Algebraic methods in the congested clique
Censor-Hillel, Keren
Kaski, Petteri
Korhonen, Janne
Lenzen, Christoph
Paz, Ami
Suomela, Jukka
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:
1. triangle and 4-cycle counting in O(n0.158) rounds, improving upon the O(n1/3) algorithm of Dolev et al. [DISC 2012],
2. 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
3. computing the girth in O(n0.158) rounds, which is the first non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.
Springer Nature
2019
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/7150
Censor-Hillel K, Kaski P, Korhonen J, Lenzen C, Paz A, Suomela J. Algebraic methods in the congested clique. <i>Distributed Computing</i>. 2019;32(6):461-478. doi:<a href="https://doi.org/10.1007/s00446-016-0270-2">10.1007/s00446-016-0270-2</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00446-016-0270-2
info:eu-repo/semantics/altIdentifier/issn/0178-2770
info:eu-repo/semantics/altIdentifier/issn/1432-0452
info:eu-repo/semantics/altIdentifier/arxiv/1503.04963
info:eu-repo/semantics/openAccess