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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© 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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