Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Efficient Algorithms for k-Terminal Cuts on Planar Graphs

  • 124 Accesses

  • 8 Citations


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).

This is a preview of subscription content, log in to check access.

Author information

Correspondence to Xiadong Wu.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chen, D., Wu, X. Efficient Algorithms for k-Terminal Cuts on Planar Graphs. Algorithmica 38, 299–316 (2004). https://doi.org/10.1007/s00453-003-1061-2

Download citation


  • Planar Graph
  • Steiner Tree
  • Articulation Point
  • Minimum Steiner Tree
  • Extended Graph