Planar point location using persistent search trees
Communications of the ACM
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A fast planar partition algorithm, I
Journal of Symbolic Computation
Methods for achieving fast query times in point location data structures
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On the exact worst case query complexity of planar point location
Proceedings of the ninth 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
Efficient Expected-Case Algorithms for Planar Point Location
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
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
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Discrete & Computational Geometry
Optimal Expected-Case Planar Point Location
SIAM Journal on Computing
Distribution-sensitive point location in convex subdivisions
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A static optimality transformation with applications to planar point location
Proceedings of the twenty-seventh annual symposium on Computational geometry
Distance-Sensitive planar point location
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision G of size n and a query distribution D to produce a point location data structure for G. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to D, is &Htilde; + O(&Htilde;1/2+1) where &Htilde;=&Htilde;(G,D) is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in G under the query distribution D. The preprocessing algorithm runs in O(n log n) time and produces a data structure of size O(n). These results are obtained by creating a Steiner triangulation of G that has near-minimum entropy.