Determining the consistency of partial tree descriptions Original Research Article

We present an efficient algorithm that decides the consistency of partial descriptions of ordered trees. The constraint language of these descriptions was introduced by Cornell in computational linguistics; the constraints specify for pairs of nodes sets of admissible relative positions in an ordered tree. Cornell asked for an algorithm to find a tree structure satisfying these constraints. This computational problem generalizes the common-supertree problem studied in phylogenetic analysis, and also generalizes the network consistency problem of the so-called left-linear point algebra. We present the first polynomial time algorithm for Cornellʹs problem, which runs in time image, where m is the number of constraints and n the number of variables in the constraint.