On dynamic shortest paths problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3221, Issue , 2004, Pages 580-591

  Roditty, Liam ^a   Zwick, Uri ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIRECTED GRAPHS; TREES (MATHEMATICS);

ALL PAIRS SHORTEST PATHS; FULLY DYNAMIC ALGORITHMS; SIMPLE ALGORITHM; SINGLE-SOURCE SHORTEST PATHS; TIME ALGORITHMS; UNDIRECTED GRAPH; UNWEIGHTED GRAPHS; WEIGHTED UNDIRECTED GRAPH;

GRAPH THEORY;

EID: 35048837075     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30140-0_52     Document Type: Article

References (30)

1. I. Althöfer, G. Das, D. Dobkin, D. Joseph, and J. Soares. On sparse spanners of weighted graphs. Discrete & Computational Geometry, 9:81-100, 1993.
2. S. Baswana, R. Hariharan, and S. Sen. Improved decremental algorithms for transitive closure and all-pairs shortest paths. In Proc. of 34th STOC, pages 117-123, 2002.
3. S. Baswana, R. Hariharan, and S. Sen. Maintaining all-pairs approximate shortest paths under deletion of edges. In Proc. of 14th SODA, pages 394-403, 2003.
4. 1+1/k) size for weighted graphs. In Proc. of 30th ICALP, pages 384-296, 2003.
5. T. Chan. Dynamic subgraph connectivity with geometric applications. In Proc. of 34th STOC, pages 7-13, 2002.
6. B. Chandra, G. Das, G. Narasimhan, and J. Scares. New sparseness results on graph spanners. Internat. J. Comput. Geom. Appl., 5:125-144, 1995.
7. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9:251-280, 1990.
8. C. Demetrescu and G. Italiano. A new approach to dynamic all pairs shortest paths. In Proc. of 35th STOC, pages 159-166, 2003.
9. S. Even and Y. Shiloach. An on-line edge-deletion problem. Journal of the ACM, 28(1): 1-4, 1981.
10. M. Predman and R. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34:596-615, 1987.
11. Z. Galil and O. Margalit. All pairs shortest distances for graphs with small integer length edges. Information and Computation, 134:103-139, 1997.
12. J. Gudmundsson, C. Levcopoulos, and G. Narasimhan. Fast greedy algorithm for constructing sparse geometric spanners. SIAM J. Comput., 31:1479-1500, 2002.
13. T. Hagerup. Improved shortest paths on the word RAM. In Proc. of 27th ICALP, pages 61-72, 2000.
14. M. Henzinger and V. King. Fully dynamic biconnectivity and transitive closure. In Proc. of 36th FOCS, pages 664-672, 1995.
15. D. Karger, D. Koller, and S. Phillips. Finding the hidden path: time bounds for all-pairs shortest paths. SIAM Journal on Computing, 22:1199-1217, 1993.
16. D. Peleg and A. Schäffer. Graph spanners. J. Graph Theory, 13:99-116, 1989.
17. S. Pettie. A new approach to all-pairs shortest paths on real-weighted graphs. Theoretical Computer Science, 312(1):47-74, 2004.
18. S. Pettie and V. Ramachandran. Computing shortest paths with comparisons and additions. In Proc. of 13th SODA, pages 267-276, 2002.
19. G. Ramalingam and T. Reps. An incremental algorithm for a generalization of the shortest-path problem. Journal of Algorithms, 21(2):267-305, 1996.
20. L. Roditty and U. Zwick. Improved dynamic reachability algorithms for directed graphs. In Proc. of 43rd FOGS, pages 679-688, 2002.
21. L. Roditty and U. Zwick. A fully dynamic reachability algorithm for directed graphs with an almost linear update time. In Proc. of 36th STOC, pages 184-191, 2004.
22. L. Roditty and U. Zwick. Dynamic approximate all-pairs shortest paths in undirected graphs. In Proc. of 45th FOCS, 2004. To appear.
23. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci., 51:400-403, 1995.
24. A. Shoshan and U. Zwick. All pairs shortest paths in undirected graphs with integer weights. In Proc. of 40th FOCS, pages 605-614, 1999.
25. M. Thorup. Undirected single-source shortest paths with positive integer weights in linear time. Journal of the ACM, 46:362-394, 1999.
26. M. Thorup. Fully-dynamic all-pairs shortest paths: Faster and allowing negative cycles. In Proc. of 9th SWAT, 2004. To appear.
27. M. Thorup and U. Zwick. Approximate distance oracles. In Proc. of 33rd STOC, pages 183-192, 2001.
28. Full version to appear in the Journal of the ACM.
29. J. Ullman and M. Yannakakis. High-probability parallel transitive-closure algorithms. SIAM Journal on Computing, 20:100-125, 1991.
30. R. Yuster and U. Zwick. Fast sparse matrix multiplication. In Proc. of l2h ESA, 2004.