All-pairs bottleneck paths for general graphs in truly sub-cubic time

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 585-589

  Vassilevska, Virginia ^a   Williams, Ryan ^a   Yuster, Raphael ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF HAIFA   (Israel)

Author keywords

Bottleneck path; Matrix multiplication; Maximum capacity path; Subcubic

Indexed keywords

GRAPH THEORY; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING; REAL TIME SYSTEMS;

BOTTLENECK PATH; DENSE GRAPHS; MATRIX MULTIPLICATION; MAXIMUM CAPACITY PATH;

COMPUTATION THEORY;

EID: 35548966040     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250876     Document Type: Conference Paper

References (21)

1. A. V. Aho, J. E. Hopcroft, and J. Ullman. The Design and Analysis of Computer Algorithms, Addison- Wesley Longman Publishing Co., Boston, MA, 1974.
2. 3/log n) time. In Proc. Workshop on Algorithms and Data Struct., Springer-Verlag LNCS 3608:318-324, 2005.
3. T. M. Chan, More algorithms for all-pairs shortest paths in weighted graphs. To appear in Proc. of STOC, 2007.
4. D. Coppersmith, S. Winograd, Matrix multiplication via arithmetic progressions, J. Symbolic Computation 9(3):251-280, 1990.
5. D. Dubois and H. Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, 1980.
6. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. JACM 34(3):596-615, 1987.
7. Z. Galil and O. Margalit. All-pairs shortest paths for graphs with small integer length edges. JCSS 54:243-254, 1997.
8. 5/4) Time Algorithm for All Pairs Shortest Paths. In Proc. of ESA, Springer-Verlag LNCS 4168:411-417, 2006.
9. T. C. Hu. The Maximum Capacity Route Problem. Operations Research 9(6):898-900, 1961.
10. D. Karger, D. Koller, and S. Phillips. Finding the Hidden Path: Time Bounds for All-Pairs Shortest Paths. SIAM J. Computing 22(6):1199-1217, 1993.
11. M. Kowaluk and A. Lingas, LCA queries in directed acyclic graphs. In Proc. of ICALP, Springer-Verlag LNCS 3580:241-248, 2005.
12. n. Information Processing Letters 38(5):277-278, 1991.
13. M. Pollack. The Maximum Capacity Through a Network. Operations Research 8(5):733-736, 1960.
14. R. Seidel. On the all-pairs-shortest-path problem in unweighted undirected graphs. JCSS 51:400-403, 1995.
15. A. Shapira, R. Yuster and U. Zwick. All-Pairs Bottleneck Paths in Vertex Weighted Graphs. In Proc. of SODA, 978-985, 2007.
16. A. Shoshan and U. Zwick. All Pairs Shortest Paths in Undirected Graphs with Integer Weights. Proc. of FOCS, 605-614, 1999.
17. C. R. Subramanian. A generalization of Janson inequalities and its application to finding shortest paths. In Proc. of SODA, 795-804, 1999.
18. 3-δ time, with applications. In Proc. of STOC, 225-231, 2006.
19. V. Vassilevska, R. Williams, and R. Yuster. Finding the smallest H-subgraph in real weighted graphs and related problems. In Proc. of ICALP, Springer-Verlag LNCS 4051:262-273, 2006.
20. R. Yuster and U. Zwick. Fast sparse matrix multiplication. ACM Trans. on Algorithms 1(1):2-13, 2005.
21. Uri Zwick. All pairs shortest paths using bridging sets and rectangular matrix multiplication. JACM 49(3):289-317, 2002.