{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article9396","name":"Detecting communities is Hard (And Counting Them is Even Harder)","abstract":"We consider the algorithmic problem of community detection in networks. Given an undirected friendship graph G, a subset\r\nS of vertices is an (a,b)-community if: * Every member of the community is friends with an (a)-fraction of the community; and\r\n* every non-member is friends with at most a (b)-fraction of the\r\ncommunity. \r\n\r\n[Arora, Ge, Sachdeva, Schoenebeck 2012] gave a quasi-polynomial\r\ntime algorithm for enumerating all the (a,b)-communities\r\nfor any constants a>b. \r\n\r\nHere, we prove that, assuming the Exponential Time Hypothesis (ETH),\r\nquasi-polynomial time is in fact necessary - and even for a much weaker\r\napproximation desideratum. Namely, distinguishing between:\r\n* G contains an (1,o(1))-community; and\r\n* G does not contain a (b,b+o(1))-community\r\nfor any b.\r\n\r\nWe also prove that counting the number of (1,o(1))-communities\r\nrequires quasi-polynomial time assuming the weaker #ETH.","keywords":["Community detection","stable communities","quasipolynomial time"],"author":{"@type":"Person","name":"Rubinstein, Aviad","givenName":"Aviad","familyName":"Rubinstein"},"position":42,"pageStart":"42:1","pageEnd":"42:13","dateCreated":"2017-11-28","datePublished":"2017-11-28","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Rubinstein, Aviad","givenName":"Aviad","familyName":"Rubinstein"},"copyrightYear":"2017","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ITCS.2017.42","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6270","volumeNumber":67,"name":"8th Innovations in Theoretical Computer Science Conference (ITCS 2017)","dateCreated":"2017-11-28","datePublished":"2017-11-28","editor":{"@type":"Person","name":"Papadimitriou, Christos H.","givenName":"Christos H.","familyName":"Papadimitriou"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article9396","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6270"}}}