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.
@article{arxiv.1602.03718,
title = {Fast Distributed Algorithms for Testing Graph Properties},
author = {Keren Censor-Hillel and Eldar Fischer and Gregory Schwartzman and Yadu Vasudev},
journal= {arXiv preprint arXiv:1602.03718},
year = {2016}
}