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An Optimal Parallel Algorithm for Minimum Spanning Trees in Planar Graphs

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Algorithms, Probability, Networks, and Games

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9295))

Abstract

We present an optimal deterministic O(n)-work parallel algorithm for finding a minimum spanning tree on an n-vertex planar graph. The algorithm runs in \(O(\log n)\) time on a CRCW PRAM and in \(O(\log n\log ^*n)\) time on an EREW PRAM. Our results hold for any sparse graph that is closed under taking of minors, as well as for a class of graphs with non-bounded genus.

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Acknowledgements

The last author is indebted to his mentor Paul Spirakis, who taught him by example to be a scientist and who uniquely affected the shaping of his career.

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Authors and Affiliations

  1. Department of Computer Science, The University of Hong-Kong, Porfulam Road, Porfulam, Hong Kong

    Ka Wong Chong

  2. Department of Computer Engineering and Informatics, University of Patras, 26504, Patras, Greece

    Christos Zaroliagis

  3. Computer Technology Institute and Press “Diophantus”, N. Kazantzaki Str., Patras University Campus, 26504, Patras, Greece

    Christos Zaroliagis

Authors
  1. Ka Wong Chong
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  2. Christos Zaroliagis
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Correspondence to Christos Zaroliagis .

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Editors and Affiliations

  1. University of Patras, Patras, Greece

    Christos Zaroliagis

  2. Technological Educational Institute of Athens, Athens, Greece

    Grammati Pantziou

  3. University of Ioannina, Ioannina, Greece

    Spyros Kontogiannis

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Chong, K.W., Zaroliagis, C. (2015). An Optimal Parallel Algorithm for Minimum Spanning Trees in Planar Graphs. In: Zaroliagis, C., Pantziou, G., Kontogiannis, S. (eds) Algorithms, Probability, Networks, and Games. Lecture Notes in Computer Science(), vol 9295. Springer, Cham. https://doi.org/10.1007/978-3-319-24024-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-24024-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24023-7

  • Online ISBN: 978-3-319-24024-4

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