The locality of distributed symmetry breaking

Leonid Barenboim, Michael Elkin, Seth Pettie, Johannes Schneider

Research output: Contribution to journalConference articlepeer-review

89 Scopus citations

Abstract

We present new bounds on the locality of several classical symmetry breaking tasks in distributed networks. A sampling of the results include 1) A randomized algorithm for computing a maximal matching (MM) in O(log Δ + (log log n)4) rounds, where Δ is the maximum degree. This improves a 25-year old randomized algorithm of Israeli and Itai that takes O(log n) rounds and is provably optimal for all log Δ in the range [(log log n)4, √log n]. 2) A randomized maximal independent set (MIS) algorithm requiring O(log Δ√log n) rounds, for all Δ, and only 2{O(√log log n) rounds when Δ = poly(log n). These improve on the 25-year old O(log n)-round randomized MIS algorithms of Luby and Alon, Babai, and Itai when log Δ ≪ √log n. 3) A randomized (Δ + 1)-coloring algorithm requiring O(log Δ + 2 O(√ log log n)) rounds, improving on an algorithm of Schneider and Wattenhofer that takes O(log Δ + √log n) rounds. This result implies that an O(Δ)-coloring can be computed in 2 O(√log log n) rounds for all Δ, improving on Kothapalli et al.'s O(√log n})-round algorithm. We also introduce a new technique for reducing symmetry breaking problems on low arboricity graphs to low degree graphs. Corollaries of this reduction include MM and MIS algorithms for low arboricity graphs (e.g., planar graphs and graphs that exclude any fixed minor) requiring O(√log n) and O(log2/3 n) rounds w.h.p., respectively.

Original languageEnglish
Article number6375310
Pages (from-to)321-330
Number of pages10
JournalProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
DOIs
StatePublished - 1 Dec 2012
Event53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012 - New Brunswick, NJ, United States
Duration: 20 Oct 201223 Oct 2012

Keywords

  • Coloring
  • Maximal Independent Set
  • Maximal Matching

ASJC Scopus subject areas

  • Computer Science (all)

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