Adaptation of the deterministic fixed-embedding data structure

Determine whether the deterministic dynamic reachability data structure of Diks and Sankowski can be adapted to the specific setting of the randomized online dynamic planar reachability data structure so as to eliminate randomization and amortization while retaining subquadratic update and query bounds.

Background

The online algorithm presented in the paper obtains an amortized bound of O(n^0.664) and uses randomization through the decremental transitive-closure structure of Karczmarz. The authors observe that a deterministic structure based on the work of Diks and Sankowski might replace this component and potentially yield worst-case bounds below n^{2/3}, but they do not establish that the required adaptation is possible.