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 - 10.1145/2767386.2767414
DO - 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 -