Identifying other data-structural problems that benefit from an augmented array

Identify data-structural problems beyond static retrieval and filters that can be reformulated to leverage a jointly stored augmented array so as to bypass known time–space barriers and achieve low redundancy without degrading asymptotic operation times.

Background

A central insight of the paper is that storing a retrieval structure together with an augmented array of queries can circumvent the lower bounds that constrain standalone static retrieval, enabling constant-time queries with near-optimal space under suitable parameters.

The authors ask whether similar augmented formulations can unlock improvements for other problems, noting prior success of augmented retrieval as a tool for constructing space-optimal static dictionaries and suggesting potential for a broader theory of augmented data structures.