Efficient algorithms for κ-terminal cuts on planar graphs

Abstract

The minimum κ-terminal cut problem is of considerable theoretical interest and arises in several applied areas such as parallel and distributed computing, VLSI circuit design, and networking. In this paper, we present two new approximation and exact algorithms for this problem on an n-vertex undirected weighted planar graph G. For the case when the κ terminals are covered by the boundaries of m > 1 faces of G, we give a minO n 2 log n log m, O(m 2 n 1.5 log2 n+κn) time algorithm with a (2 - 2/κ)-approximation ratio (clearly, m k). For the case when all k terminals are covered by the boundary of one face of G, we give an O(nκ3 +(n log n)κ2) time exact algorithm, or a linear time exact algorithm if κ = 3, for computing an optimal k-terminal cut. Our algorithms are based on interesting observations and improve the previous algorithms when they are applied to planar graphs. © 2001 Springer Berlin Heidelberg.