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Optimal External Memory Planar Point Enclosure

Summary: Optimal External Memory
Planar Point Enclosure
Lars Arge 1# , Vasilis Samoladas 2 , and Ke Yi 1#
1 Department of Computer Science, Duke University, Durham, NC 27708, USA.
2 Technical University of Crete, Greece. vsam@softnet.tuc.gr
Abstract. In this paper we study the external memory planar point en­
closure problem: Given N axis­parallel rectangles in the plane, construct
a data structure on disk (an index) such that all K rectangles containing
a query point can be reported I/O­e#ciently. This problem has important
applications in e.g. spatial and temporal databases, and is dual to the
important and well­studied orthogonal range searching problem. Surpris­
ingly, we show that one cannot construct a linear sized external memory
point enclosure data structure that can be used to answer a query in
O(log B N + K/B) I/Os, where B is the disk block size. To obtain this
bound,# (N/B 1-# ) disk blocks are needed for some constant # > 0. With
linear space, the best obtainable query bound is O(log 2 N + K/B). To
show this we prove a general lower bound on the tradeo# between the
size of the data structure and its query cost. We also develop a family of
structures with matching space and query bounds.


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


Collections: Computer Technologies and Information Sciences