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DOI: 10.4230/LIPIcs.ESA.2018.7
URN: urn:nbn:de:0030-drops-94705
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9470/
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Becchetti, Luca ; Clementi, Andrea ; Manurangsi, Pasin ; Natale, Emanuele ; Pasquale, Francesco ; Raghavendra, Prasad ; Trevisan, Luca

Average Whenever You Meet: Opportunistic Protocols for Community Detection

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LIPIcs-ESA-2018-7.pdf (0.5 MB)


Abstract

Consider the following asynchronous, opportunistic communication model over a graph G: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local computations. Under this model, we study the following random process: The first time a vertex is an endpoint of an active edge, it chooses a random number, say +/- 1 with probability 1/2; then, in each round, the two endpoints of the currently active edge update their values to their average. We provide a rigorous analysis of the above process showing that, if G exhibits a two-community structure (for example, two expanders connected by a sparse cut), the values held by the nodes will collectively reflect the underlying community structure over a suitable phase of the above process. Our analysis requires new concentration bounds on the product of certain random matrices that are technically challenging and possibly of independent interest. We then exploit our analysis to design the first opportunistic protocols that approximately recover community structure using only logarithmic (or polylogarithmic, depending on the sparsity of the cut) work per node.

BibTeX - Entry

@InProceedings{becchetti_et_al:LIPIcs:2018:9470,
  author =	{Luca Becchetti and Andrea Clementi and Pasin Manurangsi and Emanuele Natale and Francesco Pasquale and Prasad Raghavendra and Luca Trevisan},
  title =	{{Average Whenever You Meet: Opportunistic Protocols for Community Detection}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9470},
  URN =		{urn:nbn:de:0030-drops-94705},
  doi =		{10.4230/LIPIcs.ESA.2018.7},
  annote =	{Keywords: Community Detection, Random Processes, Spectral Analysis}
}

Keywords: Community Detection, Random Processes, Spectral Analysis
Seminar: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 08.08.2018


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