extended-abstract

Brief announcement: fair maximal independent sets in trees

Authors:

Jeremy Fineman,

Calvin Newport,

Tonghe WangAuthors Info & Claims

PODC '13: Proceedings of the 2013 ACM symposium on Principles of distributed computing

Pages 51 - 53

https://doi.org/10.1145/2484239.2484291

Published: 22 July 2013 Publication History

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Abstract

Finding a maximal independent set (MIS) is a classic problem in graph theory that has been widely study in the context of distributed algorithms. Standard distributed MIS solutions focus on time complexity. Here we focus on a novel attribute, fairness, where we consider an MIS algorithm fair if all nodes have similar probabilities of joining the set. In many contexts, fairness is important because a node's election to the MIS can have an impact on the resources it consumes. This paper addresses fairness by providing a provably fair and efficient distributed MIS algorithm for unrooted trees. The algorithm runs in O(logn) time and guarantees a correct MIS such that each node enters the set with probability at least 1/4 - ε, for arbitrarily small ε.

References

[1]

L. Barenboim, M. Elkin, S. Pettie, and J. Schneider. The locality of distributed symmetry breaking. In Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, FOCS '12, pages 321--330, Washington, DC, USA, 2012. IEEE Computer Society.

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D. G. Harris, E. Morsy, G. Pandurang, P. Robinson, and A. Srinivasan. Efficient Computation of Balanced Structures. In Proceedings of the International Colloquium on Automata, Languages and Programming, 2013.

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F. Kuhn, T. Moscibroda, and R. Wattenhofer. Local computation: Lower and upper bounds. CoRR, abs/1011.5470, 2010.

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C. Lenzen and R. Wattenhofer. MIS on trees. In Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, PODC '11, pages 41--48, New York, NY, USA, 2011. ACM.

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M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 15(4):1036--1055, Nov. 1986.

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Index Terms

Brief announcement: fair maximal independent sets in trees
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Trees
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

PODC '13: Proceedings of the 2013 ACM symposium on Principles of distributed computing

July 2013

422 pages

ISBN:9781450320658

DOI:10.1145/2484239

General Chair:
Panagiota Fatourou
FORTH ICS & University of Crete, Greece
,
Program Chair:
Gadi Taubenfeld
IDC, Israel

Permission to make digital or hard copies of part or all 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 third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Published: 22 July 2013

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PODC '13: ACM Symposium on Principles of Distributed Computing

July 22 - 24, 2013

Québec, Montréal, Canada

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PODC '13 Paper Acceptance Rate 37 of 145 submissions, 26%;

Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Brief Announcement: Symmetry Breaking in the CONGEST Model: Time- and Message-Efficient Algorithms for Ruling Sets

Brief Announcement: An Exponential Separation Between Randomized and Deterministic Complexity in the LOCAL Model

Brief Announcement: Using Read-k Inequalities to Analyze a Distributed MIS Algorithm

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Brief Announcement: Symmetry Breaking in the CONGEST Model: Time- and Message-Efficient Algorithms for Ruling Sets

Brief Announcement: An Exponential Separation Between Randomized and Deterministic Complexity in the LOCAL Model

Brief Announcement: Using Read-k Inequalities to Analyze a Distributed MIS Algorithm

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