Range searching is a fundamental primitive in several large-scale applications, and in recent years there has therefore been much effort in developing efficient data structures for range searching in the external memory model. In this model it is assumed that each external-memory access transmits one page of B units of data and one measures the efficiency of an algorithm in terms of the number of such accesses (I/O operations) it performs [1]. While B-trees and their variants have been an unqualified success in supporting external dynamic 1dimensional range searching, they are inefficient at handling more general problems like 2-dimensional or higher-dimensional range searching. Also most of the many elegant main memory data structures developed for 2-dimensional range searching and its special cases are not efficient when mapped to external memory. Recently however, some progress has been made on the construction of external 2-dimensional range searching structures with provably good performance. In [6] the dynamic interval management problem is considered, in which intervals can be inserted and deleted, and given a query interval all current intervals that intersect the query interval must be reported. A key component of external dynamic interval management is answering stabbing queries. Given a set of intervals, to answer a stabbing query with a point q one has to report all intervals that contain q. By regarding an interval [x; y] as the point (x; y) in the plane, a stabbing query with q reduces to the special case of two-sided 2-dimensional range searching called diagonal corner queries with corner (q; q) on the x = y line. The metablock tree developed in [6] answers diagonal corner queries in optimal O(log B N + T=B) I/Os using optimal O(N=B) blocks of external memory, where T denotes the number of points reported. The structure is fairly involved and supports only insertions (not deletions)
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