Affiliation:
1. Princeton Univ., Princeton, NJ
Abstract
We establish lower bounds on the complexity of orthogonal range reporting in the static case. Given a collection of
n
points in
d
-space and a box [
a
1
,
b
1
] X … X [
a
d
,
b
d
], report every point whose
i
th coordinate lies in [
a
i
, b
i
], for each
i
= l, … ,
d
. The collection of points is fixed once and for all and can be preprocessed. The box, on the other hand, constitutes a query that must be answered online. It is shown that on a pointer machine a query time of
O
(
k
+ polylog(
n
)), where
k
is the number of points to be reported, can only be achieved at the expense of Ω(
n
(log
n
/log log
n
)
d
-1
) storage. Interestingly, these bounds are optimal in the pointer machine model, but they can be improved (ever so slightly) on a random access machine. In a companion paper, we address the related problem of adding up weights assigned to the points in the query box.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
85 articles.
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