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.