Tree structured data often appear in bioinformatics. For example, glycans, RNA secondary structures and phylogenetic trees usually have tree structures. Comparison of trees is one of fundamental tasks in analysis of these data. Various distance measures have been proposed and utilized for comparison of trees, among which extensive studies have been done on tree edit distance. In this paper, we review key results and our recent results on the tree edit distance problem and related problems. In particular, we review polynomial time exact algorithms and more efficient approximation algorithms for the edit distance problem for ordered trees, and approximation algorithms for the largest common sub-tree problem for unordered trees. We also review applications of tree edit distance and its variants to bioinformatics with focusing on comparison of glycan structures.
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