Fix #1095: MinimumDominatingSet/i32 to MinimumSetCovering/i32

[isPANN]

Summary

Add the weighted closed-neighborhood reduction from Minimum Dominating Set to Minimum Set Covering.

Fixes #1095

[isPANN]

Implementation Summary

Changes

• Added MinimumDominatingSet<SimpleGraph, i32> -> MinimumSetCovering<i32> using one deduplicated closed-neighborhood set per vertex, copied signed weights, identity witness extraction, and exact target-size metadata.
• Added focused closed-loop, structure, signed-weight, empty/isolated, and self-loop/parallel-edge tests.
• Added the canonical weighted path example to the example database and documented the reduction with a fixture-backed worked example and references.
• Updated the topology expectation for the newly dominated direct MinimumDominatingSet -> ILP path.

Verification

• Mathematical constructor: 93,254 checks, 0 failures.
• Independent adversary: 170,347 checks, 0 failures; two Hypothesis strategies.
• Cross-comparison: 1,103 targets / 33,867 configurations, 0 disagreements.
• make paper, make test, make clippy, and make coverage passed.
• Coverage: 97.49% lines, 97.89% regions.

Deviations from Plan

• Added the topology expectation update after the full suite showed that the new two-step route dominates the pre-existing direct ILP edge.
• The PR is stacked on 1075-growth-domain at requested base commit a9067297 instead of main.

Open Questions

• None.

[isPANN]

Agentic Review Report

Structural Check

Structural Completeness

Check	Status
Rule file, #[reduction(...)], ReductionResult, and ReduceTo	PASS
Test link and dedicated test file	PASS
Closed-loop test and focused edge-case tests	PASS
Registration in rules/mod.rs	PASS
Canonical rule example and example-db coverage	PASS
Paper reduction-rule entry	PASS
Blacklisted generated files absent	PASS

Build Status

• make test: PASS — 5,436 library tests, 75 integration tests, 330 CLI tests, 17 pred_sym tests, 26 macro tests, 151 crate doc-tests, and 2 macro doc-tests passed with zero failures.
• make clippy: PASS — all targets with ilp-highs and -D warnings.
• git diff --check: PASS.

Semantic Review

• Construction: PASS — creates one sorted, deduplicated closed-neighborhood set per source vertex and copies weights coordinate-for-coordinate.
• Correctness: PASS — selecting source vertices dominates exactly when the corresponding target sets cover the universe; copied signed weights preserve every configuration's objective.
• Extraction: PASS — the identity map is correct because target set D_v and source vertex v share a coordinate.
• Overhead: PASS — exact target dimensions are universe_size = n and num_sets = n, including n = 0.
• Worked trace: PASS — on P5, [0,1,0,1,0] selects D_1 ∪ D_3 = V, has cost 2, and extracts to dominating set {1,3}.
• Edge cases: PASS — empty graphs, isolated vertices, signed weights, self-loops, and repeated edges are covered.
• Paper proof and example: PASS — construction, both feasibility directions, objective preservation, identity extraction, commands, and the canonical witness are sound.

Issue Compliance

All 6 checks pass: source/target variants, construction, extraction, correctness, overhead expressions, and the weighted-path example match issue #1095.

Structural summary: 12/12 structural checks and 6/6 issue-compliance checks passed; no FAIL or ISSUE findings.

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Quality Check

Design Principles

• DRY: OK — reuses MinimumDominatingSet::closed_neighborhood and the shared optimization round-trip helper.
• KISS: OK — direct one-pass construction plus identity extraction, without unnecessary abstraction or branching.
• High cohesion / low coupling: OK — construction, extraction, example registration, and tests remain in their established narrow modules.
• HCI: Not applicable — the actual six-file stacked diff contains no CLI or MCP changes.

Test Quality

The suite has strong value-level coverage: exact nontrivial target structure and optimal extraction, signed weights, empty and isolated graphs, and adversarial self-loop/repeated-edge input.

Important — missing explicit infeasible-configuration preservation test. The shared round-trip helper enumerates optimal target witnesses and verifies their extracted source solutions, but it does not directly evaluate a known infeasible source configuration and the identical target configuration. Add a semantic assertion such as selecting only an endpoint of P5, verifying that it is both non-dominating and non-covering.

Quality Summary

• Critical: none.
• Important: one test-coverage finding above.
• Minor: none.

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Agentic Feature Tests

Feature: MinimumDominatingSet<SimpleGraph, i32> → MinimumSetCovering<i32>
Profile: ephemeral downstream CLI user
Verdict: PASS
Critical issues: 0
Repository modifications: none

Area	Result
Catalog discovery with pred list / pred show	PASS
Source build/setup	PASS
Canonical example creation	PASS
Source solve/evaluate	PASS
Reduction construction	PASS
Independent target solve/evaluate	PASS
Bundle round trip and extraction	PASS
Signed-weight behavior	PASS
Coordinate and objective preservation	PASS

The canonical weighted P5 flow produced the expected target sets and [0,1,0,1,0] witness with Min(2). The source, independently solved target, and extracted bundle agreed. A signed-weight path with weights [-5,10,-7] also agreed across source, target, and bundle at [1,0,1] with Min(-12). Both brute-force and the paper-documented default ILP flow passed.

No candidate agentic finding required reproduction; there were no confirmed agentic issues.

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