Efficient data structures for range searching on a grid
Journal of Algorithms
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
Closest-point problems simplified on the RAM
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal bounds for the predecessor problem and related problems
Journal of Computer and System Sciences - STOC 1999
Optimal finger search trees in the pointer machine
Journal of Computer and System Sciences - STOC 2002
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
Data Structures with Local Update Operations
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Cross-document pattern matching
Journal of Discrete Algorithms
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Given a bounded universe {0,1,...,U-1}, we show how to perform predecessor searches in O(loglog@D) expected time, where @D is the difference between the element being searched for and its predecessor in the structure, while supporting updates in O(loglog@D) expected amortized time, as well. This unifies the results of traditional bounded universe structures (which support predecessor searches in O(loglogU) time) and hashing (which supports membership queries in O(1) time). We also show how these results can be applied to approximate nearest neighbour queries and range searching.