An NC algorithm for minimum cuts

SIAM Journal on Computing

Volumn 26, Issue 1, 1997, Pages 255-272

  Karger, David R ^a,b   Motwant, Rajeev ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c Stanford University   (United States)

Author keywords

Connectivity certificate; Derandomization; Edge connectivity; Minimum cut; Multiway cut; Parallel alogorithms; Randomized algorithms

Indexed keywords

EID: 0002960637     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794273083     Document Type: Article

References (34)

1. A. AGGARWAL AND R. J. ANDERSON, A random NC algorithm for depth first search, Combinatorica, 8 (1988), pp. 1-12.
2. M. AJTAI, J. KOMLÓS, AND E. SZEMERÉDI, Deterministic simulation in logspace, in Proc. 19th ACM Symposium on Theory of Computing, ACM, New York, 1987, pp. 132-140.
3. D. APPLEGATE, AT&T Bell Labs, Murray Hill, NJ, personal communication, 1992.
4. M. BELLARE, O. GOLDREICH, AND S. GOLDWASSER, Randomness in interactive proofs, Comput. Complexity, 3 (1993), pp. 319-354; abstract in Proc. 31st Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 563-572.
5. M. BELLARE, O. GOLDREICH, AND S. GOLDWASSER, Randomness in interactive proofs, Comput. Complexity, 3 (1993), pp. 319-354; abstract in Proc. 31st Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 563-572.
6. R. A. BOTAFOGO, Cluster analysis for hypertext systems, in Proc. 16th Annual International ACM Conference on Research and Development in Information Retrieval (SIGIR), ACM, New York, 1993, pp. 116-125.
7. J. CHERIYAN, M. Y. KAO, AND R. THURIMELLA, Scan-first search and sparse certificates: An improved parallel algorithm for k-vertex connectivity, SIAM J. Comput., 22 (1993), pp. 157-174.
8. B. CHOR AND O. GOLDREICH, On the power of two-point sampling, J. Complexity, 5 (1989), pp. 96-106.
9. A. COHEN AND A. WIGDERSON, Dispersers, deterministic amplification, and weak random sources, in Proc. 30th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp 14-19.
10. C. J. COLBOURN, The Combinatorics of Network Reliability, International Series of Monographs on Computer Science, Vol. 4. Oxford University Press, Oxford, UK, 1987.
11. E. A. DINITZ, A. V. KARZANOV, AND M. V. LOMONOSOV, On the structure of a family of minimum weighted cuts in a graph, in Studies in Discrete Optimization, A. A. Fridman, ed., Nauka, Moscow, 1976, pp. 290-306.
12. L. R. FORD, JR. AND D. R. FULKERSON, Maximal flow through a network, Canad. J. Math., 8 (1956), pp. 399-404.
13. L. R. FORD, JR. AND D. R. FULKERSON, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
14. O. GABBER AND Z. GALIL, Explicit construction of linear-sized superconcentrators, J. Comput. System Sci., 22 (1981), pp. 407-420.
15. L. M. GOLDSCHLAGER, R. A. SHAW, AND J. STAPLES, The maximum flow problem is logspace complete for P, Theoret. Comput. Sci., 21 (1982), pp. 105-111.
16. J. HAO AND J. B. ORLIN, A faster algorithm for finding the minimum cut in a directed graph, J. Algorithms, 17 (1994), pp. 424-446: preliminary version in Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Phialdelphia, 1992, pp. 165-174.
17. J. HAO AND J. B. ORLIN, A faster algorithm for finding the minimum cut in a directed graph, J. Algorithms, 17 (1994), pp. 424-446: preliminary version in Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Phialdelphia, 1992, pp. 165-174.
18. R. IMPAGLIAZZO AND D. ZUCKERMAN, How to recycle random bits, in Proc. 30th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1989, pp. 222-227.
19. A. ISRAELI AND Y. SHILOACH, An improved parallel algorithm for maximal matching, Inform. Process. Lett., 22 (1986), pp. 57-60.
20. D. R. KARGER, Global min-cuts in RNC and other ramifications of a simple mincut algorithm, in Proc. 4th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1993, pp. 21-30.
21. D. R. KARGER, Random sampling in graph optimization problems, Ph.D. thesis, Stanford University, Stanford, CA, 1994; contact author at (karger@lcs.mit.edu); available by ftp from (theory.lcs.mit.edu), directory (pub/karger).
22. D. R. KARGER, Using randomized sparsification to approximate minimum cuts, in Proc. 5th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1994, pp. 424-432.
23. D. R. KARGER, A randomized fully polynomial approximation scheme for the all terminal networks reliability problem, in Proc. 27th ACM Symposium on Theory of Computing, ACM, New York, 1995, pp. 11-17.
24. D. R. KARGER AND R. MOTWANI, Derandomization through approximation: An NC algorithm for minimum cuts, in Proc. 25th ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 497-606.
25. 2) algorithm for minimum cuts, Proc. 25th ACM Symposium on Theory of Computing, ACM, New York, 1993, pp. 757-765.
26. R. M. KARP, E. UPFAL, AND A. WIGDERSON, Constructing a perfect matching is in random NC, Combinatorica, 6 (1986), pp. 35-48.
27. M. G. LUBY, A simple parallel algorithm for the maximal independent set problem, SIAM J. Comput., 15 (1986), pp. 1096-1063.
28. M. G. LUBY, J. NAOR, AND M. NAOR, On removing randomness from a parallel algorithm for minimum cuts, Technical report TR-093-007, International Computer Science Institute, Berkeley, CA, 1993.
29. D. W. MATULA, A linear time 2 + ∈ approximation for edge connectivity, in Proc. 4th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1993, pp. 500-504.
30. R. MOTWANI AND P. RAGHAVAN, Randomized Algorithms, Cambridge University Press, New York, 1995.
31. K. MULMULEY, U. V. VAZIRANI, AND V. V. VAZIRANI, Matching is as easy as matrix inversion, Combinatorica, 7 (1987), pp. 105-113.
32. H. NAGAMOCHI AND T. IBARAKI, Computer edge connectivity in multigraphs and capacitated graphs, SIAM J. Discrete Math., 5 (1992), pp. 54-66.
33. M. PADBERG AND G. RINALDI, An efficient algorithm for the minimum capacity cut problem, Math. Programming, 47 (1990), pp 19-39.
34. J. C. PICARD AND M. QUEYRANNE, Selected applications of minimum cuts in networks, INFOR: Canad. J. Oper. Res. Inform. Process., 20 (1982), pp. 394-422.