--- res: bibo_abstract: - "In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an O(n1−2/ω) round matrix multiplication algorithm, where ω<2.3728639 is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include:\r\n\r\n1. triangle and 4-cycle counting in O(n0.158) rounds, improving upon the O(n1/3) algorithm of Dolev et al. [DISC 2012],\r\n2. a (1+o(1))-approximation of all-pairs shortest paths in O(n0.158) rounds, improving upon the O~(n1/2)-round (2+o(1))-approximation algorithm given by Nanongkai [STOC 2014], and\r\n 3. computing the girth in O(n0.158) rounds, which is the first non-trivial solution in this model.\r\n \r\nIn addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.@eng" bibo_authorlist: - foaf_Person: foaf_givenName: Keren foaf_name: Censor-Hillel, Keren foaf_surname: Censor-Hillel - foaf_Person: foaf_givenName: Petteri foaf_name: Kaski, Petteri foaf_surname: Kaski - foaf_Person: foaf_givenName: Janne foaf_name: Korhonen, Janne foaf_surname: Korhonen foaf_workInfoHomepage: http://www.librecat.org/personId=C5402D42-15BC-11E9-A202-CA2BE6697425 - foaf_Person: foaf_givenName: Christoph foaf_name: Lenzen, Christoph foaf_surname: Lenzen - foaf_Person: foaf_givenName: Ami foaf_name: Paz, Ami foaf_surname: Paz - foaf_Person: foaf_givenName: Jukka foaf_name: Suomela, Jukka foaf_surname: Suomela bibo_doi: 10.1007/s00446-016-0270-2 bibo_issue: '6' bibo_volume: 32 dct_date: 2019^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0178-2770 - http://id.crossref.org/issn/1432-0452 dct_language: eng dct_publisher: Springer Nature@ dct_title: Algebraic methods in the congested clique@ ...