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A parallelization of Dijkstra's shortest path algorithm

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in [0,1]. We use the G (n, d/n) model: the graph consists of n nodes and each edge is chosen with probability d/n. Our PRAM algorithm needs O(n 1/3 log n) log n) time and O (n log n+dn) work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.

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Author information

Authors and Affiliations

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

    A. Crauser, K. Mehlhorn, U. Meyer & P. Sanders

Authors
  1. A. Crauser
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  2. K. Mehlhorn
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  3. U. Meyer
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  4. P. Sanders
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Crauser, A., Mehlhorn, K., Meyer, U., Sanders, P. (1998). A parallelization of Dijkstra's shortest path algorithm. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055823

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  • DOI: https://doi.org/10.1007/BFb0055823

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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