TY - CONF
T1 - Entropy-preserving cuttings and space-efficient planar point location
T2 - Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Y1 - 2001
A1 - Arya,Sunil
A1 - Malamatos,Theocharis
A1 - Mount, Dave
AB - 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.
JA - Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
T3 - SODA '01
PB - Society for Industrial and Applied Mathematics
CY - Philadelphia, PA, USA
SN - 0-89871-490-7
UR - http://dl.acm.org/citation.cfm?id=365411.365456
ER -