Pure dominance constraints

Abstract

We present an efficient algorithm that checks the satisfiability of pure dominance constraints, which is a tree description language contained in several constraint languages studied in computational linguistics. Pure dominance constraints partially describe unlabeled rooted trees. For arbitrary pairs of nodes they specify sets of admissible relative positions in a tree. The task is to find a tree structure satisfying these constraints. Our algorithm constructs such a solution in time O(m2) where m is the number of constraints. This solves an essential part of an open problem posed by Cornell.