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
Randomized multidimensional search trees (extended abstract): dynamic sampling
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
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
Entropy-preserving cuttings and space-efficient planar point location
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
Entropy-preserving cuttings and space-efficient planar point location
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Proximate planar point location
Proceedings of the nineteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry CCCG02
Expected asymptotically optimal planar point location
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
Distribution-sensitive point location in convex subdivisions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An experimental study of point location in planar arrangements in CGAL
Journal of Experimental Algorithmics (JEA)
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
Entropy, triangulation, and point location in planar subdivisions
ACM Transactions on Algorithms (TALG)
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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. 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. This problem has been considered before, but existing data structures are all quite complicated. In this paper, 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 &Ogr;(H) average time. We also present empirical evidence for the practical efficiency of this approach.