An O (n3 (log log n/ log n)5/4) time algorithm for all pairs shortest paths

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

Volumn 4168 LNCS, Issue , 2006, Pages 411-417

  Han, Yijie ^a  

^a UNIVERSITY OF MISSOURI KANSAS CITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; MOTION PLANNING;

SHORTEST PATHS; TIME ALGORITHMS;

ALGORITHMS;

EID: 33750693389     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11841036_38     Document Type: Conference Paper

References (21)

1. A. V. Aho, J. E. Hopcroft, J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
2. A. V. Aho, J. E. Hopcroft, J. D. Ullman. Data Structures and Algorithms, Addison-Wesley, Reading, MA, 1983.
3. S. Albers, T. Hagerup. Improved parallel integer sorting without concurrent writing. Information and Computation 136, 25-51(1997).
4. K.E. Batcher. Sorting networks and their applications. Proc. 1968 AFIPS Spring Joint Summer Computer Conference, 307-314(1968).
5. 3/log n) time. Proc. 9th Workshop Algorithms Data Structures, Lecture Notes in Computer Science, Vol. 3608, Spriner-Verlag, 318-324(2005).
6. W. Dobosiewicz. A more efficient algorithm for min-plus multiplication. Inter. J. Comput. Math. 32, 49-60(1990).
7. M. L. Fredman. New bounds on the complexity of the shortest path problem. SIAM J. Computing 5, 83-89(1976).
8. M. L. Fredman, R. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34, 596-615, 1987.
9. Z. Galil, O. Margalit, All pairs shortest distances for graphs with small integer length edges. Information and Computation, 134, 103-139(1997).
10. Y. Han. Improved algorithms for all pairs shortest paths. Information Processing Letters, 91, 245-250(2004).
11. 3 / log n) time for all pairs shortest paths by using a smaller table. Proc. 21st Int. Conf. on Computers and Their Applications (CATA-2006), Seattle, Washington, 36-37(2006).
12. S. Pettie. A faster all-pairs shortest path algorithm for real-weighted sparse graphs. Proceedings of 29th International Colloquium on Automata, Languages, and Programming (ICALP'02), LNCS Vol. 2380, 85-97(2002).
13. S. Pettie, V. Ramachandran. A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput., Vol. 34, No. 6, 1398-1431(2005).
14. P. Sankowski. Shortest paths in matrix multiplication time. Proceedings of 13th Annual European Symposium on Algorithms. Lecture Notes in Computer Science 3669, 770-778(2005).
15. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. J. Comput. Syst. Sci., 51, 400-403(1995).
16. T. Takaoka. A new upper bound on the complexity of the all pairs shortest path problem. Information Processing Letters 43, 195-199(1992).
17. 3 log log n/ log n) time algorithm for the all-pairs shortest path problem. Information Processing Letters 96, 155-161(2005).
18. M. Thorup. Undirected single source shortest paths with positive integer weights in linear time. Journal of ACM, 46(3), 362-394(1999).
19. R. Yuster, U. Zwick. Answering distance queries in directed graphs using fast matrix multiplication. 46th Annual IEEE Symposium on Foundations of Computer Science . IEEE Comput. Soc. 2005, pp. 389-96. Los Alamitos, CA, USA.
20. U. Zwick. All pairs shortest paths using bridging sets and rectangular matrix multiplication. Journal of the ACM, vol.49, no.3, May 2002, pp. 289-317.
21. U. Zwick. A slightly improved sub-cubic algorithm for the all pairs shortest paths problem. Proceedings of ISAAC 2004, Lecture Notes in Computer Science, Vol. 3341, Springer, Berlin, 921-932(2004).