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Segmental Mapping and Distance for Rooted Labeled Ordered Trees

Kan T., Higuchi S., Hirata K.

Fundamenta Informaticae

2014

Vol. 132, nr 4

461--483

In this paper, as variations of a Tai mapping between rooted labeled ordered trees (trees, for short), we introduce a segmentalmapping to preserve the parent-children relationship as possible, and also top-down segmengal and bottom-up segmental mappings as the segmental mappings that contain the pair of the roots and the pair of the leaves, respectively. Then, we show that these mappings provide a new hierarchy for the variations of the Tai mapping in addition to a well-known one, in particular, the top-down segmental mapping coincides with a top-down mapping. Also we show that both segmental and bottom-up segmental distances as the minimumcosts of segmental and bottom-up segmental mappings are metrics. Next, we design algorithms to compute the segmental and the bottom-up segmental distances in quadratic time and space. Finally, we give experimental results for the segmental distance.