## Efficient Computation of the Tree Edit Distance

*Mateusz Pawlik, Nikolaus Augsten* - TODS'15

We consider the classical tree edit distance between ordered labelled trees, which is defined as the minimum-cost sequence of node edit operations that transform one tree into another. The state-of-the-art solutions for the tree edit distance are not satisfactory. The main competitors in the field either have optimal worst-case complexity but the worst case happens frequently, or they are very efficient for some tree shapes but degenerate for others. This leads to unpredictable and often infeasible runtimes. There is no obvious way to choose between the algorithms.

In this article we present RTED, a robust tree edit distance algorithm.
The asymptotic complexity of our algorithm is smaller than or equal to the
complexity of the best competitors for any input instance, that is, our
algorithm is both efficient and worst-case optimal. This is achieved by
computing a dynamic decomposition strategy that depends on the input trees.
RTED is shown optimal among all algorithms that use LRH
(*left-right-heavy*) strategies, which include RTED and the fastest
tree edit distance algorithms presented in literature. In our experiments
on synthetic and real-world data we empirically evaluate our solution and
compare it to the state-of-the-art.