Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 06-08-January-2002, Issue , 2002, Pages 713-722

  Pettie, Seth ^a   Ramachandran, Vijaya ^a  

^a University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES; SENSITIVITY ANALYSIS; TELECOMMUNICATION NETWORKS;

CONNECTED COMPONENT; EXPONENTIAL NUMBERS; MINIMUM SPANNING TREE PROBLEM; MINIMUM SPANNING TREES; NON-UNIFORM; RANDOMIZED ALGORITHMS; SHORTEST PATH TREE; SPANNING TREE;

ALGORITHMS;

EID: 84968750748     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (50)

1. [ABI86] N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms, 7:567-583, 1986.
2. [Bac91] B. Bach. Realistic analysis of some randomized algorithms. J. of Comput. and Syst. Sci., 42:30-53, 1991.
3. [BNMN92] Amotz Bar-Noy, Rajeev Motwani, and Joseph Naor. A linear time approach to the set maxima problem. SIAM J. on Discrete Math., 5(1):1-9, 1992.
4. [BR91] Bonnie Berger and John Rompel. Simulating (logcn)-wise independence in NC. J. of the ACM, 38(4):1026-1046, 1991.
5. [CG89] Benny Chor and Oded Goldreich. On the power of two-point based sampling. Journal of Complexity, 5(1):96-106, 1989.
6. [ChaOOa] B. Ghazelle. A minimum spanning tree slgorithm with inverse-ackermann type complexity. J. of the ACM, 47(6) :1028-1047, 2000.
7. [ChaOOb] B. Chazelle. The soft heap: an approximate priority queue with optimal error rate. J. of the ACM, 47(6):1012-1027, 2000.
8. [ChaOOc] Bernard Chazelle. The Discrepancy Method. Cambridge University Press, 2000.
9. [CHL99] Ka Wong Chong, Yijie Han, and Tak Wah Lam. On the parallel time complexity of undirected connectivity and minimum spanning trees. In Proc. SODA '99, pages 225-234, 1999.
10. [CKT96] Richard Cole, Philip N. Klein, and Robert E. Tarjan. Finding minimum spanning forests in logarithmic time and linear work using random sampling. In Proc. SPAA '96, pages 243-250, 1996.
11. [CLR90] Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Mass., 1990.
12. [CM89] W. Cunto and J. I. Munro. Average case selection. J. of the ACM, 36(2):270-279, 1989.
13. [CRSOO] Chari, Rohatgi, and Srinivasan A. Improved algorithms via approximations of probability distributions. J. of Comput. and Syst. Sci., 61, 2000.
14. [CV91] Richard Cole and Uzi Vishkin. Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms. Information and Computation, 92(1):l-47, May 1991.
15. [DRT92] B. Dixon, U. Rauch, and R. E. Tarjan. Verification and sensitivity analysis of minimum spanning trees in linear time. SICOMP, 21(6):1184-1192, 1992.
16. [DZ99] D. Dor and U. Zwick. Selecting the median. SICOMP, 28(5):1722-1758, 1999.
17. [DZ01] D. Dor and U. Zwick. Median selection requires (2+e)n comparisons. SIAM J. Discr. Math., 14(3):312-325, 2001.
18. [EGL+98] Even, Goldreich, Luby, Nisan, and Velickovic. Efficient approximation of product distributions. J. Random Struct. Alg., 13, 1998.
19. [FLW92] A. M. Ferrenberg, D. F. Landau, and Y. J. Wong. Monte Carlo simulations: Hidden errors from "good" random number generators. Physical Review Letters, 69(23) :3382-3388, 1992.
20. [FR75] Robert W. Floyd and Ronald L. Rivest. Expected time bounds for selection. CACM, 18(3):165-172, 1975.
21. [FT87] M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithm. J. of the ACM, 34(3):596-615, 1987.
22. [Gaz91] Hillel Gazit. An optimal randomized parallel algorithm for finding connected components in a graph. SIAM J. on Comput., 20(6):1046-1067, 1991.
23. [GKKS93] W. Goddard, C. Kenyon, V. King, and L. Schul-man. Optimal randomized algorithms for local sorting and set-maxima. SICOMP, 22(2):272-283, 1993.
24. [GMR99] P. B. Gibbons, Y. Matias, and V. Ramachandran. Can a shared-memory model serve as a bridging model for parallel computation? Theory of Computing Systems, 32:327-359, 1999.
25. [GYY80] R. L. Graham, A. C. Yao, and F. F. Yao. Information bounds are weak in the shortest distance problem. JACM, 27(3):428-444, 1980.
26. [Hoa61] C. A. R. Hoare. Algorithm 63 (partition) and algorithm 65 (find). CACM, 4(7):321-322, 1961.
27. [HR96] T-s Hsu and Vijaya Ramachandran. Efficient massively parallel implementation of some combinatorial algorithms. Theor. Comp. Sci., 162(2):297-322, 1996.
28. [HZ96] S. Halperin and U-Zwick. An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM. J. Comput. Syst. Sci., 53(3):395-416, 1996.
29. [HZ01] S. Halperin and U. Zwick. Optimal randomized EREW PRAM algorithms for finding spanning forests. J. of Algorithms, 39, 2001.
30. [Jof74] A. Joffe. On a set of almost deterministic k-independent random variables. Ann. Probability, 2(1):161-162, 1974.
31. [Kar93] D. R. Karger. Random sampling in matroids, with applications to graph connectivity and minimum spanning trees. In Proc. FOCS'93, pages 84-93, 1993.
32. [Kin97] V. King. A simpler minimum spanning tree verification algorithm. Aigorithmica, 18(2)-.263-270, 1997.
33. [KKT95] D. Karger, P. N. Klein, and R. E. Tarjan. A randomized linear-time algorithm for finding minimum spanning trees. JACM, 42:321-329, 1995.
34. [Kom85] J. Komlos. Linear verification for spanning trees. Combinatorica, 5(1):57-65, 1985.
35. [KPRS97] Valerie King, Chung Keung Poon, Vijaya Ramachandran, and Santanu Sinha. An optimal EREW PRAM algorithm for minimum spanning tree verification. Info. Proc. Lett., 62(3):153-159, 1997.
36. [KR92] R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Computer Science. MIT Press/Elsevier, 1992.
37. [KR93] Howard J. Karloff and Prabhakar Raghavan. Randomized algorithms and pseudorandom numbers. J. of the ACM, 40(3):454-476, 1993.
38. [KS01] Adam R. Klivans and Daniel A. Spielman. Randomness efficient identity testing of multivariate polynomials. In Proc. STOC'01, page ?, 2001.
39. [KW85] R. M. Karp and A. Wigderson. A fast parallel algorithm for the maximal independent set problem. J. of the ACM, 32(4):762-773, 1985.
40. [Lib98] Vincenzo Liberatore. Matroid decomposition methods for the set maxima problem. In Proc. SO DA'98, pages 400-409, 25-27 January 1998.
41. [Lub86] Michael Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. on Comput., 15(4):1036-1053, 1986.
42. [Lub93] Michael Luby. Removing randomness in parallel computation without a processor penalty. J. of Comput. and Syst. Sci., 47(2):250-286, 1993.
43. [NN93] Joseph Naor and Moni Naor. Small-bias probability spaces: Efficient constructions and applications. SIAM J. on Comput., 22(4):838-856, 1993.
44. [PR99] S. Pettie and V. Ramachandran. A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. Proc. RANDOM'99, LNCS Series, 1671:233-244, 1999.
45. [PR00] S. Pettie and V. Ramachandran. An optimal minimum spanning tree algorithm. Proc. ICALP'00, LNCS Series, 1853:49-60, 2000.
46. [PR01] S. Pettie and V. Ramachandran. Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms. Technical Report CS-TR-01-25, University of Texas-Austin, 2001.
47. [Rab80] M. O. Rabin. Probabilistic algorithm for testing primality. J. Number Theory, 12(1):128-138, 1980.
48. [SSS95] J. P. Schmidt, A. Siegel, and A. Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. SIAM J. on Discrete Math., 8(2):223-250, 1995.
49. [Tar82] R. E. Tarjan. Sensitivity analysis of minimum spanning trees and shortest path problems (see also corrigendum ipl 14(1), pp. 30-33). Info. Proc. Lett., 14(1):30-33, 1982.
50. [Val90] L. G. Valiant. A bridging model for parallel computation. CACM, 33(8):103-111, 1990.