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Summary: I/O-EÆcient Structures for Orthogonal
Range-Max and Stabbing-Max Queries
Pankaj K. Agarwal ? , Lars Arge ?? , Jun Yang, and Ke Yi
Department of Computer Science
Duke University, Durham, NC 27708, USA
fpankaj,large,junyang,yikeg@cs.duke.edu
Abstract. We develop several linear or near-linear space and I/O-
eÆcient dynamic data structures for orthogonal range-max queries and
stabbing-max queries. Given a set of N weighted points in R d , the range-
max problem asks for the maximum-weight point in a query hyper-
rectangle. In the dual stabbing-max problem, we are given N weighted
hyper-rectangles, and we wish to nd the maximum-weight rectangle
containing a query point. Our structures improve on previous structures
in several important ways.
1 Introduction
Range searching and its variants have been studied extensively in the computa-
tional geometry and database communities because of their many important ap-
plications. Range-aggregate queries, such as range-count, range-sum, and range-
max queries, are some of the most commonly used versions of range searching in
database applications. Since many such applications involve massive amounts of
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