Deterministic Near-Optimal Distributed Listing of Cliques

TL;DR

This paper presents the first deterministic distributed algorithms for listing cliques in large graphs, achieving near-optimal round complexity and improving previous results for triangles.

Contribution

It introduces deterministic algorithms for clique listing in the extsc{congest} model, matching known lower bounds up to subpolynomial factors, and improves triangle listing complexity.

Findings

Deterministic algorithms for clique listing in extsc{congest} model.

Triangle listing complexity improved from n^{2/3+o(1)} to n^{1/3+o(1)}.

Algorithms are tight up to a subpolynomial factor.

Abstract

The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether deterministic algorithms can be as efficient as their randomized counterparts, where the latter are known to be tight up to polylogarithmic factors. We give deterministic distributed algorithms for listing cliques of size $p$ in $n^{1 - 2/p + o(1)}$ rounds in the \congest model. For triangles, our $n^{1/3+o(1)}$ round complexity improves upon the previous state of the art of $n^{2/3+o(1)}$ rounds [Chang and Saranurak, FOCS 2020]. For cliques of size $p \geq 4$, ours are the first non-trivial deterministic distributed algorithms. Given known lower bounds, for all values $p \geq 3$ our algorithms are tight up to a $n^{o(1)}$ subpolynomial factor, which comes from the deterministic routing procedure we use.