Optimal External Memory Planar Point Enclosure

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Optimal External Memory Planar Point Enclosure
Abstract. In this paper we study the external memory planar point enclosure problem: Given N axis-parallel 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/O-efficiently. This problem has important applications in e.g. spatial and temporal databases, and is dual to the important and well-studied orthogonal range searching problem. Surprisingly, 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(logB N + K/B) I/Os, where B is the disk block size. To obtain this bound, Ω(N/B1− ) disk blocks are needed for some constant > 0. With linear space, the best obtainable query bound is O(log2 N + K/B). To show this we prove a general lower bound on the tradeoff between the size of the data structure and its query cost. We also develop a family of structures with matching space and query bounds.
Lars Arge, Vasilis Samoladas, Ke Yi
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where ESA
Authors Lars Arge, Vasilis Samoladas, Ke Yi
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