TY - JOUR
T1 - A simple entropy-based algorithm for planar point location
JF - ACM Transactions on Algorithms (TALG)
Y1 - 2007
A1 - Arya,Sunil
A1 - Malamatos,Theocharis
A1 - Mount, Dave
KW - Entropy
KW - expected-case complexity
KW - Point location
KW - polygonal subdivision
KW - randomized algorithms
KW - trapezoidal maps
AB - 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. This problem has been considered before, but existing data structures are all quite complicated. 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. In this article, 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 O(H) average time. We also present empirical evidence for the practical efficiency of this approach.
VL - 3
SN - 1549-6325
UR - http://doi.acm.org/10.1145/1240233.1240240
CP - 2
M3 - 10.1145/1240233.1240240
ER -