Fast local searches and updates in bounded universes

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.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Prosenjit Bose, Karim Douïeb, Vida Dujmovic, John Howat, Pat Morin
• Keywords: Amortized Time, Approximate Nearest Neighbour, CCCG 2010, Computational Geometry, Successor Searches