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Abstract: We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence... (Update)
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BibTeX entry: (Update)
David Eppstein, "Finding the k shortest paths", Proc. 35 th Symp. Foundations of Computer Science, IEEE, pp.154-165, 1994. http://citeseer.ist.psu.edu/eppstein97finding.html More
@inproceedings{ eppstein94finding,
author = "David Eppstein",
title = "Finding the k Shortest Paths",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "154-165",
year = "1994",
url = "citeseer.ist.psu.edu/eppstein97finding.html" }
Citations (may not include all citations):353 Fibonacci heaps and their uses in improved network optimizat.. (context) - Fredman, Tarjan - 1987
101 Sparsification -- A technique for speeding up dynamic graph .. (context) - Eppstein, Galil et al. - 1992
97 Trans-dichotomous algorithms for minimum spanning trees and .. (context) - Fredman, Willard - 1990
83 Princeton Univ (context) - Ford, Fulkerson et al. - 1962
72 a routing problem (context) - Bellman - 1958
63 Faster algorithms for the shortest path problem (context) - Ahuja, Mehlhorn et al. - 1990
54 Ambivalent data structures for dynamic 2-edge-connectivity a.. - Frederickson - 1991
51 Disjoint paths in a network (context) - Suurballe - 1974
39 Faster shortest-path algorithms for planar graphs - Klein, Rao et al. - 1994
33 shortest loopless paths in a network (context) - Yen - 1971
32 A priority queue in which initialization and queue operation.. (context) - Johnson - 1982
26 Scaling algorithms for the shortest paths problem (context) - Goldberg - 1995
26 An appraisal of some shortest path algorithms (context) - Dreyfus - 1969
23 best solutions to discrete optimization problems and its app.. (context) - Lawler, for et al. - 1972
18 shortest simple paths (context) - Katoh, Ibaraki et al. - 1982
15 Computers and Operations Research (context) - Chen, for et al. - 1993
13 shortest paths in a network (context) - Shier, for - 1979
13 Algorithms for proximity problems in higher dimensions - Dickerson, Eppstein - 1996
13 Algorithms for the quickest path problem and the enumeration.. (context) - Rosen, Sun et al. - 1991
11 On near-optimal alignments of biological sequences (context) - Naor, Brutlag - 1994
11 An optimal algorithm for selection in a min-heap (context) - Frederickson - 1993
10 Finding two disjoint paths between two pairs of vertices in .. (context) - Perl, Shiloach - 1978
10 Finding a minimum weight K -link path in graphs with Monge p.. (context) - Aggarwal, Schieber et al. - 1993
10 Information and Computer Science (context) - Eppstein, Galil et al. - 1993
9 Information Processing Letters (context) - Chen, simple et al. - 1994
9 An algorithm for the ranking of shortest paths (context) - Azevedo, Costa et al. - 1993
9 An algorithm for ranking paths that may contain cycles (context) - Martins - 1984
8 On finding single-source single-destination k shortest paths (context) - Chong, Maddila et al. - 1995
8 shortest loopless paths (context) - Perko, algorithms - 1986
7 Determining all optimal and near-optimal solutions when solv.. (context) - Byers, Waterman - 1984
7 Iterative methods for determining the k shortest paths in a .. (context) - Shier - 1976
7 Another algorithm for finding the K shortest-loopless networ.. (context) - Yen - 1972
5 Enumerating suboptimal alignments of multiple biological seq.. - Shibuya, Imai - 1997
4 Mathematica in Education and Research (context) - Eppstein, for - 1995
4 New flexible approaches for multiple sequence alignment (context) - Shibuya, Imai - 1997
4 th shortest paths and applications to the probabilistic netw.. (context) - Fox - 1975
4 On computing sets of shortest paths in a graph (context) - Minieka - 1974
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3 Mathematics and Its Applications (context) - Minieka, Shier et al. - 1973
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3 Unification-based glossing - Hatzivassiloglou, Knight - 1995
3 Algorithms for the constrained quickest path problem and the.. (context) - Chen, Hung - 1994
3 A binary enumeration tree to find K shortest paths (context) - Carraresi, Sodini - 1983
3 How to treat delete requests in semi-online problems (context) - Dai, Imai et al. - 1993
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3 Semirings and path spaces (context) - Wongseelashote - 1979
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3 Mathematische Operationsforschung und Statistik (context) - Bako, in et al. - 1976
2 shortest paths in a graph (context) - Lawler, computing - 1977
2 shortest simple paths in an undirected graph with nonnegativ.. (context) - Katoh, Ibaraki et al. - 1978
2 An expert system for transmission line route selection (context) - Al-Ghamdi - 1993
2 shortest loopless paths in a directed network (context) - Sugimoto, Katoh et al. - 1985
2 A method for selecting the shortest path of a network (context) - Thumer - 1975
2 Finding common ancestors and disjoint paths in DAGs - Eppstein - 1995
2 Parallel algorithm for finding first K shortest paths (context) - Kumar, Ghosh - 1994
2 th shortest path by matrix method (context) - Bako, Kas et al. - 1977
2 th shortest path problem (context) - Minieka - 1975
2 A new algorithm for the solution of the k-th best route prob.. (context) - Weigand - 1976
2 least cost paths in an acyclic activity network (context) - Horne - 1980
2 An electrical method for finding suboptimal routes (context) - Jin, Chan - 1989
1 TIMS Joint National Mtg (context) - Shier, finding et al. - 1976
1 shortest paths by AI search techniques (context) - Shibuya - 1995
1 Using simulated annealing to solve the K -shortest path prob.. (context) - Consiglio, Pecorella - 1995
1 ath algorithms. Proc. 11th UK Performance Engineering Worksh (context) - Brander, Sinclair et al. - 1995
1 Sequence alignments in the neighborhood of the optimum (context) - Waterman - 1983
1 Numerical Mathematics and Computing (context) - Law, Rezazadeh et al. - 1993
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