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Efficient Algorithms for k-Terminal Cuts on Planar Graphs

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Book cover Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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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 minO n 2 log n log m, O(m 2 n 1.5 log2 n+kn) time algorithm with a (2 . 2k )-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(nk3 +(n log n)k2) 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.

This research was supported in part by the National Science Foundation under Grants CCR-9623585 and CCR-9988468.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame Notre Dame, 46556, IN, USA

    Danny Z. Chen & Xiaodong Wu

Authors
  1. Danny Z. Chen
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  2. Xiaodong Wu
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Wu, X. (2001). Efficient Algorithms for k-Terminal Cuts on Planar Graphs. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_29

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  • DOI: https://doi.org/10.1007/3-540-45678-3_29

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  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

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