Minimum $s-t$ cut in undirected planar graphs when the source and the sink are close

Haim Kaplan (1) , Yahav Nussbaum (1)

1 TAU-CS - School of Computer Science

Consider the minimum $s-t$ cut problem in an embedded undirected planar graph. Let $p$ be the minimum number of faces that a curve from $s$ to $t$ passes through. If $p=1$, that is, the vertices $s$ and $t$ are on the boundary of the same face, then the minimum cut can be found in $O(n)$ time. For general planar graphs this cut can be found in $O(n \log n)$ time. We unify these results and give an $O(n \log p)$ time algorithm. We use cut-cycles to obtain the value of the minimum cut, and study the structure of these cycles to get an efficient algorithm.

Mots clés: planar graph; minimum cut; shortest path; cut cycle

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Haim Kaplan, Yahav Nussbaum. Minimum $s-t$ cut in undirected planar graphs when the source and the sink are close. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.117-128. ⟨hal-00573605⟩