feat: batch add 14 reduction rules (hard rules phase 2)

[GiggleLiu]

Summary

• Add 14 new reduction rules connecting isolated/sparse problem nodes in the reduction graph
• Fix bounded path search in domination analysis to prevent SIGKILL on large graphs
• Add affine relation regression test for MAX-2-SAT → MaxCut

New reductions (by category):

Decision wrapper reductions (Batch 2):

• DecisionMinimumVertexCover → HamiltonianCircuit ([Rule] VERTEX COVER to HAMILTONIAN CIRCUIT #198)
• DecisionMinimumDominatingSet → MinMaxMulticenter ([Rule] DOMINATING SET to MIN-MAX MULTICENTER #379)
• DecisionMinimumDominatingSet → MinimumSumMulticenter ([Rule] DOMINATING SET to MIN-SUM MULTICENTER #380)

Connecting isolated nodes (Batch 3):

• ExactCoverBy3Sets → MinimumAxiomSet ([Rule] X3C to MinimumAxiomSet #870)
• ExactCoverBy3Sets → MinimumFaultDetectionTestSet ([Rule] X3C to MinimumFaultDetectionTestSet #928)
• KColoring → Clustering ([Rule] Graph 3-Colorability to Clustering #924)
• MinimumFeedbackArcSet → MaximumLikelihoodRanking ([Rule] FEEDBACK ARC SET to MAXIMUM LIKELIHOOD RANKING #922)
• MinimumFeedbackVertexSet → MinimumCodeGenerationUnlimitedRegisters ([Rule] FEEDBACK VERTEX SET to MinimumCodeGenerationUnlimitedRegisters #908)
• MinimumVertexCover → MinimumWeightAndOrGraph ([Rule] VertexCover to MinimumWeightAndOrGraph #929)
• KSatisfiability(3-SAT) → QuadraticDiophantineEquations ([Rule] 3SAT to QUADRATIC DIOPHANTINE EQUATIONS #560)

Adding density:

• Maximum2Satisfiability → MaxCut ([Rule] MAX 2-SATISFIABILITY to MAX CUT #825, already existed, added affine test)
• PartitionIntoCliques → MinimumCoveringByCliques
• 3SAT → RegisterSufficiency

Bug fixes:

• Fix MaximumLikelihoodRanking to allow negative matrix entries (c=0 skew-symmetric)
• Bound domination analysis path search to prevent OOM/SIGKILL

Test plan

• cargo fmt --check passes
• cargo clippy clean (0 warnings)
• cargo test passes (4976+ tests)
• All new reductions have closed-loop tests
• Paper entries for new reductions (follow-up)
• make regenerate-fixtures for canonical examples (follow-up)

🤖 Generated with Claude Code

[Copilot]

Pull request overview

Adds a second batch of reduction rules to connect previously sparse/isolated nodes in the reduction graph, and hardens reduction-graph domination analysis to avoid runaway path enumeration on large graphs. It also expands unit/integration coverage around the new rules and updates a few affected models (FaultDetection semantics, MaximumLikelihoodRanking matrix validation, QuadraticDiophantineEquations bigint encoding).

Changes:

• Add multiple new reductions (incl. decision-wrapper reductions and “density” edges) with closed-loop/unit tests and example-db specs.
• Fix/limit reduction-graph path enumeration used in domination analysis to prevent OOM/SIGKILL on dense graphs.
• Update several models/test suites to support the new reductions (e.g., QDE BigUint witness encoding, MLR allowing negative/skew-symmetric matrices, FaultDetection internal-vertex semantics).

Reviewed changes

Copilot reviewed 50 out of 50 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
tests/suites/register_assignment_reductions.rs	Formatting-only updates to assertions for readability.
tests/suites/reductions.rs	Adds integration tests for PartitionIntoCliques -> MinimumCoveringByCliques.
tests/main.rs	Ensures reductions suite is always included (not feature-gated).
src/unit_tests/rules/registersufficiency_ilp.rs	Unit tests for RegisterSufficiency -> ILP (structure + closed-loop + example-db spec).
src/unit_tests/rules/partitionintocliques_minimumcoveringbycliques.rs	Unit tests for Orlin reduction correctness and extraction behavior.
src/unit_tests/rules/minimumvertexcover_minimumweightandorgraph.rs	Unit tests for MinimumVertexCover -> MinimumWeightAndOrGraph (incl. weighted sink-arc charging).
src/unit_tests/rules/minimumfeedbackvertexset_minimumcodegenerationunlimitedregisters.rs	Closed-loop test for MinimumFeedbackVertexSet -> MinimumCodeGenerationUnlimitedRegisters.
src/unit_tests/rules/minimumfeedbackarcset_maximumlikelihoodranking.rs	Unit tests for MinimumFeedbackArcSet -> MaximumLikelihoodRanking (matrix + extraction + constraints).
src/unit_tests/rules/maximum2satisfiability_maxcut.rs	Adds affine-relation regression test over all MaxCut partitions for the issue instance.
src/unit_tests/rules/ksatisfiability_registersufficiency.rs	Unit tests for 3SAT -> RegisterSufficiency (structure + extraction + optional ILP loop).
src/unit_tests/rules/ksatisfiability_quadraticdiophantineequations.rs	Closed-loop tests for 3SAT -> QuadraticDiophantineEquations and reference-witness encoding.
src/unit_tests/rules/ksatisfiability_feasibleregisterassignment.rs	Formatting-only updates to assertions for readability.
src/unit_tests/rules/kcoloring_clustering.rs	Unit tests for KColoring(K=3) -> Clustering (distance matrix + edge cases).
src/unit_tests/rules/exactcoverby3sets_minimumfaultdetectiontestset.rs	Unit tests for X3C -> MinimumFaultDetectionTestSet (gap + structure + identity extraction).
src/unit_tests/rules/exactcoverby3sets_minimumaxiomset.rs	Unit tests for X3C -> MinimumAxiomSet (gap + structure + extraction behavior).
src/unit_tests/rules/decisionminimumvertexcover_hamiltoniancircuit.rs	Unit tests for Decision<MVC> -> HamiltonianCircuit (counts + witness + corner cases).
src/unit_tests/rules/decisionminimumdominatingset_minmaxmulticenter.rs	Unit tests for Decision<MDS> -> MinMaxMulticenter (structure + closed-loop).
src/unit_tests/rules/decisionminimumdominatingset_minimumsummulticenter.rs	Unit tests for Decision<MDS> -> MinimumSumMulticenter (YES/NO instances).
src/unit_tests/reduction_graph.rs	Adds discovery tests for newly registered reductions + adjusts path-limit test expectations.
src/unit_tests/models/misc/minimum_fault_detection_test_set.rs	Updates tests to reflect “internal vertices only” semantics + adds a boundary-only case.
src/unit_tests/models/misc/maximum_likelihood_ranking.rs	Adds tests for comparison_count and skew-symmetric matrices.
src/unit_tests/models/algebraic/quadratic_diophantine_equations.rs	Updates tests for BigUint-based encoding/serialization and witness round-trips.
src/rules/registersufficiency_ilp.rs	Implements RegisterSufficiency -> ILP<i32> reduction with overhead metadata and example-db spec.
src/rules/partitionintocliques_minimumcoveringbycliques.rs	Implements Orlin reduction PartitionIntoCliques -> MinimumCoveringByCliques + extraction logic.
src/rules/mod.rs	Registers the new rule modules and wires canonical example specs.
src/rules/minimumvertexcover_minimumweightandorgraph.rs	Implements MinimumVertexCover -> MinimumWeightAndOrGraph reduction + example-db spec.
src/rules/minimumfeedbackvertexset_minimumcodegenerationunlimitedregisters.rs	Implements Aho–Johnson–Ullman chain gadget reduction for unlimited-register codegen.
src/rules/minimumfeedbackarcset_maximumlikelihoodranking.rs	Implements unit-weight FAS -> MLR via skew-symmetric (c=0) matrix encoding.
src/rules/ksatisfiability_registersufficiency.rs	Implements Sethi 3SAT -> RegisterSufficiency reduction with corrected extraction rule.
src/rules/ksatisfiability_quadraticdiophantineequations.rs	Implements 3SAT -> QDE by translating existing quadratic congruence construction.
src/rules/ksatisfiability_feasibleregisterassignment.rs	Minor formatting change in extraction logic for readability.
src/rules/kcoloring_clustering.rs	Implements 3-Coloring -> Clustering reduction (0/1 distances, K=3, B=0).
src/rules/graph.rs	Adds bounded path enumeration API used by domination analysis and find_paths_up_to*.
src/rules/feasibleregisterassignment_ilp.rs	Minor formatting change (constraint vec construction) for readability.
src/rules/exactcoverby3sets_minimumfaultdetectiontestset.rs	Implements X3C -> MinimumFaultDetectionTestSet reduction (single-output DAG).
src/rules/exactcoverby3sets_minimumaxiomset.rs	Implements X3C -> MinimumAxiomSet reduction (4 implications per subset).
src/rules/decisionminimumvertexcover_hamiltoniancircuit.rs	Implements G&J Thm 3.4 gadget reduction for decision MVC to Hamiltonian circuit.
src/rules/decisionminimumdominatingset_minmaxmulticenter.rs	Implements Decision<MDS> -> MinMaxMulticenter (unit weights/lengths, radius-1 equivalence).
src/rules/decisionminimumdominatingset_minimumsummulticenter.rs	Implements Decision<MDS> -> MinimumSumMulticenter (unit weights/lengths, sum bound property).
src/rules/analysis.rs	Uses bounded path enumeration to avoid blowups during dominated-rule detection.
src/models/misc/register_sufficiency.rs	Adds num_sinks() helper used in reduction overhead/counts.
src/models/misc/mod.rs	Updates model docs to reflect FaultDetection “internal vertices” semantics.
src/models/misc/minimum_fault_detection_test_set.rs	Changes objective feasibility to cover internal vertices only and updates schema/notes.
src/models/misc/maximum_likelihood_ranking.rs	Validates constant pairwise sum (c) and exposes comparison_count().
src/models/graph/minimum_dominating_set.rs	Adds One weight variant and registers decision variant inventory entries for One.
src/models/graph/min_max_multicenter.rs	Adds One weight variant declaration.
src/models/formula/ksat.rs	Adds register_sufficiency_padding() accessor for overhead expressions.
src/models/algebraic/quadratic_diophantine_equations.rs	Switches to BigUint coefficients and binary witness encoding; updates schema/size fields/variants.
docs/paper/references.bib	Adds bibliography entries supporting new reductions (Brucker/Orlin/Kou-Stockmeyer-Wong).

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

[Copilot]

petgraph::algo::all_simple_paths interprets the last argument as a maximum path length in edges (hops), not “max intermediate nodes”. Passing max_intermediate_nodes directly will undercount by ~1 (intermediate_nodes = hops - 1), and the doc comment is currently misleading. Consider either (a) renaming this parameter to max_hops and updating the doc, or (b) translating via max_hops = max_intermediate_nodes.map(|k| k + 1) before calling all_simple_paths so the bound matches the stated semantics.