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.ITCS.2017.42
URN: urn:nbn:de:0030-drops-81496
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8149/
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Rubinstein, Aviad

Detecting communities is Hard (And Counting Them is Even Harder)

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LIPIcs-ITCS-2017-42.pdf (0.6 MB)

Abstract

We consider the algorithmic problem of community detection in networks. Given an undirected friendship graph G, a subset
S of vertices is an (a,b)-community if: * Every member of the community is friends with an (a)-fraction of the community; and
* every non-member is friends with at most a (b)-fraction of the
community.

[Arora, Ge, Sachdeva, Schoenebeck 2012] gave a quasi-polynomial
time algorithm for enumerating all the (a,b)-communities
for any constants a>b.

Here, we prove that, assuming the Exponential Time Hypothesis (ETH),
quasi-polynomial time is in fact necessary - and even for a much weaker
approximation desideratum. Namely, distinguishing between:
* G contains an (1,o(1))-community; and
* G does not contain a (b,b+o(1))-community
for any b.

We also prove that counting the number of (1,o(1))-communities
requires quasi-polynomial time assuming the weaker #ETH.

BibTeX - Entry

@InProceedings{rubinstein:LIPIcs:2017:8149,
  author =	{Aviad Rubinstein},
  title =	{{Detecting communities is Hard (And Counting Them is Even Harder)}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{42:1--42:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8149},
  URN =		{urn:nbn:de:0030-drops-81496},
  doi =		{10.4230/LIPIcs.ITCS.2017.42},
  annote =	{Keywords: Community detection, stable communities, quasipolynomial time}
}

Keywords: Community detection, stable communities, quasipolynomial time
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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