Implement remaining reduction rules

[GiggleLiu]

Summary

The reduction framework is complete with core reductions implemented (IS↔VC, IS↔SP, SG↔QUBO, SG↔MaxCut). Additional reductions are needed for full feature parity with ProblemReductions.jl.

Remaining Reductions to Implement

Each reduction follows the established pattern:

1. Create reduction result struct
2. Implement ReductionResult trait
3. Implement ReduceTo trait
4. Write tests
5. Update src/rules/mod.rs
6. Register in ReductionGraph

Set/Graph Reductions

• src/rules/vertexcovering_setcovering.rs - VertexCovering → SetCovering
• src/rules/matching_setpacking.rs - Matching → SetPacking

SAT-based Reductions

• src/rules/sat_3sat.rs - SAT → 3-SAT (clause splitting)
• src/rules/sat_independentset.rs - SAT → IndependentSet
• src/rules/sat_coloring.rs - SAT → Coloring
• src/rules/sat_dominatingset.rs - SAT → DominatingSet
• src/rules/spinglass_sat.rs - SpinGlass → SAT
• src/rules/circuit_sat.rs - CircuitSAT → SAT (Tseitin transformation)
• src/rules/factoring_sat.rs - Factoring → SAT

Implementation Notes

• Use the existing ReduceTo and ReductionResult traits from src/rules/traits.rs
• Follow the pattern established in existing reductions (e.g., vertexcovering_independentset.rs)
• Register each new reduction in ReductionGraph::register_reductions()
• Maintain >95% code coverage

References

• Implementation Plan - Task 6
• Design Document