Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
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We show that a random walk on a tournament on n vertices finds either a sink or a 3-cycle in expected time $O\left(\sqrt{n} \cdot \log n \cdot \sqrt{\log^{*}n}\right)$, that is, sublinear both in the size of the description of the graph as well as in the number of vertices. This result is motivated by the search of a generic algorithm for solving a large class of search problems called Local Search, LS . LS is defined by us as a generalisation of the well-known class PLS .