A Faster Algorithm for the Single Source Shortest Path Problem with Few Distinct Positive Lengths
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https://public.me.com/orlin2
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Author(s)
Orlin, James B.
Madduri, Kamesh
Subramani, K.
Williamson, M.
Date Issued
June 2010
Journal
Journal of Discrete Algorithms
Publisher
Elsevier
Citation
James B. Orlin, Kamesh Madduri, K. Subramani, and M. Williamson. 2010. A faster algorithm for the single source shortest path problem with few distinct positive lengths. J. of Discrete Algorithms 8, 2 (June 2010), 189-198. DOI=10.1016/j.jda.2009.03.001 http://dx.doi.org/10.1016/j.jda.2009.03.001
Version
Author's final manuscript
Abstract
In this paper, we propose an efficient method for implementing Dijkstra's algorithm for the Single Source Shortest Path Problem (SSSPP) in a graph whose edges have positive length, and where there are few distinct edge lengths. The SSSPP is one of the most widely studied problems in theoretical computer science and operations research. On a graph with n vertices, m edges and K distinct edge lengths, our algorithm runs in O(m) time if nK=<2m, and O(mlognKm) time, otherwise. We tested our algorithm against some of the fastest algorithms for SSSPP on graphs with arbitrary but positive lengths. Our experiments on graphs with few edge lengths confirmed our theoretical results, as the proposed algorithm consistently dominated the other SSSPP algorithms, which did not exploit the special structure of having few distinct edge lengths.
MIT Department
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1016/j.jda.2009.03.001
