Expected asymptotically optimal planar point location
نویسندگان
چکیده
منابع مشابه
Optimal Expected-Case Planar Point Location
Point location is the problem of preprocessing a planar polygonal subdivision S of size n into a data structure in order to determine efficiently the cell of the subdivision that contains a given query point. We consider this problem from the perspective of expected query time. We are given the probabilities pz that the query point lies within each cell z ∈ S. The entropy H of the resulting dis...
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We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which cell of the subdivision contains a given query point, so as to minimize the expected search time....
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Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worst-case query time, there has been surprisingly little theoretical work on expected-case query time. We are given an n-vertex planar polygonal subdivision S satisfying some weak assumptions (satisfied, for example, by all convex...
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Given a planar polygonal subdivision S, the point location problem is to preprocess S into a data structure so that the cell of the subdivision that contains a given query point can be reported efficiently. Suppose that we are given for each cell z ∈ S the probability pz that a query point lies in z. The entropy H of the resulting discrete probability distribution is a lower bound on the expect...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2004
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2004.03.010