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European Symposium on Algorithms

ESA 2010: Algorithms – ESA 2010 pp 100–111Cite as

Shortest Cut Graph of a Surface with Prescribed Vertex Set

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6347))

Abstract

We describe a simple greedy algorithm whose input is a set P of vertices on a combinatorial surface \(\mathcal{S}\) without boundary and that computes a shortest cut graph of \(\mathcal{S}\) with vertex set P. (A cut graph is an embedded graph whose removal leaves a single topological disk.) If \(\mathcal{S}\) has genus g and complexity n, the running-time is O(nlogn + (g + |P|)n).

This is an extension of an algorithm by Erickson and Whittlesey [Proc. ACM-SIAM Symp. on Discrete Algorithms, 1038–1046 (2005)], which computes a shortest cut graph with a single given vertex. Moreover, our proof is simpler and also reveals that the algorithm actually computes a minimum-weight basis of some matroid.

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Author information

Authors and Affiliations

  1. Laboratoire d’informatique, École normale supérieure, CNRS, Paris, France

    Éric Colin de Verdière

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  1. Éric Colin de Verdière
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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de Verdière, É.C. (2010). Shortest Cut Graph of a Surface with Prescribed Vertex Set. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15781-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-15781-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15780-6

  • Online ISBN: 978-3-642-15781-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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