License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2017.6
URN: urn:nbn:de:0030-drops-86445
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8644/
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Gonen, Tzlil ; Oshman, Rotem

Lower Bounds for Subgraph Detection in the CONGEST Model

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LIPIcs-OPODIS-2017-6.pdf (0.6 MB)

Abstract

In the subgraph-freeness problem, we are given a constant-sized graph H, and wish to de- termine 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 H_{0}, . . . , H_{k−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.

BibTeX - Entry

@InProceedings{gonen_et_al:LIPIcs:2018:8644,
  author =	{Tzlil Gonen and Rotem Oshman},
  title =	{{Lower Bounds for Subgraph Detection in the CONGEST Model}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{James Aspnes and Alysson Bessani and Pascal Felber and Jo{\~a}o Leit{\~a}o},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8644},
  URN =		{urn:nbn:de:0030-drops-86445},
  doi =		{10.4230/LIPIcs.OPODIS.2017.6},
  annote =	{Keywords: subgraph freeness, CONGEST, lower bounds}
}

Keywords: subgraph freeness, CONGEST, lower bounds
Collection: 21st International Conference on Principles of Distributed Systems (OPODIS 2017)
Issue Date: 2018
Date of publication: 28.03.2018

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