Property testing of planarity in the CONGEST model

Reut Levi, Moti Medina, Dana Ron

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

2 Scopus citations

Abstract

We give a distributed algorithm in the CONGEST model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (DISC 2016), who recently initiated the study of property testing in the distributed setting, our algorithm gives the following guarantee: For a graph G = (V, E) and a distance parameter, if G is planar, then every node outputs accept, and if G is -far from being planar (i.e., more than · |E| edges need to be removed in order to make G planar), then with probability 1 − 1/poly(n) at least one node outputs reject. The algorithm runs in O(log |V | · poly(1/)) rounds, and we show that this result is tight in terms of the dependence on |V |. Our algorithm combines several techniques of graph partitioning and local verification of planar embeddings. Furthermore, we show how a main subroutine in our algorithm can be applied to derive additional results for property testing of cycle-freeness and bipartiteness, as well as the construction of spanners, in minor-free (unweighted) graphs.

Original languageEnglish
Title of host publicationPODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages347-356
Number of pages10
ISBN (Print)9781450357951
DOIs
StatePublished - 23 Jul 2018
Event37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom
Duration: 23 Jul 201827 Jul 2018

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018
Country/TerritoryUnited Kingdom
CityEgham
Period23/07/1827/07/18

Keywords

  • Congest
  • Distributed algorithms
  • Distributed property testing
  • Planarity testing

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