@conference {15645, title = {Entropy-preserving cuttings and space-efficient planar point location}, booktitle = {Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms}, series = {SODA {\textquoteright}01}, year = {2001}, month = {2001///}, pages = {256 - 261}, publisher = {Society for Industrial and Applied Mathematics}, organization = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, abstract = {Point location is the problem of preprocessing a planar polygonal subdivision S into a data structure in order to determine efficiently the cell of the subdivision that contains a given query point. Given the probabilities pz that the query point lies within each cell z ∈ S, a natural question is how to design such a structure so as to minimize the expected-case query time. The entropy H of the probability distribution is the dominant term in the lower bound on the expected-case search time. Clearly the number of edges n of the subdivision is a lower bound on the space required. There is no known approach that simultaneously achieves the goals of H + \&Ogr;(H) query time and \&Ogr;(n) space. In this paper we introduce entropy-preserving cuttings and show how to use them to achieve query time H + \&Ogr;(H), using only \&Ogr;(n log* n) space.}, isbn = {0-89871-490-7}, url = {http://dl.acm.org/citation.cfm?id=365411.365456}, author = {Arya,Sunil and Malamatos,Theocharis and Mount, Dave} }