Worst-case update times for fully-dynamic all-pairs shortest paths

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2005, Pages 112-119

  Thorup, Mikkel ^a  

^a AT AND T LABS RESEARCH   (United States)

Author keywords

Dynamic graph algorithms; Shortest paths; Worst case up date times

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; GRAPH THEORY; MATRIX ALGEBRA;

DYNAMIC GRAPH ALGORITHMS; SHORTEST PATHS; WORST-CASE UP-DATE TIMES;

PROBLEM SOLVING;

EID: 34848821960     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060607     Document Type: Conference Paper

References (28)

1. G. M. Ade'lson-Velskiǐ and E. M. Landis. An algorithm for the organization of information. Dokladi Akademia Nauk SSSR, 146(2):1259-1262, 1962.
2. R. Bellman. On a routing problem. Quart. Appl. Math., 16(1):87-90, 1958.
3. N. Blum. On the single-operation worst-case time complexity of the disjoint set union problem. SIAM J. Computing, 15(4):1021-1024, 1986.
4. G. S. Brodal, G. Lagogiannis, C. Makris, A. Tsakalidis, and Kostas Tsichlas. Optimal finger search trees in the pointer machine. J. Computer and System Sciences, 67(2):381-418, 2003.
5. 2) barrier. In Proc. 41st FOCS, pages 381-389, 2000.
6. C. Demetrescu and G. Italiano. A new approach to dynamic all pairs shortest paths. J. ACM, 51(6):968-992, 2004. Announced at STOC'03.
7. C. Demetrescu and M. Thorup. Oracles for distances avoiding a link-failure. In Proc. 13th SODA, pages 838-843, 2002.
8. E.W. Dijkstra. A note on two problems in connexion with graphs. Numer. Math., 1:269-271, 1959.
9. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification - a technique for speeding up dynamic graph algorithms. J. ACM, 44(5):669-696, 1997.
10. R.W. Floyd. Algorithm 97: Shortest path. Comm. ACM, 5(6):345, 1962.
11. L. R. Ford and D. R. Fulkerson. Flows in networks. Princeton University Press, 1962.
12. G. N. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Computing, 14(4):781-798, 1985.
13. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM, 34(3):596-615, 1987.
14. M.L, Fredman. New bounds on the complexity of the shortest path problem. SIAM J. Computing, 5(1):83-89, 1976.
15. M.L. Fredman and M.E. Saks. The cell probe complexity of dynamic data structures. In Proc. 21st STOC, pages 345-354, 1989.
16. H. N. Gabow. Efficiency of a good but not linear set union algorithm. J. ACM, 19(2):248-264, 1975.
17. M. R. Henzinger and V. King. Randomized dynamic graph algorithms with polylogarithmic time per operation. J. ACM, 46(502-536), 1999. Announced at STOC'95.
18. M. R. Henzinger and V. King. Maintaining minimum spanning forests in dynamic graphs. SIAM J. Computing, 31(2):364-374, 2001.
19. J. Holm, K. Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge and biconnectivity. J. ACM, 48(4):723-760, 2001.
20. V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. 40th FOCS, pages 81-89, 1999.
21. M. H. Overmars and C. Levcopoulos. A balanced search tree with O(1) worst-case update time. Acta Informatica, 26:269-277, 1988.
22. L. Roditty, A faster and simpler fully dynamic transitive closure. In Proc, 14th SODA, pages 404-412, 2003.
23. L. Roditty and U. Zwick. Dynamic approximate all-pairs shortest paths in undirected graphs. In Proc, 45th FOCS, pages 499-508, 2004.
24. P. Sankowski, Dynamic transitive closure via dynamic matrix inverse. In Proc. 45th FOCS, pages 509-517, 2004.
25. M. Thorup. Fully-dynamic all-pairs shortest paths: faster and allowing negative cycles. In Proc. 9th SWAT, pages 384-396, 2004.
26. S. Warshall. A theorem on boolean matrices. J. ACM, 9(1):11-12, 1962.
27. D. E. Willard and G. S. Lueker. Adding range restriction capability to dynamic data structures. J. ACM, 32(3):597-617, 1985.
28. J. W. J. Williams. Algorithm 232. Comm. ACM, 7(6):347-348, 1964.