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(log B N+K/B) I/Os, where B is the disk block size. To obtain this bound, Ω(N/B 1 − ε) disk blocks are needed for some constant ε> 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.
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Arge, L., Samoladas, V., Yi, K. (2004). Optimal External Memory Planar Point Enclosure. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_6
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DOI: https://doi.org/10.1007/978-3-540-30140-0_6
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