RTED: A Robust Algorithm for the Tree Edit Distance

TL;DR

RTED is a new algorithm for tree edit distance that guarantees worst-case optimality and efficiency across all input types, outperforming previous algorithms in both theory and practice.

Contribution

The paper introduces RTED, a robust and worst-case optimal tree edit distance algorithm, and establishes the class of LRH algorithms, demonstrating RTED's superior performance.

Findings

RTED has asymptotic complexity equal or better than existing algorithms.

RTED outperforms previous LRH algorithms in runtime.

Experimental results show RTED's efficiency on synthetic and real data.

Abstract

We consider the classical tree edit distance between ordered labeled 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 paper we present RTED, a robust tree edit distance algorithm. The asymptotic complexity of RTED is smaller or equal to the complexity of the best competitors for any input instance, i.e., RTED is both efficient and worst-case optimal. We introduce the class of LRH (Left-Right-Heavy) algorithms, which includes RTED and the fastest tree edit distance algorithms presented in literature. We prove that RTED outperforms all previously proposed LRH algorithms in terms of runtime complexity. In our experiments on synthetic and real world data we empirically evaluate our solution and compare it to the state-of-the-art.