English

A polynomial-time algorithm for planar multicuts with few source-sink pairs

Discrete Mathematics 2012-06-19 v1 Data Structures and Algorithms

Abstract

Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its corresponding sink. We give the first polynomial-time algorithm to solve this problem in planar graphs, when k is fixed. Previously, this problem was known to remain NP-hard in general graphs with fixed k, and in trees with arbitrary k; the most noticeable tractable case known so far was in planar graphs with fixed k and sources and sinks lying on the outer face.

Keywords

Cite

@article{arxiv.1206.3999,
  title  = {A polynomial-time algorithm for planar multicuts with few source-sink pairs},
  author = {Cédric Bentz},
  journal= {arXiv preprint arXiv:1206.3999},
  year   = {2012}
}

Comments

11 pages, 1 figure

R2 v1 2026-06-21T21:21:26.560Z