Self-adjusting binary search trees
Journal of the ACM (JACM)
The pairing heap: a new form of self-adjusting heap
Algorithmica
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Randomized algorithms
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Methods for achieving fast query times in point location data structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Entropy-preserving cuttings and space-efficient planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A simple entropy-based algorithm for planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Alternatives to splay trees with O(log n) worst-case access times
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the Dynamic Finger Conjecture for Splay Trees. Part I: Splay Sorting log n-Block Sequences
SIAM Journal on Computing
On the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
SIAM Journal on Computing
Skip Lists: A Probabilistic Alternative to Balanced Trees
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Proximate planar point location
Proceedings of the nineteenth annual symposium on Computational geometry
Navigating low-dimensional and hierarchical population networks
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A pedagogic JavaScript program for point location strategies
Proceedings of the twenty-seventh annual symposium on Computational geometry
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
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In the 2D point searching problem, the goal is to preprocess n points P = {P1,..., pn} in the plane so that, for an online sequence of query points q1, ...,qm, it can quickly be determined which (if any) of the elements of P are equal to each query point qi. This problem can be solved in O(logn) time by mapping the problem to one dimension. We present a data structure that is optimized for answering queries quickly when they are geometrically close to the previous successful query. Specifically, our data structure executes queries in time O(log d(qi-1, qi)), where d is some distance function between two points, and uses O(n logn) space. Our structure works with a variety of distance functions. In contrast, it is proved that, for some of the most intuitive distance functions d, it is impossible to obtain an O (log d(qi-1, qi)) runtime, or any bound that is o(log n).