License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2023.94
URN: urn:nbn:de:0030-drops-175970
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17597/
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Rush, Cynthia ; Skerman, Fiona ; Wein, Alexander S. ; Yang, Dana

Is It Easier to Count Communities Than Find Them?

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LIPIcs-ITCS-2023-94.pdf (0.7 MB)

Abstract

Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions has emerged. A natural unanswered question is: might it be possible to infer properties of the community structure (for instance, the number and sizes of communities) even in situations where actually finding those communities is believed to be computationally hard? We show the answer is no. In particular, we consider certain hypothesis testing problems between models with different community structures, and we show (in the low-degree polynomial framework) that testing between two options is as hard as finding the communities.
In addition, our methods give the first computational lower bounds for testing between two different "planted" distributions, whereas previous results have considered testing between a planted distribution and an i.i.d. "null" distribution.

BibTeX - Entry

@InProceedings{rush_et_al:LIPIcs.ITCS.2023.94,
  author =	{Rush, Cynthia and Skerman, Fiona and Wein, Alexander S. and Yang, Dana},
  title =	{{Is It Easier to Count Communities Than Find Them?}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{94:1--94:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17597},
  URN =		{urn:nbn:de:0030-drops-175970},
  doi =		{10.4230/LIPIcs.ITCS.2023.94},
  annote =	{Keywords: Community detection, Hypothesis testing, Low-degree polynomials}
}

Keywords: Community detection, Hypothesis testing, Low-degree polynomials
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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