Deterministic stateless centralized local algorithms for bounded degree graphs

Guy Even, Moti Medina, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We design centralized local algorithms for: maximal independent set, maximal matching, and graph coloring. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes is O(log* n), where n is the number of vertices of the input graph. Our algorithms for maximal independent set and maximal matching improves over previous randomized algorithms by Alon et al. (SODA 2012) and Mansour et al. (ICALP 2012). In these previous algorithms, the number of probes and the space required for storing the state between queries are poly(logn). We also design the first centralized local algorithm for graph coloring. Our graph coloring algorithms are deterministic and stateless. Let Δ denote the maximum degree of a graph over n vertices. Our algorithm for coloring the vertices by Δ+1 colors requires O(log* n) probes for constant degree graphs. Surprisingly, for the case where the number of colors is O(Δ2 logΔ), the number of probes of our algorithm is O(Δ· log* n+Δ2), that is, the number of probes is sublinear if Δ =o9√n), i.e., our algorithm applies for graphs with unbounded degrees.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings
PublisherSpringer Verlag
Pages394-405
Number of pages12
ISBN (Print)9783662447765
DOIs
StatePublished - 2014
Event22nd Annual European Symposium on Algorithms, ESA 2014 - Wroclaw, Poland
Duration: 8 Sep 201410 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8737 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference22nd Annual European Symposium on Algorithms, ESA 2014
Country/TerritoryPoland
CityWroclaw
Period8/09/1410/09/14

Keywords

  • Centralized Local Algorithms
  • Graph Algorithms
  • Sublinear Approximation Algorithms

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