abstract

Brief announcement: full reversal routing as a linear dynamical system

Authors:

Bernadette Charron-Bost,

Matthias Fuegger,

Jennifer L. Welch,

Josef WidderAuthors Info & Claims

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

Pages 129 - 130

https://doi.org/10.1145/1989493.1989510

Published: 04 June 2011 Publication History

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Abstract

Although substantial analysis has been done on the Full Reversal (FR) routing algorithm since its introduction by Gafni and Bertsekas in 1981, a complete understanding of its functioning---especially its time complexity---has been missing until now. In this paper, we derive the first exact formula for the time complexity of FR: given any (acyclic) graph the formula provides the exact time complexity of any node in terms of some simple properties of the graph. Our major technical insight is to describe executions of FR as a dynamical system, and to observe that this system is linear in the min-plus algebra.

As a consequence of the insight provided by the new formula, we are able to prove that FR is time-efficient when executed on tree networks. This result exposes an unstable aspect of the time complexity of FR that has not previously been reported. Finally, our results for FR are instrumental in providing an exact formula for the time complexity of a generalization of FR, as we show in a companion paper that the generalization can be reduced to FR.

References

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V. C. Barbosa and E. Gafni. Concurrency in heavily loaded neighborhood-constrained systems. ACM Trans. Program. Lang. Syst., 11(4):562--584, 1989.

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C. Busch, S. Surapaneni, and S. Tirthapura. Analysis of link reversal routing algorithms for mobile ad hoc networks. In Proc. 15th ACM SPAA, pp. 210--219, 2003.

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C. Busch and S. Tirthapura. Analysis of link reversal routing algorithms. SIAM Journal on Computing, 35(2):305--326, 2005.

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[4]

B. Charron-Bost, M. Függer, J. L. Welch, and J. Widder. Partial is Full, 2011. Manuscript.

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B. Charron-Bost, A. Gaillard, J. L. Welch, and J. Widder. Routing without ordering. In Proc. 21st ACM SPAA, pp. 145--153, 2009.

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E. Gafni and D. P. Bertsekas. Distributed algorithms for generating loop-free routes in networks with frequently changing topology. IEEE Transactions on Communications, 29(1):11--18, January 1981.

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Y. Malka and S. Rajsbaum. Analysis of distributed algorithms based on recurrence relations. In Proc. 5th Int'l Workshop on Distributed Algorithms (WDAG), pp. 242--253, 1991.

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Index Terms

Brief announcement: full reversal routing as a linear dynamical system
1. Computer systems organization
  1. Architectures
    1. Distributed architectures
2. Software and its engineering
  1. Software organization and properties
    1. Software system structures
      1. Distributed systems organizing principles

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Published In

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

June 2011

404 pages

ISBN:9781450307437

DOI:10.1145/1989493

Co-chairs:
Friedhelm Meyer auf der Heide
University of Paderborn, Germany
,
Rajmohan Rajaraman
Northeastern University, USA

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EATCS: European Association for Theoretical Computer Science

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Association for Computing Machinery

New York, NY, United States

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Published: 04 June 2011

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SPAA '11: 23rd ACM Symposium on Parallelism in Algorithms and Architectures

June 4 - 6, 2011

California, San Jose, USA

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

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Time Complexity of Link Reversal Routing

Routing without ordering

Brief announcement: the theory of network tracing

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