Delta-Fast Tries: Local Searches in Bounded Universes with Linear Space

Let w ∈ N and U = {0, 1, . . . , 2−1} be a bounded universe of w-bit integers. We present a dynamic data structure for predecessor searching in U . Our structure needs O(log log∆) time for queries and O(log log∆) expected time for updates, where∆ is the difference between the query element and its nearest neighbor in the structure. Our data structure requires linear space. This improves a result by Bose et al. [CGTA, 46(2), pp. 181–189]. The structure can be applied for answering approximate nearest neighbor queries in low dimensions and for dominance queries on a grid.