Given a bounded universe {0, 1, . . . , U −1}, we show how to perform (successor) searches in O(log log ∆) expected time and updates in O(log log ∆) expected amortized time, where ∆ is the rank difference between the element being searched for and its successor in the structure. This unifies the results of traditional bounded universe structures (which support successor searches in O(log log U ) time) and hashing (which supports exact searches in O(1) time). We also show how these results can be extended to answer approximate nearest neighbour queries in low dimensions.
Finally, a query time of O(log log Δ), where Δ is the difference between the element queried and the element returned, can also be obtained REF .
Fast local searches and updates in bounded universes
CCCG
Mathematics Computer Science