feat: Implement set-theoretic reduction path finding (#12)

* docs: Add set-theoretic reduction path finding design

Design document addressing issues #10 and #11:
- Parametric problem modeling with graph type + weight type
- Set-theoretic path validation (A ⊆ C, D ⊆ B)
- Automatic registration via inventory crate
- Polynomial overhead model for output size
- Customizable cost functions for path optimization

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* docs: Add implementation plan for set-theoretic reductions

Detailed step-by-step plan with 25+ bite-sized tasks across 7 phases:
1. Foundation types (graph markers, NumericWeight, Polynomial)
2. Reduction registration (inventory, ReductionEntry, overhead)
3. Update Problem trait (NAME, GraphType, Weight parameters)
4. Update problem implementations (all 14+ problem types)
5. Rewrite ReductionGraph (set-theoretic validation, Dijkstra)
6. Update reduction implementations (add registration)
7. Integration tests

Each task includes exact file paths, complete code, and commit points.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* deps: Add inventory and ordered-float crates

* feat: Add graph marker traits for parametric problems

* feat: Add inventory-based graph subtype registration

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Add NumericWeight marker trait

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Add Polynomial type for reduction overhead

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Add reduction registration with inventory

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Add PathCostFn trait and built-in cost functions

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Add NAME, GraphType, Weight to Problem trait

Add three new associated items to the Problem trait for parametric
problem modeling and registration:
- const NAME: Base name of the problem type (e.g., "IndependentSet")
- type GraphType: The graph type marker this problem operates on
- type Weight: The numeric weight type for this problem

Update test problem types (SimpleWeightedProblem, SimpleCsp,
MultiFlavorProblem) to implement the new requirements.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* refactor: Add NAME, GraphType, Weight to all Problem implementations

- Add const NAME, type GraphType, and type Weight to all Problem trait
  implementations across graph, set, satisfiability, optimization, and
  specialized problem types
- Update CSP implementations to use 'static bounds for compatibility
- Add blanket implementation for NumericWeight trait to support generic
  weight types that satisfy the required bounds
- Update all reduction rules with 'static lifetime bounds
- Update test problems in brute_force.rs and traits.rs

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* refactor: Implement set-theoretic path finding with cost functions

- Add ReductionEdge struct to store graph type info and overhead on edges
- Build graph hierarchy from GraphSubtypeEntry via inventory
- Implement transitive closure for graph type subtyping
- Add is_graph_subtype() and rule_applicable() for set-theoretic validation
- Add find_cheapest_path() using Dijkstra with custom cost functions
- Auto-discover reductions from inventory::iter::<ReductionEntry>
- Export ReductionEdge from rules module
- Keep backward compatibility with manual reduction registration
- Add comprehensive tests for new functionality

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: Register all reductions with inventory for auto-discovery

Add inventory::submit! blocks to all reduction files to enable automatic
registration with the ReductionGraph. This allows the graph to discover
all available reductions at runtime without manual registration.

Changes:
- Modified ReductionEntry to use overhead_fn (function pointer) instead
  of overhead field to avoid static allocation issues with Vec/Polynomial
- Added inventory::submit! to 12 reduction files with proper overhead
  polynomials:
  - vertexcovering_independentset.rs (2 reductions)
  - independentset_setpacking.rs (2 reductions)
  - matching_setpacking.rs (1 reduction)
  - vertexcovering_setcovering.rs (1 reduction)
  - spinglass_maxcut.rs (2 reductions)
  - spinglass_qubo.rs (2 reductions)
  - sat_independentset.rs (1 reduction)
  - sat_coloring.rs (1 reduction)
  - sat_dominatingset.rs (1 reduction)
  - sat_ksat.rs (2 reductions)
  - factoring_circuit.rs (1 reduction)
  - circuit_spinglass.rs (1 reduction)
- Updated graph.rs to use overhead() method instead of field access
- Fixed test_find_cheapest_path_multi_step to use compatible graph types

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* test: Add integration tests for set-theoretic reduction system

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* test: Improve coverage for new modules

Add additional tests to improve test coverage for:
- graph_types.rs: declared subtype relationships, Default/Clone/Copy traits, BipartiteGraph and UnitDiskGraph entries
- cost.rs: CustomCost function, Minimize with missing field, MinimizeMax with empty vector
- registry.rs: ReductionEntry overhead evaluation, debug formatting, registered entries verification
- polynomial.rs: zero polynomial, constant polynomial, monomial scale, polynomial scale, multi-variable monomial

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* fix: Address PR review comments

- Remove redundant clone() on Copy type (clippy fix)
- Add comment explaining why explicit subtype declarations are needed
- Remove extra blank line in polynomial.rs
- Document round() usage in registry.rs

---------

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

Author: GiggleLiu

Cargo.lock

@@ -20,6 +20,8 @@ serde_json = "1.0"
 thiserror = "1.0"
 num-traits = "0.2"
 good_lp = { version = "1.8", default-features = false, features = ["highs"], optional = true }
+inventory = "0.3"
+ordered-float = "5.0"
 
 [dev-dependencies]
 rand = "0.8"