Dynamic approximate all-pairs shortest paths in undirected graphs

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2004, Pages 499-508

  Roditty, Liam ^a   Zwick, Uri ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DECREMENTAL ALGORITHM; INITIAL GRAPH; SHORTEST PATHS; UNDIRECTED GRAPHS;

ALGORITHMS; APPROXIMATION THEORY; INTEGER PROGRAMMING; PARAMETER ESTIMATION; PROBLEM SOLVING; QUERY LANGUAGES;

GRAPH THEORY;

EID: 17744392469     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2004.22     Document Type: Conference Paper

References (30)

1. D. Aingworth, C. Chekuri, P. Indyk, and R. Motwani. Fast estimation of diameter and shortest paths (without matrix multiplication). SIAM Journal on Computing, 28:1167-1181, 1999.
2. G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. Incremental algorithms for minimal length paths. J. Algorithms, 12(4):615-638, 1991.
3. G. Ausiello, G.F. Italiano, A. Marchetti-Spaccamela, and U. Nanni. On-line computation of minimal and maximal length paths. Theoretical Computer Science, 95(2):245-261, 1992.
4. B. Awerbuch, B. Berger, L. Cowen, and D. Peleg. Near-linear time construction of sparse neighborhood covers. SIAM Journal on Computing, 28:263-277, 1999.
5. 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.
6. 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.
7. E. Cohen. Fast algorithms for constructing t-spanners and paths with stretch t. SIAM Journal on Computing, 28:210-236, 1999.
8. E. Cohen and U. Zwick. All-pairs small-stretch paths. Journal of Algorithms, 38:335-353, 2001.
9. T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein. Introduction to algorithms. The MIT Press, 2nd edition, 2001.
10. C. Demetrescu and G.F. Italiano. A new approach to dynamic all pairs shortest paths. In Proc. of 35th STOC, pages 159-166, 2003.
11. C. Demetrescu and G.F. Italiano. Experimental analysis of dynamic all pairs shortest path algorithms. In Proc. of 15th SODA, pages 362-371, 2004.
12. M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, and R.E. Tarjan. Dynamic perfect hashing: upper and lower bounds. SIAM Journal on Computing, 23(4):738-761, 1994.
13. D. Dor, S. Halperin, and U. Zwick. All pairs almost shortest paths. SIAM Journal on Computing, 29:1740-1759, 2000.
14. M. Elkin. Computing almost shortest paths. In Proc. of 20th PODC, pages 53-62, 2001.
15. M.L. Elkin and D. Peleg. (1 + ε, β)-Spanner constructions for general graphs. SIAM Journal on Computing, 33(3):608-631, 2004.
16. S. Even and Y. Shiloach. An on-line edge-deletion problem. Journal of the ACM, 28(1):1-4, 1981.
17. Z. Galil and O. Margalit. All pairs shortest paths for graphs with small integer length edges. Journal of Computer and System Sciences, 54:243-254, 1997.
18. M. Henzinger and V. King. Fully dynamic biconnectivity and transitive closure. In Proc. of 36th FOCS, pages 664-672, 1995.
19. V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. of 40th FOCS, pages 81-91, 1999.
20. R. Pagh and F.F. Rodler. Cuckoo hashing. Journal of Algorithms, 51(2):122-144, 2004.
21. L. Roditty and U. Zwick. Improved dynamic reachability algorithms for directed graphs. In Proc. of 43rd FOCS, pages 679-688, 2002.
22. 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.
23. L. Roditty and U. Zwick. On dynamic shortest paths problems. In Proc. of 12th ESA, 2004. To appear.
24. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. Journal of Computer and System Sciences, 51:400-403, 1995.
25. A. Shoshan and U. Zwick. All pairs shortest paths in undirected graphs with integer weights. In Proc. of 40th FOCS, pages 605-614, 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. Full version to appear in the Journal of the ACM.
28. M. Thorup and U. Zwick. Approximate distance oracles. In Proc. of 33rd STOC, pages 183-192, 2001. Full version to appear in the Journal of the ACM.
29. J.D. Ullman and M. Yannakakis. High-probability parallel transitive-closure algorithms. SIAM Journal on Computing, 20:100-125, 1991.
30. U. Zwick. All-pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, 49:289-317, 2002.