1+ ε approximation of tree edit distance in quadratic time

Abstract

Edit distance is one of the most fundamental problems in computer science. Tree edit distance is a natural generalization of edit distance to ordered rooted trees. Such a generalization extends the applications of edit distance to areas such as computational biology, structured data analysis (e.g., XML), image analysis, and compiler optimization. Perhaps the most notable application of tree edit distance is in the analysis of RNA molecules in computational biology where the secondary structure of RNA is typically represented as a rooted tree. The best-known solution for tree edit distance runs in cubic time. Recently, Bringmann et al. show that an O(n2.99) algorithm for weighted tree edit distance is unlikely by proving a conditional lower bound on the computational complexity of tree edit distance. This shows a substantial gap between the computational complexity of tree edit distance and that of edit distance for which a simple dynamic program solves the problem in quadratic time. In this work, we give the first non-trivial approximation algorithms for tree edit distance. Our main result is a quadratic time approximation scheme for tree edit distance that approximates the solution within a factor of 1+є for any constant є > 0.