Generating all forest extensions of a partially ordered set

Abstract

Let P and P′ be partially ordered sets, with ground set E, |E| = n, and relation sets R and R′, respectively. Say that P′ is an extension of P when R ⊆ R′. A partially ordered set is a forest when the set of ancestors of any given element forms a chain. We describe an algorithm for generating the complete set of forest extensions of an order P. The algorithm requires O(n2) time between the generation of two consecutive forests. The initialization of the algorithm requires O(n|R|) time. © Springer-Verlag Berlin Heidelberg 2003.