Summary: An Optimal Dynamic Interval Stabbing­Max Data Structure? #
Pankaj K. Agarwal + Lars Arge # Ke Yi §
Abstract
In this paper we consider the dynamic stabbing­max prob­
lem, that is, the problem of dynamically maintaining a set
S of n axis­parallel hyper­rectangles in R d , where each rect­
angle s # S has a weight w(s) # R, so that the rectangle
with the maximum weight containing a query point can be
determined e#ciently. We develop a linear­size structure
for the one­dimensional version of the problem, the interval
stabbing­max problem, that answers queries in worst­case
O(log n) time and supports updates in amortized O(log n)
time. Our structure works in the pointer­machine model of
computation and utilizes many ingredients from recently de­
veloped external memory structures. Using standard tech­
niques, our one­dimensional structure can be extended to
higher dimensions, while paying a logarithmic factor in
space, update time, and query time per dimension. Fur­
thermore, our structure can easily be adapted to external
memory, where we obtain a linear­size structure that answers

Source: Arge, Lars - Department of Computer Science, Aarhus Universitet

Collections: Computer Technologies and Information Sciences