The (unweighted) tree edit distance problem for n node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in O(n ^ 3) time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007]. The same paper also showed that O(n ^ 3) is the best possible running time for any algorithm using the so-called decomposition strategy , which underlies almost all the known algorithms for this problem. These algorithms would also work for the weighted tree edit distance problem, which cannot be solved in truly sub-cubic time under the APSP conjecture [Bringmann, Gawrychowski, Mozes, and Weimann, SODA 2018]. In this paper, we break the cubic barrier by showing an O(n ^ {2.9546}) time algorithm for the unweighted tree edit distance problem. We consider an equivalent maximization problem and use a dynamic programming scheme involving matrices with many special properties. By using a decomposition scheme as well as several combinatorial techniques, we reduce tree edit distance to the max-plus product of bounded-difference matrices, which can be solved in truly sub-cubic time [Bringmann, Grandoni, Saha, and Vassilevska Williams, FOCS 2016].
The (unweighted) tree edit distance problem for n node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in O(n ^ 3) time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007]. The same paper also showed that O(n ^ 3) is the best possible running time for any algorithm using the so-called decomposition strategy , which underlies almost all the known algorithms for this problem. These algorithms would also work for the weighted tree edit distance problem, which cannot be solved in truly sub-cubic time under the APSP conjecture [Bringmann, Gawrychowski, Mozes, and Weimann, SODA 2018]. In this paper, we break the cubic barrier by showing an O(n ^ {2.9546}) time algorithm for the unweighted tree edit distance problem. We consider an equivalent maximization problem and use a dynamic programming scheme involving matrices with many special properties. By using a decomposition scheme as well as several combinatorial techniques, we reduce tree edit distance to the max-plus product of bounded-difference matrices, which can be solved in truly sub-cubic time [Bringmann, Grandoni, Saha, and Vassilevska Williams, FOCS 2016].
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tree edit distance
tree edit distance
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decomposition strategy
decomposition strategy
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weighted
weighted
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unweighted
unweighted