Math @ Duke

Publications [#235433] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Arge, L; Erickson, J; Franciosa, PG; Vitter, JS, Efficient searching with linear constraints,
Journal of Computer and System Sciences, vol. 61 no. 2
(2000),
pp. 194216 [doi]
(last updated on 2017/12/16)
Abstract: We show how to preprocess a set S of points in Rd into an external memory data structure that efficiently supports linearconstraint queries. Each query is the form of linear constraints xd≤a0+Σi = 1d1 aixi; the data structure must report all the points of S that satisfy, the constraint. This problem is called halfspace range searching in the computational geometry literature. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d = 2, we present the first data structure that uses linear space and answers linearconstraint queries using an optimal number of I/Os in the worst case. For d = 3, we present a nearlinearsize data structure that answers queries using an optimal number of I/Os on the average. We present linearsize data structures that can answer ddimensional linearconstraint queries (and even more general ddimensional simplex queries) efficiently in the worst case. For the d = 3 case, we also show how to obtain tradeoffs between space and query time.


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