On time analysis of random walk based token circulation algorithms

Abstract

The problem of evaluating time complexity of random distributed algorithms is considered. A common and natural way to randomize a distributed algorithm is to use random walks i.e. memoryless stochastic processes: a. "token" message circulates in the system and, at each step, the node that owns it sends it to one of its neighbors chosen at random. The token usually contains some pieces of information or part of the result of some distributed computing for instance. In this paper we focus on the cover time, defined by the expected time to visit all nodes in the system. This quantity often appears in the complexity of random walk based distributed algorithms. We provide a general method to compute the cover time on any arbitrary graph modeling a distributed system. © Springer-Verlag Berlin Heidelberg 2005.