Output polynomial enumeration of all fixed-cardinality ideals of a poset, respectively all fixed-cardinality subtrees of a tree

摘要

The N cardinality k ideals of any w-element poset (w, k variable) can beenumerated in time O(Nw^3). The corresponding bound for k-element subtrees of aw-element tree is O(Nw^5). An algorithm is described that by the use ofwildcards displays all order ideals of a poset in a compact manner, i.e. notone by one.