Single-source shortest-paths on arbitrary directed graphs in linear average-case time

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2001, Pages 797-806

  Meyer, Ulrich ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Algorithms; Theory; Verification

Indexed keywords

EID: 65549167819     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (27)

1. Ravindra K. Ahuja , Thomas L. Magnanti , James B. Orlin, Network flows: theory, algorithms, and applications, Prentice-Hall, Inc., Upper Saddle River, NJ, 1993
2. K. B. Athreya. Large deviation rates for branching processes - I, single type case. Annals of Applied Probability, 4(3):779-790, 1994.
3. R. Bellman. On a routing problem. Quart. Appl. Math., 16:87-90, 1958.
4. Boris V. Cherkassky , Andrew V. Goldberg , Tomasz Radzik, Shortest paths algorithms: theory and experimental evaluation, Mathematical Programming: Series A and B, v.73 n.2, p.129-174, May 31, 1996 [doi〉10.1007/BF02592101]
5. Colin Cooper , Alan Frieze , Kurt Mehlhorn , Volker Priebe, Average-case complexity of shortest-paths problems in the vertex-potential model, Random Structures & Algorithms, v.16 n.1, p.33-46, Jan.1.2000 [doi〉10.1002/ (SICI)1098-2418(200001)16:1〈33::AIDRSA3〉 3.0.CO;2-0]
6. E. V. Denardo and B. L. Fox. Shortest route methods: 1. reaching pruning and buckets. Operations Research, 27:161-186, 1979.
7. Robert B. Dial, Algorithm 360: shortest-path forest with topological ordering [H], Communications of the ACM, v.12 n.11, p.632-633, Nov. 1969 [doi〉10.1145/363269.363610]
8. E. W. Dijkstra. A note on two problems in connexion with graphs. Num. Math., 1:269-271, 1959.
9. E. A. Dinic. Economical algorithms for finding shortest paths in a network. In Transportation Modeling Systems, pages 36-44, 1978.
10. L. R. Ford and D. R. Fulkerson. Flows in Networks. Princeton Univ. Press, Princeton, N J, 1963.
11. Michael L. Fredman , Robert Endre Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms, Journal of the ACM (JACM), v.34 n.3, p.596-615, July 1987 [doi〉10.1145/28869.28874]
12. A. M. Frieze and G. R. Grimmett. The shortest-path problem for graphs with random arclengths. Discrete Applied Mathematics, 10:57-77, 1985.
13. A. V. Goldberg and R. E. Tarjan. Expected performance of Dijkstra's shortest path algorithm. Technical Report TR-96-062, NEC Research, 1996.
14. Torben Hagerup, Improved Shortest Paths on the Word RAM, Proceedings of the 27th International Colloquium on Automata, Languages and Programming, p.61-72, July 09-15, 2000
15. R. Hassin and E. Zemel. On shortest paths in graphs with random weights. Math. Oper. Res., 10(4):557-564, 1985.
16. C. McDiarmid. Concentration. In Michel Habib, Colin McDiarmid, Jorge Ramirez-Alfonsin, and Bruce Reed, editors, Probabilistic Methods for Algorithmic Discrete Mathematics, volume 16 of Algorithms Combin., pages 195 248. Springer, 1998.
17. Kurt Mehlhorn , Volker Priebe, On the all-pairs shortest-path algorithm of Moffat and Takaoka, Random Structures & Algorithms, v.10 n.1-2, p.205-220, Jan.-March 1997 [doi〉10.1002/(SICI)1098-2418(199701/03)10:1/ 2〈205::AID-RSA11〉3.0.CO;2-7]
18. Ulrich Meyer , Peter Sanders, Delta-Stepping: A Parallel Single Source Shortest Path Algorithm, Proceedings of the 6th Annual European Symposium on Algorithms, p.393-404, August 24-26, 1998
19. Alistair Moffat , Tadao Takaoka, An all pairs shortest path algorithm with expected time O (n2logn), SIAM Journal on Computing, v.16 n.6, p.1023-1031, December 1, 1987 [doi〉10.1137/0216065]
20. K. Noshita. A theorem on the expected complexity of Dijkstra's shortest path algorithm. Journal o} Algorithms, 6:400-408, 1985.
21. S. Pallottino. Shortest-path methods: Complexity, interrelations and new propositions. Networks, 14:257- 267, 1984.
22. Rajeev Raman, Priority Queues: Small, Monotone and Trans-dichotomous, Proceedings of the Fourth Annual European Symposium on Algorithms, p.121-137, September 25-27, 1996
23. Rajeev Raman, Recent results on the single-source shortest paths problem, ACM SIGACT News, v.28 n.2, p.81-87, June 1997 [doi〉10.1145/261342.261352]
24. P. M. Spira. A new algorithm for finding all shortest paths in a graph of positive arcs in average time O(n 2 log 2 n). SL4M Journal on Computing, 2:28-32, 1973.
25. Mikkel Thorup, Undirected single-source shortest paths with positive integer weights in linear time, Journal of the ACM (JACM), v.46 n.3, p.362-394, May 1999 [doi〉10.1145/316542.316548]
26. Mikkel Thorup, On RAM Priority Queues, SIAM Journal on Computing, v.30 n.1, p.86-109, 2000 [doi〉10.1137/S0097539795288246]
27. F. Benjamin Zhan , Charles E. Noon, Shortest Path Algorithms: An Evaluation Using Real Road Networks, Transportation Science, v.32 n.1, p.65-73, January 1998