Searching in random partially ordered sets

Abstract

We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders under two classical models for random partial orders, the random graph model and the uniform model. We shall show that the problem of determining an optimal strategy is NP -hard, but there are simple, fast algorithms able to produce near-optimal search strategies for typical partial orders under the two models of random partial orders that we consider. We present a (1+o(1))-approximation algorithm for typical partial orders under the random graph model (constant p) and present a 6.34-approximation algorithm for typical partial orders under the uniform model. Both algorithms run in polynomial time.