Sublinear-time approximation and query access for tree edit distance

Determine the best approximation guarantees achievable for tree edit distance under truly sublinear time constraints, and establish whether there is a natural query-access model for rooted ordered forests that supports approximation results analogous to those known for string edit distance.

Background

Sublinear-time approximation algorithms for string edit distance have been studied under query-access models for more than two decades. In contrast, the paper states that no sublinear-time TED approximation was previously known and that even an appropriate way to access the two input forests was unclear.

The paper introduces balanced-parentheses access to the Euler-tour representations of the input forests and obtains the first sublinear-time TED approximation. Nevertheless, the optimal approximation–query-complexity tradeoff and the most natural or powerful access model remain unresolved.