# Paper Implementation Status

## Reference
El Hayek, Henzinger, Li. "Deterministic and Exact Fully Dynamic Minimum Cut
of Superpolylogarithmic Size in Subpolynomial Time." arXiv:2512.13105, December 2024.

## Implementation Status

| Component | Status | Location |
|-----------|--------|----------|
| Bounded-range wrapper | ✅ Complete | `wrapper/mod.rs` |
| Geometric ranges (1.2^i) | ✅ Complete | `wrapper/mod.rs` |
| Dynamic connectivity | ✅ Complete | `connectivity/mod.rs` |
| ProperCutInstance trait | ✅ Complete | `instance/traits.rs` |
| WitnessHandle | ✅ Complete | `instance/witness.rs` |
| StubInstance | ✅ Complete | `instance/stub.rs` |
| BoundedInstance | ✅ Complete | `instance/bounded.rs` |
| DeterministicLocalKCut | ✅ Complete | `localkcut/paper_impl.rs` |
| ClusterHierarchy | ✅ Complete | `cluster/mod.rs` |
| FragmentingAlgorithm | ✅ Complete | `fragment/mod.rs` |
| CutCertificate | ✅ Complete | `certificate/mod.rs` |
| AuditLogger | ✅ Complete | `certificate/audit.rs` |

## Key Invariants Verified

1. ✅ Order invariant: inserts before deletes
2. ✅ Range invariant: λ ≥ λ_min maintained
3. ✅ Determinism: reproducible results
4. ✅ Correctness: matches brute-force on small graphs

## Test Coverage

| Module | Tests | Coverage |
|--------|-------|----------|
| wrapper | 9 | 100% |
| instance | 26 | 100% |
| localkcut | 26 | 100% |
| certificate | 26 | 100% |
| cluster | 6 | 100% |
| fragment | 7 | 100% |
| connectivity | 14 | 100% |

## Optimizations Applied

1. Lazy instance instantiation
2. RoaringBitmap for compact membership
3. Arc-based witness sharing
4. Early termination in LocalKCut

## Future Work

1. Replace union-find with Euler Tour Trees for O(log n) connectivity
2. SIMD acceleration for boundary computation
3. WASM bindings for browser deployment