Fix #207: [Rule] MinimumVertexCover to MinimumFeedbackVertexSet

[GiggleLiu]

Summary

Add the plan and implementation for the MinimumVertexCover -> MinimumFeedbackVertexSet reduction.

Fixes #207

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.59%. Comparing base (ca2110e) to head (5895c4b).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #713      +/-   ##
==========================================
+ Coverage   97.57%   97.59%   +0.02%     
==========================================
  Files         381      385       +4     
  Lines       47649    47886     +237     
==========================================
+ Hits        46494    46736     +242     
+ Misses       1155     1150       -5     

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[GiggleLiu]

Implementation Summary

Changes

• Added src/rules/minimumvertexcover_minimumfeedbackvertexset.rs implementing the MinimumVertexCover -> MinimumFeedbackVertexSet reduction with identity solution extraction and overhead num_vertices = num_vertices, num_arcs = 2 * num_edges.
• Registered the new rule and its canonical example in src/rules/mod.rs.
• Added src/unit_tests/rules/minimumvertexcover_minimumfeedbackvertexset.rs covering round-trip correctness on a cyclic source graph, target structure, weight preservation, identity extraction, and example-db witness validation.
• Added the corresponding paper reduction entry in docs/paper/reductions.typ using the exported canonical example data.

Deviations from Plan

• The repo no longer has make regenerate-fixtures; I used cargo run --features "example-db" --example export_examples, which is the current fixture export path wired into make paper.
• docs/paper/reductions.typ already had an uncommitted one-line local fix in another section of the file when I reached the paper step. I preserved it while adding the new MVC -> MinimumFeedbackVertexSet entry rather than trying to rewrite around existing worktree state.

Open Questions

• None.

[GiggleLiu]

Agentic Review Report

Structural Check

Structural Review: rule minimumvertexcover_minimumfeedbackvertexset

Structural Completeness

#	Check	Status
1	Rule file exists	PASS
2	#[reduction(...)] macro present	PASS
3	ReductionResult impl present	PASS
4	ReduceTo impl present	PASS
5	#[cfg(test)] + #[path = "..."] test link	PASS
6	Test file exists	PASS
7	Closed-loop test present	PASS
8	Registered in src/rules/mod.rs	PASS
9	Canonical rule example registered	PASS
10	Example-db lookup tests exist	PASS
11	Paper reduction-rule entry exists	PASS
12	Blacklisted autogenerated files committed	PASS — none in diff

Build Status

• make test: PASS
• make clippy: PASS
• make paper: PASS

Semantic Review

• extract_solution: OK — identity mapping is correct because the reduction preserves the vertex set and selection semantics.
• Overhead accuracy: OK — reduce_to() duplicates each undirected edge into exactly two directed arcs, matching num_vertices = num_vertices and num_arcs = 2 * num_edges.
• Mathematical correctness: OK — every target 2-cycle corresponds to a source edge, so any FVS is a vertex cover; conversely any vertex cover hits every directed cycle because each cycle is composed of source edges.
• Example quality: OK — the canonical 7-vertex example matches the linked issue and the exported witness is feasible and optimal on both source and target.
• Paper quality: OK — the new theorem statement and proof sketch are sound, and the paper build succeeds.

Issue Compliance

#	Check	Status
1	Source/target match issue	OK
2	Reduction algorithm matches	OK
3	Solution extraction matches	OK
4	Correctness preserved	OK
5	Overhead expressions match	OK
6	Example matches	OK

Summary

• 12/12 structural checks passed
• 6/6 issue compliance checks passed
• No structural correctness issues found

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Quality Check

Quality Review

Design Principles

• DRY: OK — the rule follows the existing small-reduction pattern without introducing duplicate helpers.
• KISS: OK — reduce_to() is a direct edge-to-bidirected-edge transformation with no unnecessary abstraction.
• HC/LC: OK — rule logic, tests, and paper text remain separated along existing repo boundaries.

Test Quality

• Naive test detection: OK
  • The suite includes a closed-loop optimality check, explicit arc-structure verification, weight preservation, identity extraction, and canonical example-db validation.
  • The closed-loop test uses a source graph with both 2-cycles and a longer directed cycle after reduction, so it exercises the nontrivial part of the proof rather than only a degenerate path instance.

Issues

Critical (Must Fix)

• None.

Important (Should Fix)

• None.

Minor (Nice to Have)

• docs/paper/reductions.typ:3726 is an unrelated SequencingToMinimizeWeightedCompletionTime paper fix bundled into this PR. It does not appear harmful, but it expands the review surface beyond issue [Rule] MinimumVertexCover to MinimumFeedbackVertexSet #207.

Summary

• No code-quality or test-quality defects found in the MVC -> MinimumFeedbackVertexSet implementation.
• One minor scope note: unrelated paper cleanup is bundled in the same PR.

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Agentic Feature Tests

Feature Test Report: problemreductions CLI

Feature tested: MinimumVertexCover -> MinimumFeedbackVertexSet
Profile: ephemeral
Use Case: downstream CLI user discovers the new reduction, materializes the canonical example, reduces it, and solves both sides with brute force
Expected Outcome: the new rule is discoverable in the catalog and works end-to-end through pred
Verdict: pass
Critical Issues: 0

Summary

Feature	Discoverable	Setup	Works	Expected Outcome Met	Doc Quality
MVC -> FVS rule	yes	yes	yes	yes	good

Per-Feature Details

MinimumVertexCover -> MinimumFeedbackVertexSet

• What I tried:
  • cargo run -q -p problemreductions-cli --bin pred -- list --rules
  • cargo run -q -p problemreductions-cli --bin pred -- show MVC
  • cargo run -q -p problemreductions-cli --bin pred -- show FVS
  • cargo run -q -p problemreductions-cli --bin pred -- path MVC FVS
  • cargo run -q -p problemreductions-cli --bin pred -- create --example MVC --to FVS -o /tmp/mvc_to_fvs_alias_source.json
  • cargo run -q -p problemreductions-cli --bin pred -- solve /tmp/mvc_to_fvs_source.json --solver brute-force
  • cargo run -q -p problemreductions-cli --bin pred -- reduce /tmp/mvc_to_fvs_source.json --to MinimumFeedbackVertexSet/i32 -o /tmp/mvc_to_fvs_bundle.json
  • cargo run -q -p problemreductions-cli --bin pred -- solve /tmp/mvc_to_fvs_bundle.json --solver brute-force
• Discoverability: Good. The rule appears in pred list --rules, pred show MVC exposes it as an outgoing reduction, pred show FVS shows it as an incoming reduction, and pred path MVC FVS resolves a one-step path.
• Setup: Worked as documented using the in-repo CLI.
• Functionality: Worked. Canonical rule example creation succeeded, reduction produced a target bundle with MinimumFeedbackVertexSet, and solving the bundle mapped the solution back to MinimumVertexCover with the same objective Valid(4).
• Expected vs Actual Outcome: Matched expected outcome.
• Blocked steps: None.
• Friction points: None found.
• Doc suggestions: None required for this feature based on the exercised flow.

Issues Found

• None.

Suggestions

• None.

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