Planar point location using persistent search trees
Communications of the ACM
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Journal of Algorithms
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A fast planar partition algorithm, I
Journal of Symbolic Computation
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
On the exact worst case query complexity of planar point location
Journal of Algorithms
Entropy-preserving cuttings and space-efficient 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
Nearly optimal expected-case planar point location
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
Lower bounds for expected-case planar point location
Computational Geometry: Theory and Applications
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
A pedagogic JavaScript program for point location strategies
Proceedings of the twenty-seventh annual symposium on Computational geometry
A self-adjusting data structure for multidimensional point sets
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Practical distribution-sensitive point location in triangulations
Computer Aided Geometric Design
Distance-Sensitive planar point location
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given a planar polygonal subdivision S, point location involves preprocessing this subdivision into a data structure so that given any query point q, the cell of the subdivision containing q can be determined efficiently. Suppose that for each cell z in the subdivision, the probability pz that a query point lies within this cell is also given. The goal is to design the data structure to minimize the average search time. This problem has been considered before, but existing data structures are all quite complicated. It has long been known that the entropy H of the probability distribution is the dominant term in the lower bound on the average-case search time. In this article, we show that a very simple modification of a well-known randomized incremental algorithm can be applied to produce a data structure of expected linear size that can answer point-location queries in O(H) average time. We also present empirical evidence for the practical efficiency of this approach.