A space saving trick for directed dynamic transitive closure and shortest path algorithms

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

Volumn 2108, Issue , 2001, Pages 268-277

  King, Valerie ^a   Thorup, Mikkel ^a,b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

CONSTANT TIME; EDGE WEIGHTS; REACHABILITY; SHORTEST PATH; SHORTEST PATH ALGORITHMS; SPACE REDUCTIONS; SPACE SAVINGS; TRANSITIVE CLOSURE;

DIRECTED GRAPHS;

EID: 84944040679     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44679-6_30     Document Type: Conference Paper

References (13)

1. N. Alon, Z. Galil, O. Margalit, and M. Naor. Witnesses for boolean matrix multipli- cation and for shortest paths. In Proceedings of the 33rd IEEE Annual Symposium on Foundations of Computer Science, pages 417-426, 1992.
2. G. Brown and V. King. Space-efficent methods for maintaining shortest paths and transitive closure: Theory and practice, August 2000. Presentation at Workshop on Efficient Algorithms at Oberwolfach.
3. C. Demetrescu. Fully Dynamic Algorithms for Path Problems on Directed Graphs. PhD thesis, Dip. Informatica e Sistemistica Universita' di Roma \La Sapienza", 2000.
4. C. Demetrescu and G. Italiano.: Fully dynamic transitive closure: Breaking through the o(n 2) barrier. In Proc. 41st IEEE Symp. on Foundations of Computer Science, pages 381-389, 2000.
5. S. Even and Y. Shiloach.: An on-line edge-deletion problem. J. ACM, 28(1):1-4, 1981.
6. Bernard Fortz and Mikkel Thorup. Internet traffic engineering by optimizing OSPF weights. In Proc. 19th IEEE INFOCOM - The Conference on Computer Communications, pages 519-528, 2000.
7. D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single-source shortest path problem. ACM Jounal of Experimental Algorithmics, 3, article 5, 1998.
8. M. E. Furman. Application of a method of rapid multiplication of matrices to the problem of finding the transitive closure of a graph. Soviet Math. Dokl., 11(5):1250, 1970.
9. V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. 40th IEEE Symp. on Foundations of Com- puter Science, pages 81-89, 1999.
10. I. Munro. Efficient determination of the transitive closure of a directed graph. Information Processing Letters, 1(2):56-58, 1971.
11. G. Ramalingam and T. W. Reps. An incremental algorithm for a generalization of the shortest-path problem. Jounal of Algorithms, 21(2):267-305, 1996.
12. R. E. Tarjan.: Deep-first search and linear graph algorithms. SIAM J. Computing, 1:146-160, 1972.
13. U. Zwick. All pairs shortest paths in weighted directed graphs-exact and almost exact algorithms. In Proceedings of the 39rd IEEE Annual Symposium on Foundations of Computer Science, pages 310-319, 1998.