Advertisement

Algorithmica

, Volume 38, Issue 2, pp 299–316 | Cite as

Efficient Algorithms for k-Terminal Cuts on Planar Graphs

  • Danny Z. Chen
  • Xiadong  WuEmail author
Article

Abstract

The minimum k-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 k terminals are covered by the boundaries of m > 1 faces of G, we give a min{O(n 2 log n logm), O(m 2 n 1.5 log2 n + k n)} time algorithm with a (2–2/k)-approximation ratio (clearly, m \le k). For the case when all k terminals are covered by the boundary of one face of G, we give an O(n k3 + (n log n)k 2) time exact algorithm, or a linear time exact algorithm if k = 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. To our best knowledge, no previous approximation algorithms specifically for solving the k-terminal cut problem on planar graphs were known before. The (2–2/k)-approximation algorithm of Dahlhaus et al. (for general graphs) takes O(k n 2 log n) time when applied to planar graphs. Our approximation algorithm for planar graphs runs faster than that of Dahlhaus et al. by at least an O(k/logm) factor (m \le k).

Keywords

Planar Graph Steiner Tree Articulation Point Minimum Steiner Tree Extended Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556USA
  2. 2.Department of Computer Science, University of Texas – Pan American, 1201 West University Drive, Edinburg, TX 78539USA

Personalised recommendations