Finding the k shortest paths in parallel
A concurrent-read exclusive-write PRAM algorithm is developed to find the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and m edges, using O(m + nk log2k) work and O(log3k log*k+ log n(log log k+ log*n)) time, assuming that a shortest path tree rooted at the destination is precomputed. The paths themselves can be extracted from the implicit representation in O(log k+log n) time, and O(n log n + L) work, where L is the total length of the output.
Topicsparallel algorithms data structures
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- 7.David Eppstein. Finding the k shortest paths. In Proc. 35th IEEE Symposium on Foundations of Computer Science, pages 154–165, 1994.Google Scholar
- 8.G. David Forney, Jr. The Viterbi algorithm. Proceedings of the IEEE, 61(3):268–278, March 1973.Google Scholar
- 9.B. L. Fox. Calculating kth shortest paths. INFOR; Canadian Journal of Operational Research, 11(1):66–70, 1973.Google Scholar
- 13.Y. Han, V. Pan, and J. Reif. Efficient parallel algorithms for computing all pair shortest paths in directed graphs. In 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 353–362, 1992.Google Scholar
- 15.Richard Karp and Vijaya Ramachandran. Parallel algorithms for shared-memory machines. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A, pages 871–941. Elsevier, 1990.Google Scholar
- 16.N. Katoh, T. Ibaraki, and H. Mine. An efficient algorithm for K shortest simple paths. Networks, 12:411–427, 1982.Google Scholar
- 17.Richard C. Paige and Clyde P. Kruskal. Parallel algorithms for shortest paths problems. In Proceedings of the International Conference on Parallel Processing, pages 14–20, 1985.Google Scholar
- 18.Margaret Reid-Miller, Gary L. Miller, and Francesmary Modugno. List ranking and parallel tree contraction. In John H. Reif, editor, Synthesis of Parallel Algorithms, chapter 3. Morgan Kaufmann, 1993.Google Scholar
- 19.Eric Ruppert. Parallel algorithms for the k shortest paths and related problems. Master's thesis, University of Toronto, 1996.Google Scholar
- 21.Frank K. Soong and Eng-Fong Huang. A tree-trellis based fast search for finding the N best sentence hypotheses in continuous speech recognition. In Proceedings of the International Conference on Acoustics, Speech and Signal Processing, volume 1, pages 705–708, 1991.Google Scholar
- 22.Uzi Vishkin. An optimal parallel algorithm for selection. In Advances in Computing Research, volume 4, pages 79–86. JAI Press, 1987.Google Scholar
- 23.Jin Y. Yen. Finding the K shortest loopless paths. Management Science, 17(11):712–716, July 1971.Google Scholar