A Fast Algorithm for Optimal Alignment between Similar Ordered Trees

Issue title: Computing Patterns in Strings

Article type: Research Article

Authors: Jansson, Jesper | Lingas, Andrzej

Affiliations: Department of Computer Science, Lund University, Box 118, SE-221 00 Lund, Sweden

Abstract: We present a fast algorithm for optimal alignment between two similar ordered trees with node labels. Let S and T be two such trees with |S| and |T| nodes, respectively. If there exists an optimal alignment between S and T which uses at most d blank symbols and d is known in advance, it can be constructed in O(n log n·(maxdeg)^3·d^2) time, where n=max{|S|,|T|} and maxdeg is the maximum degree of all nodes in S and T. If d is not known in advance, we can construct an optimal alignment in O(n log n·(maxdeg)^3·f^2) time, where f is the difference between the highest possible score for any alignment between two trees having a total of |S|+|T| nodes and the score of an optimal alignment between S and T, if the scoring scheme satisfies some natural assumptions. In particular, if the degrees of both input trees are bounded by a constant, the running times reduce to O(n log n·d^2) and O(n log n·f^2), respectively.

Journal: Fundamenta Informaticae, vol. 56, no. 1-2, pp. 105-120, 2003