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An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM (extended abstract)

Authors:

Uri ZwickAuthors Info & Claims

SPAA '94: Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures

Pages 1 - 10

https://doi.org/10.1145/181014.181017

Published: 01 August 1994 Publication History

Abstract

Improving a long chain of works we obtain a randomized EREW PRAM algorithm for finding the connected components of a graph G=(V,E) with n vertices and m edges in O(log n) time using an optimal number of O((m+n)/log n) processors. The result returned by the algorithm is always correct. The probability that the algorithm will not complete in O(log n) time is at most n^-c for any desired c > 0.

The best deterministic EREW PRAM connectivity algorithm, obtained by Chong and Lam, runs in O(log n log log n) time using m + n processors.

References

[1]

R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovasz, and C. Rackoff. Random walks, universal sequences and the complexity of maze problems. In Proceedings of the 20th Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 218-223, 1979.

Digital Library

[2]

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for shuffle-exchange network and P RAM. IEEE Transactions on Computers, C-36:1258-1263, 1987.

Digital Library

[3]

N. Alon and J.H. Spencer. The probabilistic method. Wiley, 1992.

[4]

G. Barnes and U. Feige. Short random walks on graphs. In Proceedings of the 25rd Annual A CM Symposium on Theory of Computing, San Diego, California, pages 728-737, 1993.

Digital Library

[5]

S. Cook, C. Dwork, and R. Reischuk. Upper and lower bounds for parallel random access machines without simultaneous writes. SIAM Journal on Computing, 15:87-97, 1986.

Digital Library

[6]

K.W. Chong and T.W. Lam. Finding connected components in O(log n log log n) time on the EREW PRAM. In Proceedings of the 4th Annual A CM-SIAM Symposium on Discrete Algorithms, Austin, Texas, pages 11-20, 1993.

Digital Library

[7]

F.Y. Chin, J. Lam, and I.N. Chen. Efficient parallel algorithms for some graph problems. Communications o} the A CM, 25(9):659-665, 1982.

Digital Library

[8]

R. Cole and U. Vishkin. Approximate parallel scheduling. Part I: The basic technique with applications to optimal parallel list ranking in logarithmic time. SIAM Journal on Computing, 17(1):128-142, 1988.

Digital Library

[9]

R. Cole and U. Vishkin. Approximate parallel scheduling. Part iI: Applications to logarithmictime optimal graph algorithms. In}ormation and Computation, 92:1-47, 1991.

Digital Library

[10]

H. Gazit. An optimal randomized parallel algorithm for finding connected components in a graph. SIAM Journal on Computing, 20(6):1046-1067, 1991.

Digital Library

[11]

J. Gil, Y. Matins, and U. Vishkin. Towards a theory of nearly constant time parallel algorithms. In Proceedings of the 32nd Annual IEEE Symposium on Foundations o} Computer Science, San Juan, Puerto Rico, pages 698-710, 1991.

Digital Library

[12]

M.T. Goodrich. Using approximation algorithms to design parallel algorithms that may ignore processor allocation. In Proceedings of the 32nd Annual IEEE Symposium on Foundations o} Computer Science, San Juan, Puerto Rico, pages 711-722, 1991.

Digital Library

[13]

T. Hagerup. Optimal parallel algorithms on planar graphs. Information and Computation, 84:71-96, 1990.

Digital Library

[14]

T. Hagerup. The log-star revolution. In Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Vol. 577, pages 259-278. Springer, 1992.

Digital Library

[15]

T. Hagerup. Fast deterministic processor allocation. In Proceedings of the 4th Annual A CM-SIAM Symposium on Discrete Algorithms, Austin, Texas, pages 1-10, 1993.

Digital Library

[16]

D.S. Hirschberg, A.K. Chandra, and D.V. Sarwate. Computing connected components on parallel computers. Communications o} the A CM, 22(8):461-464, 1979.

Digital Library

[17]

K. Iwama and Y. Kambayashi. A simpler parallel algorithm for graph connectivity. Journal of Algorithms, 16:190-217, 1994.

Digital Library

[18]

D.B. Johnson and P. Metaxas. Connected components in O(log3/2 IY{) parallel time for the CREW PRAM. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 688-697, 1991.

Digital Library

[19]

D.B. Johnson and P. Metaxas. A parallel algorithm for computing minimum spanning trees. In Proceedings of the 4th Annual A CM Symposium on Parallel algorithms and architectures, San Diego, California, pages 363-372, 1992.

Digital Library

[20]

D.R. Karger. Global rain-cuts in RNC, and other ramifications of a simple min-cut algorithm. In Proceedings of the 4th Annual A CM-SIAM Symposium on Discrete Algorithms, Austin, Texas, pages 21-30, 1993.

Digital Library

[21]

D.R. Karger, N. Nisan, and M. Parnas. Fast connected components algorithms for the EREW PRAM. In Proceedings of the 4th Annual ACM Symposium on Parallel algorithms and architectures, San Diego, California, pages 373-381, 1992.

Digital Library

[22]

R.M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume A, Algorithms and Complexity, chapter 17, pages 869-932. Elsevier and The MIT Press, 1990.

Digital Library

[23]

G.L. Miller and J.H. Reif. Parallel tree contraction, Part 1: Fundamentals. In S. Micali, editor, Advances in Computing Research, Volume 5, Randomness and Computation, pages 47-72. JAI Press, 1989.

[24]

T. Radzik. Computing connected componnets on EREW PRAM. Technical Report 94/02, King's College London, 1994.

[25]

J.H. Reif. Optimal parallel algorithms for graph connectivity. Technical Report TR-08-84, Center for Computing Research, Harvard University, 1984.

[26]

Y. Shiloach and U. Vishkin. An o(log n) parallel connectivity algorithm. Journal o} Algorithms, 3(1):57-67, 1983.

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Hong CDhulipala LShun JSarkar VKim H(2020)Exploring the Design Space of Static and Incremental Graph Connectivity Algorithms on GPUsProceedings of the ACM International Conference on Parallel Architectures and Compilation Techniques10.1145/3410463.3414657(55-69)Online publication date: 30-Sep-2020
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Wang YGu YShun JMaier DPottinger RDoan ATan WAlawini ANgo H(2020)Theoretically-Efficient and Practical Parallel DBSCANProceedings of the 2020 ACM SIGMOD International Conference on Management of Data10.1145/3318464.3380582(2555-2571)Online publication date: 11-Jun-2020
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Acar UAnderson DBlelloch GDhulipala LScheideler CBerenbrink P(2019)Parallel Batch-Dynamic Graph ConnectivityThe 31st ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3323165.3323196(381-392)Online publication date: 17-Jun-2019
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Index Terms

An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM (extended abstract)
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
  2. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods

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cover image ACM Conferences

SPAA '94: Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures

August 1994

374 pages

ISBN:0897916719

DOI:10.1145/181014

Chairmen:
Lawrence Snyder
Univ. of Washington, Seattle
,
Charles E. Leiserson
Massachusetts Institute of Technology, Cambridge

Copyright © 1994 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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European Comp Soc: European Computer Society
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGARCH: ACM Special Interest Group on Computer Architecture

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1994

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6SPAA94: 6th Annual ACM Symposium on Parallel Algorithms and Architectures

June 27 - 29, 1994

New Jersey, Cape May, USA

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Overall Acceptance Rate 447 of 1,461 submissions, 31%

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Cited By

Hong CDhulipala LShun JSarkar VKim H(2020)Exploring the Design Space of Static and Incremental Graph Connectivity Algorithms on GPUsProceedings of the ACM International Conference on Parallel Architectures and Compilation Techniques10.1145/3410463.3414657(55-69)Online publication date: 30-Sep-2020
https://dl.acm.org/doi/10.1145/3410463.3414657
Wang YGu YShun JMaier DPottinger RDoan ATan WAlawini ANgo H(2020)Theoretically-Efficient and Practical Parallel DBSCANProceedings of the 2020 ACM SIGMOD International Conference on Management of Data10.1145/3318464.3380582(2555-2571)Online publication date: 11-Jun-2020
https://dl.acm.org/doi/10.1145/3318464.3380582
Acar UAnderson DBlelloch GDhulipala LScheideler CBerenbrink P(2019)Parallel Batch-Dynamic Graph ConnectivityThe 31st ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3323165.3323196(381-392)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3323165.3323196
Assadi SSun XWeinstein ORobinson PEllen F(2019)Massively Parallel Algorithms for Finding Well-Connected Components in Sparse GraphsProceedings of the 2019 ACM Symposium on Principles of Distributed Computing10.1145/3293611.3331596(461-470)Online publication date: 16-Jul-2019
https://dl.acm.org/doi/10.1145/3293611.3331596
Behnezhad SDhulipala LEsfandiari HLacki JMirrokni V(2019)Near-Optimal Massively Parallel Graph Connectivity2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2019.00095(1615-1636)Online publication date: Nov-2019
https://doi.org/10.1109/FOCS.2019.00095
Fang MYin JZhu X(2016)Active exploration for large graphsData Mining and Knowledge Discovery10.1007/s10618-015-0424-z30:3(511-549)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1007/s10618-015-0424-z
Cacer EMongelli HNishibe CSong S(2010)Experimental results of a coarse-grained parallel algorithm for spanning tree and connected components2010 International Conference on High Performance Computing & Simulation10.1109/HPCS.2010.5547062(631-637)Online publication date: Jun-2010
https://doi.org/10.1109/HPCS.2010.5547062
Pettie SRamachandran V(1999)A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning ForestRandomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques10.1007/978-3-540-48413-4_24(233-244)Online publication date: 1999
https://doi.org/10.1007/978-3-540-48413-4_24
Halperin SZwick UTardos É(1996)Optimal randomized EREW PRAM algorithms for finding spanning forests and for other basic graph connectivity problemsProceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/313852.314099(438-447)Online publication date: 28-Jan-1996
https://dl.acm.org/doi/10.5555/313852.314099
Cole RKlein PTarjan RBlelloch G(1996)Finding minimum spanning forests in logarithmic time and linear work using random samplingProceedings of the eighth annual ACM symposium on Parallel Algorithms and Architectures10.1145/237502.237563(243-250)Online publication date: 24-Jun-1996
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