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Scandinavian Workshop on Algorithm Theory

SWAT 1990: SWAT 90 pp 288–300Cite as

Efficient parallel algorithms for shortest paths in planar graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 447))

Abstract

Efficient parallel algorithms are presented, on the CREW PRAM model, for generating a succinct encoding of all pairs shortest path information in a directed planar graph G with real-valued edge costs but no negative cycles. We assume that a planar embedding of G is given, together with a set of q faces that cover all the vertices. Then our algorithm runs in O(log2 n+log3 q) time and employs O(nq) processors. O(log2 n) time, n-processor algorithms are presented for various subproblems, including that of generating all pairs shortest path information in a directed outerplanar graph. Our work is based on the fundamental hammock-decomposition technique of G. Frederickson. We achieve this decomposition in O(log2 n) parallel time by using O(n) processors. The hammock-decomposition seems to be a fundamental operation that may help in improving efficiency of many parallel (and sequential) graph algorithms. Our algorithms avoid the matrix powering (sometimes called the transitive closure bottleneck) thus lead to a considerably smaller number of processors, and tighter processor-time products.

This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM) and by the Ministry of Industry, Energy and Technology of Greece.

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Authors and Affiliations

  1. Computer Technology Institute, P.O. Box 1122, 26110, Patras, Greece

    Grammati E. Pantziou, Paul G. Spirakis & Christos D. Zaroliagis

  2. Computer Sc and Eng Dept, University of Patras, Greece

    Grammati E. Pantziou, Paul G. Spirakis & Christos D. Zaroliagis

  3. Courant Institute of Math. Sciences, NYU, 10012, NY, USA

    Paul G. Spirakis

Authors
  1. Grammati E. Pantziou
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  2. Paul G. Spirakis
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  3. Christos D. Zaroliagis
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John R. Gilbert Rolf Karlsson

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© 1990 Springer-Verlag Berlin Heidelberg

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Pantziou, G.E., Spirakis, P.G., Zaroliagis, C.D. (1990). Efficient parallel algorithms for shortest paths in planar graphs. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_98

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  • DOI: https://doi.org/10.1007/3-540-52846-6_98

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52846-3

  • Online ISBN: 978-3-540-47164-6

  • eBook Packages: Springer Book Archive

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