Fast Distributed Algorithms for Testing Graph Properties

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We initiate a thorough study of distributed property testing -- producing algorithms for the approximation problems of property testing in the CONGEST model. In particular, for the so-called dense testing model we emulate sequential tests for nearly all graph properties having 1-sided tests, while in the sparse and 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.