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International Symposium on Algorithms and Computation

ISAAC 2009: Algorithms and Computation pp 244–254Cite as

Computing the Map of Geometric Minimal Cuts

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

Abstract

In this paper we consider the problem of computing a map of geometric minimal cuts (called MGMC problem) induced by a planar rectilinear embedding of a subgraph H = (V H , E H ) of an input graph G. We first show that unlike the classic min-cut problem on graphs, the number of all rectilinear geometric minimal cuts is bounded by a low polynomial, O(n 3). Our algorithm for identifying geometric minimum cuts runs in O(n 3 logn (loglogn)3) time in the worst case which can be reduced to O(n logn (loglogn)3) when the maximum size of the cut is bounded by a constant, where n = |V H |. Once geometric minimal cuts are identified we show that the problem can be reduced to computing the L  ∞  Hausdorff Voronoi diagram of axis aligned rectangles. We present the first output-sensitive algorithm to compute this diagram which runs in O((N + K)log2 N loglogN) time and O(Nlog2 N) space, where N is the number of rectangles and K is the complexity of the diagram.

The research of the first two authors was supported in part by NSF through a CAREER Award CCF-0546509 and a grant IIS-0713489. The research of the third author was supported in part by an SNF project 200021_127137 and partially performed while affiliating with the IBM T.J. Watson Research center, Yorktown Heights, NY, USA, and the Athens University of Economics and Business, Greece.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA

    Jinhui Xu & Lei Xu

  2. Faculty of Informatics, Università della Svizzera italiana, Via Giuseppe Buffi 13, CH 6904, Lugano, Switzerland

    Evanthia Papadopoulou

Authors
  1. Jinhui Xu
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  2. Lei Xu
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  3. Evanthia Papadopoulou
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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© 2009 Springer-Verlag Berlin Heidelberg

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Xu, J., Xu, L., Papadopoulou, E. (2009). Computing the Map of Geometric Minimal Cuts. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_26

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  • DOI: https://doi.org/10.1007/978-3-642-10631-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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