Extend quasi-subquadratic (1+ε)-approximation techniques to Tree Edit Distance

Determine whether the randomized sample-and-round framework based on curvature bounds and tree total deviation, developed for edit distance and longest common subsequence, can be adapted to tree edit distance to improve the current nearly quadratic running time of (1+ε)-approximation achieved by Boroujeni, Ghodsi, Hajiaghayi, and Seddighin (STOC 2019).

Background

Tree edit distance measures the minimum-cost sequence of node insertions, deletions, and substitutions required to transform one rooted tree into another. The best known (1+ε)-approximation algorithm for tree edit distance runs in nearly quadratic time, due to Boroujeni et al. (STOC 2019).

This paper introduces new techniques—hierarchical subsampling (“sample and round”) combined with curvature control via tree total deviation—to obtain quasi-strongly subquadratic-time (1±o(1))-approximation schemes for edit distance and longest common subsequence on strings. The open question asks whether these techniques can also yield similar speedups for tree edit distance, improving beyond the current nearly quadratic time regime.