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Improved parallel depth-first search in undirected planar graphs

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Algorithms and Data Structures (WADS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

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Abstract

We present an improved parallel algorithm for constructing a depth-first search tree in a connected undirected planar graph. The algorithm runs in O(log2 n) time with n/log n processors for an n-vertex graph. It hinges on the use of a new optimal algorithm for computing a cycle separator of an embedded planar graph in O(log n) time with n/log n processors. The best previous algorithms for computing depth-first search trees and cycle separators achieved the same time complexities, but with n processors. Our algorithms run on a parallel random access machine that permits concurrent reads and concurrent writes in its shared memory and allows an arbitrary processor to succeed in case of a write conflict.

Supported in part by NSF Grant CCR-9101385.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Duke University, 27706, Durham, NC

    Ming-Yang Kao

  2. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA

    Shang-Hua Teng

  3. Department of Computer Science, Yale University, 06520, New Haven, CT

    Kentaro Toyama

Authors
  1. Ming-Yang Kao
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  2. Shang-Hua Teng
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  3. Kentaro Toyama
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Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

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© 1993 Springer-Verlag Berlin Heidelberg

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Kao, MY., Teng, SH., Toyama, K. (1993). Improved parallel depth-first search in undirected planar graphs. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_266

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  • DOI: https://doi.org/10.1007/3-540-57155-8_266

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57155-1

  • Online ISBN: 978-3-540-47918-5

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