Lower bounds for subgraph detection in the CONGEST model

Tzlil Gonen, Rotem Oshman

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

Abstract

In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to determine whether the network graph contains H as a subgraph or not. Until now, the only lower bounds on subgraph-freeness known for the CONGEST model were for cycles of length greater than 3; here we extend and generalize the cycle lower bound, and obtain polynomial lower bounds for subgraph-freeness in the CONGEST model for two classes of subgraphs. The first class contains any graph obtained by starting from a 2-connected graph H for which we already know a lower bound, and replacing the vertices of H by arbitrary connected graphs. We show that the lower bound on H carries over to the new graph. The second class is constructed by starting from a cycle Ck of length k ≥ 4, and constructing a graph H from Ck by replacing each edge {i, (i + 1) mod k} of the cycle with a connected graph Hi, subject to some constraints on the graphs H0, ⋯, Hk-1. In this case we obtain a polynomial lower bound for the new graph H, depending on the size of the shortest cycle in H passing through the vertices of the original k-cycle.

Original languageEnglish
Title of host publication21st International Conference on Principles of Distributed Systems, OPODIS 2017
EditorsJames Aspnes, Joao Leitao, Alysson Bessani, Pascal Felber
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770613
DOIs
StatePublished - 1 Mar 2018
Event21st International Conference on Principles of Distributed Systems, OPODIS 2017 - Lisboa, Portugal
Duration: 18 Dec 201720 Dec 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume95
ISSN (Print)1868-8969

Conference

Conference21st International Conference on Principles of Distributed Systems, OPODIS 2017
Country/TerritoryPortugal
CityLisboa
Period18/12/1720/12/17

Keywords

  • CONGEST
  • Lower bounds
  • Subgraph freeness

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