Fix #141: Add MinimumFeedbackVertexSet to ILP reduction

[zazabap]

Summary

Adds a reduction from MinimumFeedbackVertexSet to ILP using the MTZ-style topological ordering formulation. The reduction uses 2n variables (n binary for vertex removal + n integer for topological order) and m + 2n constraints (one per arc + bounds).

Fixes #141

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.12%. Comparing base (9640b88) to head (d57512c).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #624      +/-   ##
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+ Coverage   97.11%   97.12%   +0.01%     
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  Files         294      296       +2     
  Lines       39220    39392     +172     
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+ Hits        38088    38259     +171     
- Misses       1132     1133       +1     

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[zazabap]

Implementation Summary

Changes

• src/rules/minimumfeedbackvertexset_ilp.rs — New reduction rule implementing MTZ-style topological ordering formulation. Maps MFVS to ILP<i32> with 2n variables (n binary x_i for vertex removal + n integer o_i for topological order) and m + 2n constraints (arc constraints + binary/order bounds). Feature-gated under ilp-solver.
• src/rules/mod.rs — Registered new module under #[cfg(feature = "ilp-solver")].
• src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs — 8 unit tests: closed-loop, structure verification, cycle-of-triangles (issue example), DAG input, single vertex, weighted, disjoint cycles, solution extraction.
• examples/reduction_minimumfeedbackvertexset_to_ilp.rs — Example using the cycle-of-triangles instance (n=9, m=15, FVS=3). Uses ILPSolver directly since BruteForce can't enumerate ILP domain.
• tests/suites/examples.rs — Registered example test.
• docs/paper/reductions.typ — Added reduction-rule entry with construction, correctness proof, and solution extraction.
• docs/src/reductions/reduction_graph.json — Updated with new reduction edge.

Deviations from Plan

• Used ILP<i32> instead of ILP<bool> because the reduction requires mixed binary + integer variables. Added explicit x_i <= 1 constraints to enforce binary semantics on selection variables, and o_i <= n-1 bounds on ordering variables.
• Example uses ILPSolver instead of BruteForce since ILP<i32> has DIMS_PER_VAR = i32::MAX + 1, making brute-force enumeration infeasible.

Open Questions

• None

[Copilot]

Pull request overview

Adds a new reduction rule from MinimumFeedbackVertexSet (directed) to ILP<i32> using an MTZ-style topological-ordering formulation, plus supporting docs/examples/tests. This expands the reduction graph so MFVS instances can be solved exactly via ILP backends.

Changes:

• Implement MinimumFeedbackVertexSet → ILP<i32> reduction with 2n variables and m + 2n constraints.
• Add unit tests + example suite coverage for the new reduction and solution extraction.
• Regenerate/update documentation artifacts (reduction graph + paper section) to include the new rule.

Reviewed changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
src/rules/minimumfeedbackvertexset_ilp.rs	Implements the MFVS→ILP reduction (variable layout, constraints, objective, extraction).
src/rules/mod.rs	Registers the new reduction module behind the ilp-solver feature.
src/unit_tests/rules/minimumfeedbackvertexset_ilp.rs	Adds correctness/structure tests comparing ILP solutions vs brute force on small instances.
examples/reduction_minimumfeedbackvertexset_to_ilp.rs	Adds a runnable/exportable example demonstrating the reduction and verification.
tests/suites/examples.rs	Hooks the new example into the example test suite.
docs/src/reductions/reduction_graph.json	Updates the generated reduction graph to include the new reduction edge.
docs/paper/reductions.typ	Adds a paper-form description of the MFVS→ILP formulation and correctness sketch.

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[zazabap]

Review Pipeline Report

Check	Result
Copilot comments	0 (approved, no actionable comments)
Issue/human comments	3 checked, 0 actionable
Structural review	11/11 passed
CI	green
Agentic test	passed
Needs human decision	none
Board	Ready → Under review → Final review

Fixes applied during review

1. Merged main — resolved conflicts in src/rules/mod.rs, tests/suites/examples.rs, docs/src/reductions/reduction_graph.json
2. Migrated example to example-db — removed old-style examples/reduction_minimumfeedbackvertexset_to_ilp.rs, added canonical_rule_example_specs() to the rule file and registered it in mod.rs
3. Fixed solve_ilp CLI dispatch — solve_ilp() only handled ILP<bool>, breaking pred solve for problems that reduce to ILP<i32>. Now handles both variants.
4. Formatting fix — after merge with main

Remaining issues for final review

• None.

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