Fast estimation of diameter and shortest paths (without matrix multiplication)

SIAM Journal on Computing

Volumn 28, Issue 4, 1999, Pages 1167-1181

  Aingworth, D ^a   Chekuri, C ^a   Indyk, P ^a   Motwani, R ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTATIONAL METHODS; GRAPH THEORY; OPTIMIZATION; PROBLEM SOLVING;

ALL PAIRS SHORTEST PATHS PROBLEM; BREADTH FIRST SEARCHES; FAST ESTIMATION; MATRIX MULTIPLICATION;

ALGORITHMS;

EID: 0032657365     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539796303421     Document Type: Article

References (17)

1. B. AWERBUCH, B. BERGER, L. COWEN, AND D. PELEG, Near-linear cost sequential and distributed constructions of sparse neighborhood covers, in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science, Palo Alto, CA, 1993, pp. 638-647.
2. N. ALON, Z. GALIL, AND O. MARGALIT, On the exponent of the all pairs shortest path problem, in Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, San Juan, PR, 1991, pp. 569-575.
3. N. ALON, Z. GALIL, O. MARGALIT, AND M. NAOR, Witnesses for Boolean matrix multiplication and for shortest paths, in Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, 1992, pp. 417-426.
4. J. BASCH, S. KHANNA, AND R. MOTWANI, On Diameter Verification and Boolean Matrix Multiplication, Report STAN-CS-95-1544, Department of Computer Science, Stanford University, Stanford, CA, 1995.
5. B. BOLLOBÁS, Random Graphs. Academic Press, New York, 1985.
6. FAN R. K. CHUNG, Diameters of graphs: Old problems and new results, Congr. Numer., 60 (1987), pp. 295-317.
7. E. COHEN, Fast algorithms fort-spanners and stretch-t paths, in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science, 1993, pp. 648-658.
8. E. COHEN, Polylog-time and near-linear work approximation scheme for undirected shortest paths, Proceedings of 26th Annual ACM Symposium on Theory of Computing, 1994, pp. 16-26.
9. D. COPPERSMITH AND S. WINOGRAD, Matrix multiplication via arithmetic progressions, J. Symbolic Comput., 9 (1990), pp. 251-280.
10. T. CORMEN, C. E. LEISERSON, AND R. L. RIVEST, Introduction to Algorithms, MIT Press and McGraw-Hill, New York, 1990.
11. D. DOR, S. HALPERIN, AND U. ZWICK, All pairs almost shortest paths, in Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, Burlington, VT, 1996, pp. 452-461.
12. T. FEDER AND R. MOTWANI. Clique partitions, graph compression and speeding-up algorithms, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 1991, pp. 123-133.
13. D. S. JOHNSON, Approximation algorithms for combinatorial problems, J. Comput. System Sci., 9 (1974), pp. 256-278.
14. D. E. KNUTH, The Stanford GraphBase: A platform for combinatorial computing, Addison-Wesley, Reading, MA, 1993.
15. L. LOVÁSZ, On the ratio of optimal integral and fractional covers, Discrete Math., 13 (1975), pp. 383-390.
16. R. G. SEIDEL, On the all-pairs-shortest-path problem, in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, Victoria, BC, 1992, pp. 745-749.
17. V. STRASSEN, Gaussian elimination is not optimal, Numer. Math., 13 (1969), pp. 354-356.