Keren Censor-Hillel · Petteri Kaski · Janne H. Korhonen · Christoph Lenzen · Ami Paz · Jukka Suomela

Algebraic methods in the congested clique

Distributed Computing · volume 32, issue 6, pages 461–478, 2019 · doi:10.1007/s00446-016-0270-2

authors’ version publisher’s version


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 $O(n^{1-2/\omega})$ round matrix multiplication algorithm, where $\omega < 2.3728639$ 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:

  • triangle and 4-cycle counting in $O(n^{0.158})$ rounds, improving upon the $O(n^{1/3})$ algorithm of Dolev et al. [DISC 2012],
  • a $(1 + o(1))$-approximation of all-pairs shortest paths in $O(n^{0.158})$ rounds, improving upon the $\tilde{O} (n^{1/2})$-round $(2 + o(1))$-approximation algorithm given by Nanongkai [STOC 2014], and
  • computing the girth in $O(n^{0.158})$ 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.

Conference Version

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.