Abstract
This paper proves three lower bounds for variants of the following rangesearching problem: Given n weighted points inR d andn axis-parallel boxes, compute the sum of the weights within each box: (1) if both additions and subtractions are allowed, we prove that Ω(n log logn) is a lower bound on the number of arithmetic operations; (2) if subtractions are disallowed the lower bound becomes Ω(n(logn/loglogn)d-1), which is nearly optimal; (3) finally, for the case where boxes are replaced by simplices, we establish a quasi-optimal lower bound of Ω(n2-2/(d+1))/polylog(n).
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A preliminary version of this paper appeared inProc. 27th Ann. ACM Symp. on Theory of Computing, May 1995, pp. 733–740. This work was supported in part by NSF Grant CCR-93-01254 and the Geometry Center, University of Minnesota, an STC funded by NSF, DOE, and Minnesota Technology, Inc.
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Chazelle, B. Lower bounds for off-line range searching. Discrete Comput Geom 17, 53–65 (1997). https://doi.org/10.1007/BF02770864
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DOI: https://doi.org/10.1007/BF02770864