In this paper, we investigate the problem of computing structural sensitive variations of an unordered tree edit distance. First, we focus on the variations tractable by the algorithms including the submodule of a network algorithm, either the minimum cost maximum flow algorithm or the maximum weighted bipartite matching algorithm. Then, we show that both network algorithms are replaceable, and hence the time complexity of computing these variations can be reduced to O(nmd) time, where n is the number of nodes in a tree, m is the number of nodes in another tree and d is the minimum degree of given two trees. Next, we show that the problem of computing the bottom-up distance is MAX SNP-hard. Note that the well-known linear-time algorithm for the bottom-up distance designed by Valiente (2001) computes just a bottom-up indel (insertion-deletion) distance allowing no substitutions.
Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (Unless APSP Can)
