feat: Implement set-theoretic reduction path finding

[GiggleLiu]

Summary

Implements set-theoretic reduction path finding with automatic registration, addressing issues #10 and #11.

Key features:

• Graph type hierarchy: GraphMarker, GraphSubtype traits with UnitDiskGraph ⊆ PlanarGraph ⊆ SimpleGraph relationships
• Automatic reduction registration: Uses inventory crate for auto-discovery of reductions at link time
• Set-theoretic path validation: Rule C→D applies for A→B only if A ⊆ C and D ⊆ B
• Custom cost functions: PathCostFn trait with Minimize, MinimizeSteps, MinimizeWeighted, etc.
• Polynomial overhead: Reduction overhead expressed as polynomials over problem size variables
• Parametric Problem trait: All problems now have NAME, GraphType, Weight associated items

Changes:

• New modules: graph_types.rs, polynomial.rs, rules/registry.rs, rules/cost.rs
• Updated Problem trait with parametric types
• Updated all 19+ Problem implementations
• Rewrote ReductionGraph with Dijkstra-based path finding
• Registered 17 reductions with overhead metadata
• Added 8 integration tests

Test Plan

• All 691 tests pass
• Clippy clean with -D warnings
• Integration tests verify:
  • Graph hierarchy (UnitDisk ⊆ Planar ⊆ Simple)
  • Rule applicability (set-theoretic validation)
  • Multi-step paths (Factoring → CircuitSAT → SpinGlass)
  • Cost function path finding
  • Bidirectional reductions

Closes #10, Closes #11

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 98.53896% with 9 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.04%. Comparing base (a4ff2df) to head (f25abea).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/rules/graph.rs	96.41%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #12      +/-   ##
==========================================
+ Coverage   97.98%   98.04%   +0.05%     
==========================================
  Files          55       59       +4     
  Lines       11659    12265     +606     
==========================================
+ Hits        11424    12025     +601     
- Misses        235      240       +5     

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[Copilot]

Pull request overview

This PR implements a comprehensive set-theoretic reduction path finding system that addresses issues #10 and #11 by introducing parametric problem modeling with automatic reduction registration. The implementation enables rigorous validation of reduction paths based on graph type hierarchies and weight type compatibility.

Changes:

• Introduces graph type markers (GraphMarker, GraphSubtype) with automatic hierarchy registration via the inventory crate
• Implements polynomial overhead model for expressing reduction complexity as polynomials over input size variables
• Rewrites ReductionGraph with Dijkstra-based path finding that validates reductions using set-theoretic rules (A ⊆ C and D ⊆ B)
• Updates the Problem trait with parametric types (NAME, GraphType, Weight) and updates all 19+ problem implementations
• Adds 5 customizable cost functions (Minimize, MinimizeSteps, MinimizeWeighted, MinimizeMax, MinimizeLexicographic) for path optimization
• Registers 17 reductions with polynomial overhead metadata using inventory auto-discovery

Reviewed changes

Copilot reviewed 46 out of 47 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
src/graph_types.rs	New module defining graph type markers and subtype hierarchy with compile-time traits and runtime registration
src/polynomial.rs	New module for polynomial representation of reduction overhead with evaluation and macro support
src/types.rs	Adds NumericWeight marker trait for weight type subsumption
src/traits.rs	Updates Problem trait with NAME, GraphType, and Weight associated items
src/rules/registry.rs	New module for automatic reduction registration via inventory crate
src/rules/cost.rs	New module defining PathCostFn trait and built-in cost functions
src/rules/graph.rs	Major rewrite implementing set-theoretic path finding with Dijkstra's algorithm and graph hierarchy validation
src/rules/mod.rs	Exports new modules and public types
src/rules/*.rs (reductions)	Updates all reduction implementations with 'static bounds and inventory registration
src/models/**/*.rs (problems)	Updates all problem implementations with new Problem trait requirements
tests/set_theoretic_tests.rs	Comprehensive integration tests for graph hierarchy, rule applicability, and path finding
Cargo.toml	Adds inventory and ordered-float dependencies
docs/plans/*.md	Extensive design and implementation documentation

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[Copilot]

The direct declaration of UnitDiskGraph => SimpleGraph on line 74 is redundant since it's already implied by the transitive closure of UnitDiskGraph => PlanarGraph (line 73) and PlanarGraph => SimpleGraph (line 75). The build_graph_hierarchy function in src/rules/graph.rs computes the transitive closure, so this relationship will be derived automatically. Consider removing this redundant declaration to keep the code DRY and make the hierarchy easier to maintain.

[Copilot]

Extra blank line that should be removed for code consistency.

Suggested change

[Copilot]

The use of round() when converting polynomial evaluations to usize could lead to unexpected behavior. For example, if a polynomial evaluates to 99.5, it will round to 100, which might not be the intended behavior for problem size calculations. Consider whether ceil() or floor() would be more appropriate, or document why round() is the correct choice for this use case.