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Perfect Matching for Biconnected Cubic Graphs in O(n log2 n) Time

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SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5901))

Abstract

The main result of this paper is a new perfect matching algorithm for biconnected cubic graphs. The algorithm runs in time O(n log2 n). It is also possible, by applying randomized data structures, to get O(n logn loglog3 n) average time. Our solution improves the one given by T. Biedl et al. [3]. The algorithm of Biedl et al. runs in time O(n log4 n). We use a similar approach. However, thanks to exploring some properties of biconnected cubic graphs we are able to replace complex fully-dynamic biconnectivity data structure with much simpler, dynamic graph connectivity and dynamic tree data structures. Moreover, we present a significant modification of the new algorithm which makes application of a decremental dynamic graph connectivity data structure possible, instead of one supporting the fully dynamic graph connectivity. It gives hope for further improvements.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Krzysztof Diks & Piotr Stanczyk

Authors
  1. Krzysztof Diks
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  2. Piotr Stanczyk
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Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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Diks, K., Stanczyk, P. (2010). Perfect Matching for Biconnected Cubic Graphs in O(n log2 n) Time. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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