Can We Break Symmetry with o(m) Communication?

TL;DR

This paper investigates whether fundamental distributed symmetry breaking problems like coloring and MIS can be solved with sublinear communication complexity, challenging the existing understanding that they require linear communication in the number of edges.

Contribution

The paper explores conditions under which coloring and MIS can be achieved with o(m) communication, providing new insights into the communication complexity of these problems.

Findings

Established conditions for sublinear communication solutions

Identified limitations of existing algorithms

Proposed new approaches for reducing message complexity

Abstract

We study the communication cost (or message complexity) of fundamental distributed symmetry breaking problems, namely, coloring and MIS. While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems. In fact, all known algorithms need at least $\Omega(m)$ communication for these problems, where $m$ is the number of edges in the graph. We address the following question in this paper: can we solve problems such as coloring and MIS using sublinear, i.e., $o(m)$ communication, and if so under what conditions? [See full abstract in pdf]