Improved Methods for Computing Distances Between Unordered Trees Using Integer Programming

Abstract

Kondo et al. (DS 2014) proposed integer linear programming formulations for computing the tree edit distance and its variants between unordered rooted trees. They showed that the tree edit distance, segmental distance, and bottom-up segmental distance problems respectively have integer linear programming formulations with O(nm) variables and \(O(n^2m^2)\) constraints, where n and m are the number of nodes of two input trees. In this work, we propose new integer linear programming formulations for these three distances and the bottom-up distance by combining with dynamic programming. For computing the tree edit distance, we solve O(nm) subproblems, each of which is formulated by an integer linear program with O(nm) variables and \(O(n + m)\) constraints. For the other three distances, each subproblem can be reduced to the maximum weight matching problem in a bipartite graph which is solvable in polynomial time. In order to compute the distances from the solutions of subproblems, we also give a unified integer linear formulation with O(nm) variables and \(O(n + m)\) constraints. We conducted a computational experiment to evaluate the performance of our methods. The experimental results show that our methods remarkably outperformed to the previous methods due to Kondo et al.