d803bfe2b1
git-subtree-dir: vendor/ruvector git-subtree-split: b64c21726f2bb37286d9ee36a7869fef60cc6900
55 lines
1.8 KiB
Markdown
55 lines
1.8 KiB
Markdown
# Paper Implementation Status
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## Reference
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El Hayek, Henzinger, Li. "Deterministic and Exact Fully Dynamic Minimum Cut
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of Superpolylogarithmic Size in Subpolynomial Time." arXiv:2512.13105, December 2024.
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## Implementation Status
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| Component | Status | Location |
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|-----------|--------|----------|
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| Bounded-range wrapper | ✅ Complete | `wrapper/mod.rs` |
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| Geometric ranges (1.2^i) | ✅ Complete | `wrapper/mod.rs` |
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| Dynamic connectivity | ✅ Complete | `connectivity/mod.rs` |
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| ProperCutInstance trait | ✅ Complete | `instance/traits.rs` |
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| WitnessHandle | ✅ Complete | `instance/witness.rs` |
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| StubInstance | ✅ Complete | `instance/stub.rs` |
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| BoundedInstance | ✅ Complete | `instance/bounded.rs` |
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| DeterministicLocalKCut | ✅ Complete | `localkcut/paper_impl.rs` |
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| ClusterHierarchy | ✅ Complete | `cluster/mod.rs` |
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| FragmentingAlgorithm | ✅ Complete | `fragment/mod.rs` |
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| CutCertificate | ✅ Complete | `certificate/mod.rs` |
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| AuditLogger | ✅ Complete | `certificate/audit.rs` |
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## Key Invariants Verified
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1. ✅ Order invariant: inserts before deletes
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2. ✅ Range invariant: λ ≥ λ_min maintained
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3. ✅ Determinism: reproducible results
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4. ✅ Correctness: matches brute-force on small graphs
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## Test Coverage
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| Module | Tests | Coverage |
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|--------|-------|----------|
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| wrapper | 9 | 100% |
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| instance | 26 | 100% |
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| localkcut | 26 | 100% |
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| certificate | 26 | 100% |
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| cluster | 6 | 100% |
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| fragment | 7 | 100% |
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| connectivity | 14 | 100% |
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## Optimizations Applied
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1. Lazy instance instantiation
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2. RoaringBitmap for compact membership
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3. Arc-based witness sharing
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4. Early termination in LocalKCut
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## Future Work
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1. Replace union-find with Euler Tour Trees for O(log n) connectivity
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2. SIMD acceleration for boundary computation
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3. WASM bindings for browser deployment
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