Dynamic indexability and lower bounds for dynamic one-dimensional range query indexes
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Dynamic external hashing: the limit of buffering
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Dynamic Indexability and the Optimality of B-Trees
Journal of the ACM (JACM)
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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, despite the fact that the problem can be solved optimally in internal memory with linear space and O(log N+K) query time, 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 ε0. With linear space, the best obtainable query bound is O(log 2 N+K/B) if a linear output term O(K/B) is desired. 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.