (4, 6), + (7, 0), // inter-triangle arcs + (2, 5), + (5, 8), + (8, 2), // more inter-triangle arcs + ]; + let graph = DirectedGraph::new(9, arcs); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 9]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + // Verify ILP structure + assert_eq!(ilp.num_vars, 18, "Should have 2*9 = 18 variables"); + assert_eq!( + ilp.constraints.len(), + 15 + 18, + "Should have 15 arc + 18 bound constraints" + ); + + 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 size = problem.evaluate(&extracted); + assert_eq!(size, SolutionSize::Valid(3), "FVS should be 3"); +} + +#[test] +fn test_dag_no_removal() { + // DAG: 0 -> 1 -> 2 (no cycles, FVS = 0) + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 3]); + let reduction: ReductionMFVSToILP = 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 size = problem.evaluate(&extracted); + assert_eq!(size, SolutionSize::Valid(0), "DAG needs no removal"); + assert_eq!(extracted, vec![0, 0, 0]); +} + +#[test] +fn test_single_vertex() { + // Single vertex, no arcs: FVS = 0 + let graph = DirectedGraph::new(1, vec![]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + assert_eq!(ilp.num_vars, 2); + // 0 arc constraints + 2 bound constraints + assert_eq!(ilp.constraints.len(), 2); + + let ilp_solver = ILPSolver::new(); + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + + assert_eq!(extracted, vec![0]); + assert_eq!(problem.evaluate(&extracted), SolutionSize::Valid(0)); +} + +#[test] +fn test_weighted() { + // 3-cycle with different weights: prefer removing the cheapest vertex + // Weights: v0=10, v1=1, v2=10 + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2), (2, 0)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![10, 1, 10]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + let ilp = reduction.target_problem(); + + // Check that weights are correctly transferred to objective + let mut coeffs: Vec = vec![0.0; ilp.num_vars]; + for &(var, coef) in &ilp.objective { + coeffs[var] = coef; + } + assert!((coeffs[0] - 10.0).abs() < 1e-9); + assert!((coeffs[1] - 1.0).abs() < 1e-9); + assert!((coeffs[2] - 10.0).abs() < 1e-9); + + let ilp_solver = ILPSolver::new(); + let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); + let extracted = reduction.extract_solution(&ilp_solution); + + // Should remove vertex 1 (cheapest) + assert_eq!(extracted[1], 1, "Should remove vertex 1 (cheapest)"); + assert_eq!(problem.evaluate(&extracted), SolutionSize::Valid(1)); +} + +#[test] +fn test_two_disjoint_cycles() { + // Two disjoint 2-cycles: 0<->1 and 2<->3 + // Need to remove at least 1 from each cycle, FVS = 2 + let graph = DirectedGraph::new(4, vec![(0, 1), (1, 0), (2, 3), (3, 2)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 4]); + + let bf = BruteForce::new(); + let bf_solutions = bf.find_all_best(&problem); + let bf_size = problem.evaluate(&bf_solutions[0]); + + let reduction: ReductionMFVSToILP = 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 ilp_size = problem.evaluate(&extracted); + + assert_eq!(bf_size, SolutionSize::Valid(2)); + assert_eq!(ilp_size, SolutionSize::Valid(2)); +} + +#[test] +fn test_solution_extraction() { + // Verify that extraction correctly takes first n values + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2), (2, 0)]); + let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 3]); + let reduction: ReductionMFVSToILP = ReduceTo::>::reduce_to(&problem); + + // Simulate ILP solution: x_0=1, x_1=0, x_2=0, o_0=0, o_1=0, o_2=1 + let ilp_solution = vec![1, 0, 0, 0, 0, 1]; + let extracted = reduction.extract_solution(&ilp_solution); + assert_eq!(extracted, vec![1, 0, 0]); + + // Verify this is a valid FVS (removing vertex 0 breaks the 3-cycle) + assert!(problem.evaluate(&extracted).is_valid()); +} diff --git a/tests/suites/examples.rs b/tests/suites/examples.rs index 3002a6838..2258f9983 100644 --- a/tests/suites/examples.rs +++ b/tests/suites/examples.rs @@ -36,6 +36,7 @@ example_test!(reduction_maximumsetpacking_to_ilp); example_test!(reduction_maximumsetpacking_to_maximumindependentset); example_test!(reduction_maximumsetpacking_to_qubo); example_test!(reduction_minimumdominatingset_to_ilp); +example_test!(reduction_minimumfeedbackvertexset_to_ilp); example_test!(reduction_minimumsetcovering_to_ilp); example_test!(reduction_minimumvertexcover_to_ilp); example_test!(reduction_minimumvertexcover_to_maximumindependentset); @@ -141,6 +142,10 @@ example_fn!( test_minimumdominatingset_to_ilp, reduction_minimumdominatingset_to_ilp ); +example_fn!( + test_minimumfeedbackvertexset_to_ilp, + reduction_minimumfeedbackvertexset_to_ilp +); example_fn!( test_minimumsetcovering_to_ilp, reduction_minimumsetcovering_to_ilp From d3d090fb9e9b67bbe76fc336117d704a1b15b258 Mon Sep 17 00:00:00 2001 From: zazabap Date: Fri, 13 Mar 2026 07:36:06 +0000 Subject: [PATCH 3/7] chore: remove plan file after implementation --- ...6-03-13-minimumfeedbackvertexset-to-ilp.md | 49 ------------------- 1 file changed, 49 deletions(-) delete mode 100644 docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md diff --git a/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md b/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md deleted file mode 100644 index 6cc57643d..000000000 --- a/docs/plans/2026-03-13-minimumfeedbackvertexset-to-ilp.md +++ /dev/null @@ -1,49 +0,0 @@ -# Plan: MinimumFeedbackVertexSet to ILP Reduction - -**Issue:** #141 -**Type:** Rule -**Source:** `MinimumFeedbackVertexSet` -**Target:** `ILP` (mixed binary + integer variables) - -## Reduction Algorithm - -MTZ-style topological ordering formulation: -- **Variables:** n binary x_i (vertex removal) + n integer o_i in {0,...,n-1} (topological order) = 2n total -- **Constraints:** For each arc (u->v): o_v - o_u >= 1 - n*(x_u + x_v). Plus binary bounds (x_i <= 1) and order bounds (o_i <= n-1) = m + 2n total -- **Objective:** minimize sum w_i * x_i -- **Solution extraction:** first n variables of ILP solution are the x_i values - -## Steps - -### Step 1: Implement the reduction rule -- Create `src/rules/minimumfeedbackvertexset_ilp.rs` -- ReductionResult struct: `ReductionMFVSToILP` with target `ILP` and `num_vertices: usize` -- `reduce_to()`: construct 2n variables, m arc constraints + n binary constraints + n order bound constraints -- `extract_solution()`: take first n values from ILP solution -- Overhead: `num_vars = "2 * num_vertices"`, `num_constraints = "num_arcs + 2 * num_vertices"` -- Feature-gate under `#[cfg(feature = "ilp-solver")]` - -### Step 2: Register in mod.rs -- Add `#[cfg(feature = "ilp-solver")] mod minimumfeedbackvertexset_ilp;` to `src/rules/mod.rs` - -### Step 3: Write unit tests -- Create `src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs` -- `test_minimumfeedbackvertexset_to_ilp_closed_loop`: 3-cycle, verify BF vs ILP -- `test_reduction_structure`: verify num_vars = 2n, num_constraints = m + 2n -- `test_cycle_of_triangles`: the example from the issue (n=9, m=15, FVS=3) -- `test_dag_no_removal`: DAG input requires FVS=0 -- `test_single_vertex`: trivial case -- `test_weighted`: verify weight transfer to objective - -### Step 4: Write example program -- Create `examples/reduction_minimumfeedbackvertexset_to_ilp.rs` -- Use the cycle-of-triangles instance from the issue -- Register in `tests/suites/examples.rs` - -### Step 5: Document in paper -- Add `reduction-rule` entry in `docs/paper/reductions.typ` - -### Step 6: Regenerate exports and verify -- `cargo run --example export_graph` -- `cargo run --example export_schemas` -- `make test clippy` From 9cfb67f073d16ec717620a7f00451cca89e596cc Mon Sep 17 00:00:00 2001 From: zazabap Date: Sun, 15 Mar 2026 12:20:36 +0000 Subject: [PATCH 4/7] chore: fix formatting after merge Co-Authored-By: Claude Opus 4.6 --- src/models/misc/minimum_tardiness_sequencing.rs | 6 +----- src/unit_tests/models/misc/minimum_tardiness_sequencing.rs | 6 +----- 2 files changed, 2 insertions(+), 10 deletions(-) diff --git a/src/models/misc/minimum_tardiness_sequencing.rs b/src/models/misc/minimum_tardiness_sequencing.rs index ed383c816..d33c17423 100644 --- a/src/models/misc/minimum_tardiness_sequencing.rs +++ b/src/models/misc/minimum_tardiness_sequencing.rs @@ -197,11 +197,7 @@ pub(crate) fn canonical_model_example_specs() -> Vec 2 (task 0 before task 2). // Deadlines: task 0 by time 2, task 1 by time 3, task 2 by time 1, task 3 by time 4. - let problem = MinimumTardinessSequencing::new( - 4, - vec![2, 3, 1, 4], - vec![(0, 2)], - ); + let problem = MinimumTardinessSequencing::new(4, vec![2, 3, 1, 4], vec![(0, 2)]); // Sample config: Lehmer code [0,0,0,0] = identity permutation (schedule order 0,1,2,3) crate::example_db::specs::optimization_example(problem, vec![vec![0, 0, 0, 0]]) }, diff --git a/src/unit_tests/models/misc/minimum_tardiness_sequencing.rs b/src/unit_tests/models/misc/minimum_tardiness_sequencing.rs index cfb1273d8..6d85c5ace 100644 --- a/src/unit_tests/models/misc/minimum_tardiness_sequencing.rs +++ b/src/unit_tests/models/misc/minimum_tardiness_sequencing.rs @@ -168,11 +168,7 @@ fn test_minimum_tardiness_sequencing_invalid_precedence() { #[test] fn test_minimum_tardiness_sequencing_cyclic_precedences() { // Cyclic precedences: 0 -> 1 -> 2 -> 0. No valid schedule exists. - let problem = MinimumTardinessSequencing::new( - 3, - vec![3, 3, 3], - vec![(0, 1), (1, 2), (2, 0)], - ); + let problem = MinimumTardinessSequencing::new(3, vec![3, 3, 3], vec![(0, 1), (1, 2), (2, 0)]); let solver = BruteForce::new(); assert!(solver.find_best(&problem).is_none()); } From f1c272331392c735a0fc0c308d50240075863fd1 Mon Sep 17 00:00:00 2001 From: zazabap Date: Sun, 15 Mar 2026 12:25:16 +0000 Subject: [PATCH 5/7] fix: migrate MFVS example to example-db pattern, add canonical specs Remove old-style example binary and add canonical_rule_example_specs() to the MFVS-to-ILP rule, matching the current project convention. Co-Authored-By: Claude Opus 4.6 --- ...duction_minimumfeedbackvertexset_to_ilp.rs | 126 ------------------ src/rules/minimumfeedbackvertexset_ilp.rs | 14 ++ src/rules/mod.rs | 1 + 3 files changed, 15 insertions(+), 126 deletions(-) delete mode 100644 examples/reduction_minimumfeedbackvertexset_to_ilp.rs diff --git a/examples/reduction_minimumfeedbackvertexset_to_ilp.rs b/examples/reduction_minimumfeedbackvertexset_to_ilp.rs deleted file mode 100644 index a41b47cdc..000000000 --- a/examples/reduction_minimumfeedbackvertexset_to_ilp.rs +++ /dev/null @@ -1,126 +0,0 @@ -// # Feedback Vertex Set to ILP Reduction -// -// ## Mathematical Formulation -// Uses MTZ-style topological ordering constraints: -// Variables: n binary x_i (vertex removal) + n integer o_i (topological order) -// Constraints: For each arc (u->v): o_v - o_u >= 1 - n*(x_u + x_v) -// Plus binary bounds (x_i <= 1) and order bounds (o_i <= n-1) -// Objective: minimize sum w_i * x_i -// -// ## This Example -// - Instance: "Cycle of triangles" (9 vertices, 15 arcs), FVS = 3 -// - Source MinimumFeedbackVertexSet: 9 vertices, unit weights -// - Target ILP: 18 variables (9 binary + 9 integer), 33 constraints -// -// ## Output -// Exports `docs/paper/examples/minimumfeedbackvertexset_to_ilp.json` and -// `minimumfeedbackvertexset_to_ilp.result.json`. - -use problemreductions::export::*; -use problemreductions::models::algebraic::ILP; -use problemreductions::models::graph::MinimumFeedbackVertexSet; -use problemreductions::prelude::*; -use problemreductions::solvers::ILPSolver; -use problemreductions::topology::DirectedGraph; - -pub fn run() { - // 1. Create MinimumFeedbackVertexSet instance: cycle of triangles - // Three directed triangles (0-1-2, 3-4-5, 6-7-8) connected in a cycle - let arcs = vec![ - (0, 1), - (1, 2), - (2, 0), // triangle 0-1-2 - (3, 4), - (4, 5), - (5, 3), // triangle 3-4-5 - (6, 7), - (7, 8), - (8, 6), // triangle 6-7-8 - (1, 3), - (4, 6), - (7, 0), // inter-triangle forward arcs - (2, 5), - (5, 8), - (8, 2), // inter-triangle cross arcs - ]; - let graph = DirectedGraph::new(9, arcs.clone()); - let problem = MinimumFeedbackVertexSet::new(graph, vec![1i32; 9]); - - // 2. Reduce to ILP - let reduction = ReduceTo::>::reduce_to(&problem); - let ilp = reduction.target_problem(); - - // 3. Print transformation - println!("\n=== Problem Transformation ==="); - println!( - "Source: MinimumFeedbackVertexSet with {} vertices, {} arcs", - problem.num_variables(), - arcs.len() - ); - println!( - "Target: ILP with {} variables, {} constraints", - ilp.num_vars, - ilp.constraints.len() - ); - - // 4. Solve target ILP using ILP solver (BruteForce can't handle ILP) - let ilp_solver = ILPSolver::new(); - let ilp_solution = ilp_solver.solve(ilp).expect("ILP should be solvable"); - println!("\n=== Solution ==="); - println!("ILP solution: {:?}", &ilp_solution[..9]); - - // 5. Extract source solution - let fvs_solution = reduction.extract_solution(&ilp_solution); - println!("Source FVS solution: {:?}", fvs_solution); - - // 6. Verify - let size = problem.evaluate(&fvs_solution); - println!("Solution size: {:?}", size); - assert!(size.is_valid()); - println!("\nReduction verified successfully"); - - // 7. Collect solutions and export JSON - let solutions = vec![SolutionPair { - source_config: fvs_solution.clone(), - target_config: ilp_solution.clone(), - }]; - - let source_variant = variant_to_map(MinimumFeedbackVertexSet::::variant()); - let target_variant = variant_to_map(ILP::::variant()); - let overhead = lookup_overhead( - "MinimumFeedbackVertexSet", - &source_variant, - "ILP", - &target_variant, - ) - .unwrap_or_default(); - - let data = ReductionData { - source: ProblemSide { - problem: MinimumFeedbackVertexSet::::NAME.to_string(), - variant: source_variant, - instance: serde_json::json!({ - "num_vertices": 9, - "num_arcs": 15, - "arcs": arcs, - }), - }, - target: ProblemSide { - problem: ILP::::NAME.to_string(), - variant: target_variant, - instance: serde_json::json!({ - "num_vars": ilp.num_vars, - "num_constraints": ilp.constraints.len(), - }), - }, - overhead: overhead_to_json(&overhead), - }; - - let results = ResultData { solutions }; - let name = "minimumfeedbackvertexset_to_ilp"; - write_example(name, &data, &results); -} - -fn main() { - run() -} diff --git a/src/rules/minimumfeedbackvertexset_ilp.rs b/src/rules/minimumfeedbackvertexset_ilp.rs index 9e11c8d30..d4c54cd07 100644 --- a/src/rules/minimumfeedbackvertexset_ilp.rs +++ b/src/rules/minimumfeedbackvertexset_ilp.rs @@ -104,6 +104,20 @@ impl ReduceTo> for MinimumFeedbackVertexSet { } } +#[cfg(feature = "example-db")] +pub(crate) fn canonical_rule_example_specs() -> Vec { + use crate::topology::DirectedGraph; + vec![crate::example_db::specs::RuleExampleSpec { + id: "minimumfeedbackvertexset_to_ilp", + build: || { + // Simple cycle: 0 -> 1 -> 2 -> 0 (FVS = 1 vertex) + let graph = DirectedGraph::new(3, vec![(0, 1), (1, 2), (2, 0)]); + let source = MinimumFeedbackVertexSet::new(graph, vec![1i32; 3]); + crate::example_db::specs::direct_ilp_example::<_, i32, _>(source, |_, _| true) + }, + }] +} + #[cfg(test)] #[path = "../unit_tests/rules/minimumfeedbackvertexset_ilp.rs"] mod tests; diff --git a/src/rules/mod.rs b/src/rules/mod.rs index b30de3b5b..59e7e703d 100644 --- a/src/rules/mod.rs +++ b/src/rules/mod.rs @@ -112,6 +112,7 @@ pub(crate) fn canonical_rule_example_specs() -> Vec Date: Sun, 15 Mar 2026 12:38:55 +0000 Subject: [PATCH 6/7] fix: support ILP in CLI solve_ilp dispatch The solve_ilp function only downcasted to ILP, causing `pred solve` to fail for problems that reduce to ILP (e.g., MinimumFeedbackVertexSet). Now tries both ILP and ILP. Co-Authored-By: Claude Opus 4.6 --- problemreductions-cli/src/dispatch.rs | 30 ++++++++++++++++++--------- 1 file changed, 20 insertions(+), 10 deletions(-) diff --git a/problemreductions-cli/src/dispatch.rs b/problemreductions-cli/src/dispatch.rs index 659bba48a..603e60241 100644 --- a/problemreductions-cli/src/dispatch.rs +++ b/problemreductions-cli/src/dispatch.rs @@ -161,17 +161,27 @@ pub struct SolveResult { pub evaluation: String, } -/// Solve an ILP problem directly. The input must be an `ILP` instance. +/// Solve an ILP problem directly. The input must be an `ILP` or `ILP` instance. fn solve_ilp(any: &dyn Any) -> Result { - let problem = any - .downcast_ref::() - .ok_or_else(|| anyhow::anyhow!("Internal error: expected ILP problem instance"))?; - let solver = ILPSolver::new(); - let config = solver - .solve(problem) - .ok_or_else(|| anyhow::anyhow!("ILP solver found no feasible solution"))?; - let evaluation = format!("{:?}", problem.evaluate(&config)); - Ok(SolveResult { config, evaluation }) + if let Some(problem) = any.downcast_ref::>() { + let solver = ILPSolver::new(); + let config = solver + .solve(problem) + .ok_or_else(|| anyhow::anyhow!("ILP solver found no feasible solution"))?; + let evaluation = format!("{:?}", problem.evaluate(&config)); + return Ok(SolveResult { config, evaluation }); + } + if let Some(problem) = any.downcast_ref::>() { + let solver = ILPSolver::new(); + let config = solver + .solve(problem) + .ok_or_else(|| anyhow::anyhow!("ILP solver found no feasible solution"))?; + let evaluation = format!("{:?}", problem.evaluate(&config)); + return Ok(SolveResult { config, evaluation }); + } + Err(anyhow::anyhow!( + "Internal error: expected ILP or ILP problem instance" + )) } #[cfg(test)] From d57512c848dfed78f1a56d4afe4935276b3a8962 Mon Sep 17 00:00:00 2001 From: GiggleLiu Date: Wed, 18 Mar 2026 02:24:34 +0800 Subject: [PATCH 7/7] Regenerate fixtures and fix formatting after merge with main - examples.json now includes MFVS-to-ILP canonical example - create.rs: remove extra blank line (rustfmt) Co-Authored-By: Claude Opus 4.6 (1M context) --- problemreductions-cli/src/commands/create.rs | 1 - src/example_db/fixtures/examples.json | 27 ++++++++++---------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/problemreductions-cli/src/commands/create.rs b/problemreductions-cli/src/commands/create.rs index 09d98d7df..695c1cd88 100644 --- a/problemreductions-cli/src/commands/create.rs +++ b/problemreductions-cli/src/commands/create.rs @@ -1721,7 +1721,6 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> { emit_problem_output(&output, out) } - /// Reject non-unit weights when the resolved variant uses `weight=One`. fn reject_nonunit_weights_for_one_variant( canonical: &str, diff --git a/src/example_db/fixtures/examples.json b/src/example_db/fixtures/examples.json index 3d8f22710..e31260a21 100644 --- a/src/example_db/fixtures/examples.json +++ b/src/example_db/fixtures/examples.json @@ -55,18 +55,18 @@ {"source":{"problem":"KColoring","variant":{"graph":"SimpleGraph","k":"KN"},"instance":{"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}},"num_colors":3}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Eq","rhs":1.0,"terms":[[0,1.0],[1,1.0],[2,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[3,1.0],[4,1.0],[5,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[6,1.0],[7,1.0],[8,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[9,1.0],[10,1.0],[11,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[12,1.0],[13,1.0],[14,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[15,1.0],[16,1.0],[17,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[18,1.0],[19,1.0],[20,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[21,1.0],[22,1.0],[23,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[24,1.0],[25,1.0],[26,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[27,1.0],[28,1.0],[29,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[3,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0],[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[12,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[13,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0],[14,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[15,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[16,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0],[17,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[3,1.0],[6,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[4,1.0],[7,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0],[8,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[3,1.0],[18,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[4,1.0],[19,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0],[20,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[6,1.0],[9,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[7,1.0],[10,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[8,1.0],[11,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[6,1.0],[21,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[7,1.0],[22,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[8,1.0],[23,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[9,1.0],[12,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[10,1.0],[13,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[11,1.0],[14,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[9,1.0],[24,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[10,1.0],[25,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[11,1.0],[26,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[12,1.0],[27,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[13,1.0],[28,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[14,1.0],[29,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[15,1.0],[21,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[16,1.0],[22,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[17,1.0],[23,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[15,1.0],[24,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[16,1.0],[25,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[17,1.0],[26,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[18,1.0],[24,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[19,1.0],[25,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[20,1.0],[26,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[18,1.0],[27,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[19,1.0],[28,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[20,1.0],[29,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[21,1.0],[27,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[22,1.0],[28,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[23,1.0],[29,1.0]]}],"num_vars":30,"objective":[],"sense":"Minimize"}},"solutions":[{"source_config":[0,2,0,1,2,1,1,2,0,0],"target_config":[1,0,0,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,0]}]}, {"source":{"problem":"KColoring","variant":{"graph":"SimpleGraph","k":"KN"},"instance":{"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[1,3,null],[2,3,null],[2,4,null],[3,4,null]],"node_holes":[],"nodes":[null,null,null,null,null]}},"num_colors":3}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[-6.0,12.0,12.0,3.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,-6.0,12.0,0.0,3.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,-6.0,0.0,0.0,3.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,-6.0,12.0,12.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,-6.0,12.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,-6.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0,12.0,3.0,0.0,0.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0,0.0,3.0,0.0,0.0,3.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,0.0,0.0,3.0,0.0,0.0,3.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0,12.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0,0.0,3.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,0.0,0.0,3.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0,12.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0,12.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.0]],"num_vars":15}},"solutions":[{"source_config":[1,2,2,1,0],"target_config":[0,1,0,0,0,1,0,0,1,0,1,0,1,0,0]}]}, {"source":{"problem":"KSatisfiability","variant":{"k":"K2"},"instance":{"clauses":[{"literals":[1,2]},{"literals":[-1,3]},{"literals":[-2,4]},{"literals":[-3,-4]}],"num_vars":4}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,1.0,-1.0,0.0],[0.0,0.0,0.0,-1.0],[0.0,0.0,0.0,1.0],[0.0,0.0,0.0,0.0]],"num_vars":4}},"solutions":[{"source_config":[0,1,0,1],"target_config":[0,1,0,1]}]}, - {"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,-3]},{"literals":[-1,3,4]},{"literals":[2,-4,5]},{"literals":[-2,3,-5]},{"literals":[1,-3,5]},{"literals":[-1,-2,4]},{"literals":[3,-4,-5]}],"num_vars":5}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0],[0.0,0.0,-2.0,-2.0,0.0,4.0,0.0,4.0,-4.0,0.0,-4.0,0.0],[0.0,0.0,2.0,-2.0,0.0,1.0,4.0,0.0,4.0,-4.0,0.0,4.0],[0.0,0.0,0.0,4.0,0.0,0.0,-1.0,-4.0,0.0,0.0,-1.0,-4.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0,-1.0,0.0,1.0],[0.0,0.0,0.0,0.0,0.0,-2.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,7.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0]],"num_vars":12}},"solutions":[{"source_config":[1,1,1,1,1],"target_config":[1,1,1,1,1,0,0,0,0,0,1,0]}]}, 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{"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,-3]},{"literals":[-1,3,4]},{"literals":[2,-4,5]},{"literals":[-2,3,-5]},{"literals":[1,-3,5]},{"literals":[-1,-2,4]},{"literals":[3,-4,-5]}],"num_vars":5}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0,0.0,4.0,-4.0,0.0],[0.0,0.0,-2.0,-2.0,0.0,4.0,0.0,4.0,-4.0,0.0,-4.0,0.0],[0.0,0.0,2.0,-2.0,0.0,1.0,4.0,0.0,4.0,-4.0,0.0,4.0],[0.0,0.0,0.0,4.0,0.0,0.0,-1.0,-4.0,0.0,0.0,-1.0,-4.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0,1.0,-1.0,0.0,1.0],[0.0,0.0,0.0,0.0,0.0,-2.0,0.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0,0.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0,0.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,7.0,0.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.0]],"num_vars":12}},"solutions":[{"source_config":[0,0,0,0,0],"target_config":[0,0,0,0,0,1,0,0,0,0,0,0]}]}, {"source":{"problem":"KSatisfiability","variant":{"k":"K3"},"instance":{"clauses":[{"literals":[1,2,3]},{"literals":[-1,-2,3]}],"num_vars":3}},"target":{"problem":"SubsetSum","variant":{},"instance":{"sizes":["10010","10001","1010","1001","111","100","10","20","1","2"],"target":"11144"}},"solutions":[{"source_config":[0,0,1],"target_config":[0,1,0,1,1,0,1,1,1,0]}]}, - {"source":{"problem":"KSatisfiability","variant":{"k":"KN"},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"target":{"problem":"Satisfiability","variant":{},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"solutions":[{"source_config":[1,1,1,1],"target_config":[1,1,1,1]}]}, + {"source":{"problem":"KSatisfiability","variant":{"k":"KN"},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"target":{"problem":"Satisfiability","variant":{},"instance":{"clauses":[{"literals":[1,-2,3]},{"literals":[-1,3,4]},{"literals":[2,-3,-4]}],"num_vars":4}},"solutions":[{"source_config":[1,1,1,0],"target_config":[1,1,1,0]}]}, {"source":{"problem":"Knapsack","variant":{},"instance":{"capacity":7,"values":[3,4,5,7],"weights":[2,3,4,5]}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[-483.0,240.0,320.0,400.0,80.0,160.0,320.0],[0.0,-664.0,480.0,600.0,120.0,240.0,480.0],[0.0,0.0,-805.0,800.0,160.0,320.0,640.0],[0.0,0.0,0.0,-907.0,200.0,400.0,800.0],[0.0,0.0,0.0,0.0,-260.0,80.0,160.0],[0.0,0.0,0.0,0.0,0.0,-480.0,320.0],[0.0,0.0,0.0,0.0,0.0,0.0,-800.0]],"num_vars":7}},"solutions":[{"source_config":[1,0,0,1],"target_config":[1,0,0,1,0,0,0]}]}, {"source":{"problem":"LongestCommonSubsequence","variant":{},"instance":{"strings":[[65,66,65,67],[66,65,67,65]]}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[1,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[3,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[3,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[2,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[3,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[4,1.0],[5,1.0]]}],"num_vars":6,"objective":[[0,1.0],[1,1.0],[2,1.0],[3,1.0],[4,1.0],[5,1.0]],"sense":"Maximize"}},"solutions":[{"source_config":[0,1,1,1],"target_config":[0,0,1,1,0,1]}]}, - {"source":{"problem":"MaxCut","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"target":{"problem":"SpinGlass","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"couplings":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"fields":[0,0,0,0,0,0,0,0,0,0],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"solutions":[{"source_config":[1,0,1,0,0,0,0,0,1,1],"target_config":[1,0,1,0,0,0,0,0,1,1]}]}, 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{"source":{"problem":"MaxCut","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"target":{"problem":"SpinGlass","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"couplings":[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],"fields":[0,0,0,0,0,0,0,0,0,0],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,4,null],[0,5,null],[1,2,null],[1,6,null],[2,3,null],[2,7,null],[3,4,null],[3,8,null],[4,9,null],[5,7,null],[5,8,null],[6,8,null],[6,9,null],[7,9,null]],"node_holes":[],"nodes":[null,null,null,null,null,null,null,null,null,null]}}}},"solutions":[{"source_config":[0,1,0,1,0,1,0,0,0,1],"target_config":[0,1,0,1,0,1,0,0,0,1]}]}, {"source":{"problem":"MaximumClique","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[0,3,null],[0,4,null],[1,2,null],[1,3,null],[1,5,null],[2,4,null],[2,5,null],[3,4,null],[3,5,null],[4,5,null]],"node_holes":[],"nodes":[null,null,null,null,null,null]}},"weights":[1,1,1,1,1,1]}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Le","rhs":1.0,"terms":[[0,1.0],[5,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[1,1.0],[4,1.0]]},{"cmp":"Le","rhs":1.0,"terms":[[2,1.0],[3,1.0]]}],"num_vars":6,"objective":[[0,1.0],[1,1.0],[2,1.0],[3,1.0],[4,1.0],[5,1.0]],"sense":"Maximize"}},"solutions":[{"source_config":[1,1,1,0,0,0],"target_config":[1,1,1,0,0,0]}]}, 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