Fast connected components algorithms for the EREW PRAM

SIAM Journal on Computing

Volumn 28, Issue 3, 1999, Pages 1021-1034

  Karger, David R ^a   Nisan, Noam ^b   Parnas, Michal ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Connected components; Graph algorithms; Parallel algorithms; Random walks

Indexed keywords

GRAPH THEORY; POLYNOMIALS; PROBLEM SOLVING; PROGRAM PROCESSORS; RANDOM ACCESS STORAGE;

CONNECTED COMPONENTS; GRAPH ALGORITHMS; RANDOM WALKS;

PARALLEL ALGORITHMS;

EID: 0032284176     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/s009753979325247x     Document Type: Article

References (25)

1. [AKL*79] R. ALELIUNAS, R. M. KARP, R. J. LIPTON, L. LOVASZ, AND C. RACKOFF, Random walks, universal traversal sequences and the complexity of maze problems, in Proc. 20th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Piscataway, NJ, 1979, pp. 218-223.
2. [AS87] B. AWERBUCH AND Y. SHILOACH, New connectivity and MSF algorithms for shuffle-exchange network and PRAM, IEEE Trans. Comput., C-36 (1987), pp. 1258-1263.
3. [BF93] G. BARNES AND U. FEIGE, Short random walks on graphs, in Proc. 25th ACM Symposium on Theory of Computing, San Diego, ACM Press, New York, 1993, pp. 728-737.
4. [BNS92] L. BABAI, N. NISAN, AND M. SZEGEDY, Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs, J. Comput. System Sci., 45 (1992), pp. 204-232.
5. [BR91] G. BARNES, AND W. L. RUZZO, Deterministic algorithms for undirected s-t connectivity using polynomial time and sublinear space, in Proc. 23rd ACM Symposium on Theory of Computing, New Orleans, ACM Press, New York, 1991, pp. 48-53.
6. [CDR86] S. COOK, C. DWORK, AND R. REISCHUK, Upper and lower bounds for parallel random access machines without simultaneous writes, SIAM J. Comput., 15 (1986), pp. 87-97.
7. [CL95] K. CHONG AND T. LAM, Finding connected components in O(log n log log n) time on the EREW PRAM, J. Algorithms, 18 (1995), pp. 378-402.
8. [CLC82] F. Y. CHIN, J. LAM, AND I. N. CHEN, Efficient parallel algorithms for some graph problems, in Comm. ACM, 25 (1982), pp. 659-665.
9. [Col88] R. COLE, Parallel merge-sort, SIAM J. Comput., 17 (1988), pp. 770-785.
10. [CV91] R. COLE AND U. VISHKIN, Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms, Inform, and Comput. (formerly Information and Control), 92 (1991), pp. 1-47.
11. [DKR94] M. DIETZFELBINGER, M. KUTYLOWSKI, AND R. REISCHUK, Exact lower time bounds for computing Boolean functions on CREW PRAMs, J. Comput. System Sci., 48 (1994), pp. 231-254; a preliminary version appeared in SPAA 1992.
12. [Gaz91] H. GAZIT, An optimal randomized parallel algorithm for finding the connected components of a graph, SIAM J. Comput., 20 (1991), pp. 1046-1067; a preliminary version appeared in FOCS 1986.
13. [HCS79] D. S. HIRSCHBERG, A. K. CHANDRA, AND D. V. SARWATE, Computing connected components on parallel computers, Comm. ACM, 22 (1979), pp. 461-464.
14. [HZ94] S. HALPERIN AND U. ZWICK, An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM, in Proc. 6th Annual ACM-SIAM Symposium on Parallel Algorithms and Architectures, ACM Press, New York, 1994, pp. 1-10.
15. [HZ6] S. HALPERIN AND U. ZWICK, Optimal randomized EREW PRAM algorithms for finding spanning forests and other basic graph connectivity problems, in Proc. 7th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM-SIAM, 1996, pp. 438-447.
16. 3/2 |V|) parallel time for the CREW PRAM, in Proc. 32nd Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Piscataway, NJ, 1991, pp. 688-697.
17. [JM92] D. B. JOHNSON AND P. METAXAS, A parallel algorithm for computing minimum spanning trees, in Proc. 4th Annual ACM Symposium on Parallel Algorithms and Architectures, ACM Press, 1992, pp. 363-372.
18. [KKT95] D. R. KARGER, P. N. KLEIN, AND R. E. TARJAN, A randomized linear-time algorithm to find minimum spanning trees, J. ACM, 42 (1995), pp. 321-328.
19. [KNP92] D. R. KARGER, N. NISAN, AND M. PARNAS, Fast connected components algorithms for the EREW PRAM, in Proc. 4th Annual ACM-SIAM Symposium on Parallel Algorithms and Architectures, 1992, pp. 562-572.
20. [KR90] R. M. KARP AND V. RAMACHANDRAN, Parallel algorithms for shared-memory machines, in Handbook of Theoretical Computer Science, Vol. A, Jan van Leeuwen, ed., MIT Press, Cambridge, MA, 1990, pp. 869-932.
21. [Lin] N. LINIAL, personal communication, 1992.
22. [Nis92] N. NISAN, Pseudorandom generators for space-bounded computation, in Combinatorica, 12 (1992), pp. 449-461; a preliminary version appeared in STOC 1990.
23. [Nis93] N. NISAN, On read-once vs. multiple access to randomness in logspace, Theoret. Comput. Sci., 107 (1993), pp. 135-144; a preliminary version appeared in Proc. 5th IEEE Structure in Complexity Theory Conference, 1990.
24. 1.5 n) space, in Proc. 33rd Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Piscataway, NJ, 1992, pp. 24-29.
25. [SV82] Y. SHILOACH AND U. VISHKIN, An O(log n) parallel connectivity algorithm, J. Algorithms, 3 (1982), pp. 57-67.