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The complexity of updating multi-writer snapshot objects

Published: 12 August 2007 Publication History

Abstract

This paper proves Ω(m) lower bounds on the step complexity of UPDATE operations for partitioned implementations of m-component multi-writer snapshot objects from base objects of any type. These are implementations in which each base object is only modifed by processes performing UPDATE operations to one specific component. In particular, we show that any space-optimal implementation of a multi-writer snapshot object from historyless objects is partitioned. This work extends a similar lower bound by Israeli and Shirazi for implementations of m-component single-writer snapshot objects from single-writer registers.

References

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James H. Anderson. Multi-writer composite registers. Distrib. Comput., 7(4): 175--195, 1994.
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Hagit Attiya and Arie Fouren. Adaptive and efficient algorithms for lattice agreement and renaming, SIAM J. Comput., 31(2): 642--664, 2001.
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Hagit Attiya and Ophir Rachman. Atomic snapshots in O(n log n) operations. SIAM J. Comput., 27(2): 319--340, 1998.
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Panagiota Fatourou, Faith Ellen Fich, and Eric Ruppert. A Tight Time Lower Bound for Space-Optimal Implementations of Multi-Writer Snapshots. In Proceedings of the 35th ACM Symposium on Theory of Computing, 259--268, 2003; J. ACM, to appear.
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Faith Fich, Maurice Herlihy, and Nir Shavit. On the Space Complexity of Randomized Synchronization. J. ACM, 45(5): 843--862, 1998.
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Michiko Inoue, Wei Chen, Toshimitsu Masuzawa, and Nobuki Tokura. Linear time snapshots using multi-writer multi-reader registers. In Proceedings of the 8th International Workshop on Distributed Algorithms LNCS 857, 130--140, 1998.
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A. Israeli, A. Shaham, and A. Shirazi. Linear-time snapshot implementations in unbalanced systems. Math. Systems Theory, 28(5): 469--486, 1995.
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Amos Israeli and Assaf Shirazi. The time complexity of updating snapshot memories. Information Processing Letters, 65(1): 33--40, 1998.
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Prasad Jayanti. f-Arrays: Implementation and Applications. In Proceedings of the 21st Annual ACM Symposium on Principles of Distributed Computing, 270--279, 2002.
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Prasad Jayanti. An Optimal Multi-Writer Snapshot Algorithm. In Proceedings of the 37th ACM Symposium on Theory of Computing, 723--732, 2005.
[12]
Prasad Jayanti, King Tan, and Sam Toueg. Time and space lower bounds for nonblocking implementations. SIAM J. Comput., 30(2): 438--456, 2000.

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cover image ACM Conferences
PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
August 2007
424 pages
ISBN:9781595936165
DOI:10.1145/1281100
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 August 2007

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Author Tags

  1. distributed computing
  2. lower bound
  3. shared memory
  4. snapshot
  5. update

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