Matching Similar Splits between Unrooted Leaf-labeled Trees

Tree comparison is ubiquitous in many areas. The simplest way for tree comparison is to define a pairwise distance measure. In a more refined comparison, one can establish a mapping between similar parts in two trees according to certain similarity measure. The best match problem for rooted leaf-labeled trees has been studied in the literature. However, no result has been found for the best match problem for unrooted leaf-labeled trees. The problem of mapping similar splits between unrooted leaf-labeled trees is considered in this paper. Based on a new similarity measure obtained from the classical Jaccard coefficient, the mapping can be computed in quadratic time.