TY - GEN

T1 - Algebraic methods in the congested clique

AU - Censor-Hillel, Keren

AU - Lenzen, Christoph

AU - Kaski, Petteri

AU - Paz, Ami

AU - Korhonen, Janne H.

AU - Suomela, Jukka

N1 - Publisher Copyright: © Copyright 2015 ACM.

PY - 2015/7/21

Y1 - 2015/7/21

N2 - 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 multipliacation 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 algorith- mics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: Triangle and 4-cycle counting in O(n0.158) rounds, imaproving upon the O(n1/3) triangle counting algorithm of Dolev et al. [DISC 2012], a (1 + o(1))-approximation of all-pairs shortest paths in O(n0.158) rounds, improving upon the Õ(n1/2)-round (2+o(1))-approximation algorithm of Nanongkai [STOC 2014], and 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.

AB - 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 multipliacation 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 algorith- mics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: Triangle and 4-cycle counting in O(n0.158) rounds, imaproving upon the O(n1/3) triangle counting algorithm of Dolev et al. [DISC 2012], a (1 + o(1))-approximation of all-pairs shortest paths in O(n0.158) rounds, improving upon the Õ(n1/2)-round (2+o(1))-approximation algorithm of Nanongkai [STOC 2014], and 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.

KW - Congested clique model

KW - Distance compuatation

KW - Distributed computing

KW - Lower bounds

KW - Matrix multiplication

KW - Subgraph detection

UR - http://www.scopus.com/inward/record.url?scp=84955729177&partnerID=8YFLogxK

U2 - https://doi.org/10.1145/2767386.2767414

DO - https://doi.org/10.1145/2767386.2767414

M3 - منشور من مؤتمر

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 143

EP - 152

BT - PODC 2015 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

T2 - ACM Symposium on Principles of Distributed Computing, PODC 2015

Y2 - 21 July 2015 through 23 July 2015

ER -