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The Complexity of Synchronous Iterative Do-All with Crashes

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Distributed Computing (DISC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2180))

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Abstract

Do-All is the problem of performing N tasks in a distributed system of P failure-prone processors [8]. Many distributed and parallel algorithms have been developed for this problem and several algorithm simulations have been developed by iterating Do-All algorithms. The efficiency of the solutions for Do-All is measured in terms of work complexity where all processing steps taken by the processors are counted. We present the first non-trivial lower bounds for Do-All that capture the dependence of work on N, Pandf, the number of processor crashes. For the model of computation where processors are able to make perfect load-balancing decisions locally, we also present matching upper bounds. We define the r-iterative Do-All problem that abstracts the repeated use of Do-All such as found in algorithm simulations. Our f-sensitive analysis enables us to derive a tight bound for r-iterative Do-All work (that is stronger than the r-fold work complexity of a single Do-All). Our approach that models perfect load-balancing allows for the analysis of specific algorithms to be divided into two parts: (i) the analysis of the cost of tolerating failures while performing work, and (ii) the analysis of the cost of implementing load-balancing. We demonstrate the utility and generality of this approach by improving the analysis of two known efficient algorithms. Finally we present a new upper bound on simulations of synchronous shared-memory algorithms on crash-prone processors.

This research is supported by the NSF Grant 9988304. The work of the second author is supported in part by the NSF Career Award 0093065. The work of the third author is supported in part by the NSF Career Award 9984774.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Chryssis Georgiou, Alexander Russell & Alex A. Shvartsman

  2. Laboratory of Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Alex A. Shvartsman

Authors
  1. Chryssis Georgiou
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  2. Alexander Russell
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  3. Alex A. Shvartsman
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843-3112, USA

    Jennifer Welch

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© 2001 Springer-Verlag Berlin Heidelberg

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Georgiou, C., Russell, A., Shvartsman, A.A. (2001). The Complexity of Synchronous Iterative Do-All with Crashes. In: Welch, J. (eds) Distributed Computing. DISC 2001. Lecture Notes in Computer Science, vol 2180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45414-4_11

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  • DOI: https://doi.org/10.1007/3-540-45414-4_11

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  • Print ISBN: 978-3-540-42605-9

  • Online ISBN: 978-3-540-45414-4

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