Module wrapper 

Instance Manager for Bounded-Range Dynamic Minimum Cut

Implements the wrapper algorithm from the December 2024 paper (arxiv:2512.13105). Manages O(log n) bounded-range instances with geometric ranges using factor 1.2.

Overview

The wrapper maintains instances with ranges:

• Instance i: [λ_min[i], λ_max[i]] where
• λ_min[i] = floor(1.2^i)
• λ_max[i] = floor(1.2^(i+1))

Algorithm

1. Buffer edge insertions and deletions
2. On query, process instances in increasing order
3. Apply inserts before deletes (order invariant)
4. Stop when instance returns AboveRange

Time Complexity

• O(log n) instances
• O(log n) query time (amortized)
• Subpolynomial update time per instance

Structs

MinCutWrapper

The main wrapper managing O(log n) bounded instances

Enums

MinCutResult

Result of a minimum cut query