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Δ-Stepping : A Parallel Single Source Shortest Path Algorithm

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Algorithms — ESA’ 98 (ESA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

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Abstract

In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial’s algorithm and the Bellman-Ford algorithm, improves this situation at least in the following “average-case” sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time \( \mathcal{O} \)(log3 n/log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Ulrich Meyer & Peter Sanders

Authors
  1. Ulrich Meyer
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  2. Peter Sanders
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

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© 1998 Springer-Verlag Berlin Heidelberg

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Meyer, U., Sanders, P. (1998). Δ-Stepping : A Parallel Single Source Shortest Path Algorithm. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_33

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  • DOI: https://doi.org/10.1007/3-540-68530-8_33

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  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

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