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Time-space tradeoffs for implementations of snapshots

Published: 21 May 2006 Publication History

Abstract

A snapshot object is an abstraction of the fundamental problem of obtaining a consistent view of the contents of the shared memory in a distributed system while other processes may concurrently update those contents. A snapshot object stores an array of m components and can be accessed by two operations: an UPDATE that changes the value of an individual component and a powerful SCAN that returns the contents of the entire array.This paper proves time-space tradeoffs for fault-tolerant implementations of a snapshot object from registers that support only Read and Write operations. For anonymous implementations (where all processes are programmed identically), we prove that a SCAN requires Ω(n/r) time, where n is the number of processes in the system and r is the number of registers used by the implementation. For the general non-anonymous case, we prove that, for any fixed r, the time required to do a SCAN grows without bound as n increases. These tradeoffs hold even in the case where the snapshot object has just two components.This is the first time a lower bound on the tradeoff between time complexity and the number of registers has been proved for any problem in asynchronous shared-memory systems. We introduce a new tool for proving distributed lower bounds: the notion of a shrinkable execution, from which an adversary can remove portions as necessary.

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cover image ACM Conferences
STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
May 2006
786 pages
ISBN:1595931341
DOI:10.1145/1132516
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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Publication History

Published: 21 May 2006

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Author Tags

  1. anonymous processes
  2. distributed computing
  3. lower bound
  4. shared memory
  5. snapshot
  6. time-space tradeoff
  7. wait-free

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STOC06: Symposium on Theory of Computing
May 21 - 23, 2006
WA, Seattle, USA

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  • (2015)Linear space bootstrap communication schemesTheoretical Computer Science10.1016/j.tcs.2014.10.013561:PB(122-133)Online publication date: 4-Jan-2015
  • (2015)Of Concurrent Data Structures and IterationsAlgorithms, Probability, Networks, and Games10.1007/978-3-319-24024-4_20(358-369)Online publication date: 22-Nov-2015
  • (2013)Linear Space Bootstrap Communication SchemesDistributed Computing and Networking10.1007/978-3-642-35668-1_25(363-377)Online publication date: 2013
  • (2011)The complexity of updating snapshot objectsJournal of Parallel and Distributed Computing10.1016/j.jpdc.2011.08.00271:12(1570-1577)Online publication date: 1-Dec-2011
  • (2008)The space complexity of unbounded timestampsDistributed Computing10.1007/s00446-008-0060-621:2(103-115)Online publication date: 1-Jul-2008
  • (2007)Time lower bounds for implementations of multi-writer snapshotsJournal of the ACM10.1145/1314690.131469454:6(30-es)Online publication date: 1-Dec-2007
  • (2007)Time-optimal, space-efficient single-scanner snapshots & multi-scanner snapshots using CASProceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing10.1145/1281100.1281108(33-42)Online publication date: 12-Aug-2007
  • (2007)Anonymous and fault-tolerant shared-memory computingDistributed Computing10.1007/s00446-007-0042-020:3(165-177)Online publication date: 1-Oct-2007
  • (2007)The Space Complexity of Unbounded TimestampsDistributed Computing10.1007/978-3-540-75142-7_19(223-237)Online publication date: 2007
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