Minimum Multi Cut Problem

Minimum Multi Cut problem is the NP-hard problem of finding the minimum multi cut in a graph.

## Problem Definition

  • Instance: A graph G(V, E), a set S ⊆ V × V of source-terminal pairs, and a weight function w: E → N.

  • Solution: Find a multi-cut E’ ⊆ E such that removing E’ disconnects each source s from its corresponding terminal t for every pair (s, t) ∈ S.

  • Measure: Minimize the weight of the cut, defined as the sum of weights in E’