Fast Distributed Algorithms for Testing Graph Properties

TL;DR

This paper develops fast distributed algorithms for graph property testing in various models, significantly improving efficiency over sequential methods and introducing new techniques like distributed random walk maintenance.

Contribution

It introduces the first comprehensive study of distributed property testing, providing faster algorithms for key graph properties and new methods for complex tasks.

Findings

Faster distributed algorithms for triangle-freeness and bipartiteness

Effective emulation of sequential property tests in distributed settings

New machinery for distributed maintenance of multiple random walks

Abstract

We initiate a thorough study of \emph{distributed property testing} -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called \emph{dense} testing model we emulate sequential tests for nearly all graph properties having $1$-sided tests, while in the \emph{sparse} and \emph{general} models we obtain faster tests for triangle-freeness and bipartiteness respectively. In most cases, aided by parallelism, the distributed algorithms have a much shorter running time as compared to their counterparts from the sequential querying model of traditional property testing. The simplest property testing algorithms allow a relatively smooth transitioning to the distributed model. For the more complex tasks we develop new machinery that is of independent interest. This includes a method for distributed maintenance of multiple random walks.