An efficient implicit data structure for path testing and searching in rooted trees and forests

Abstract

In this paper, an implicit data structure is presented which makes it possible to represent a tree-structured partial order in such a way to efficiently perform operations of path testing and searching among elements of the ground set of the poset. The data structure makes it possible to represent the order relation by referring only to internal nodes of the tree and by associating to each element of the ground set a pair of integer values derived from specific linear extensions of the partial order.