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Journal Article

Determining the Consistency of Partial Tree Descriptions


Bodirsky,  Manuel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;


Kutz,  Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Bodirsky, M., & Kutz, M. (2007). Determining the Consistency of Partial Tree Descriptions. Artificial Intelligence, 171(2/3), 185-196. doi:10.1016/j.artint.2006.12.004.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-1EE1-3
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 Cornell's problem, which runs in time O(mn) , where m is the number of constraints and n the number of variables in the constraint.