Computing a closest point to a query hyperplane in three and higher dimensions

Authors:
Pinaki Mitra;Asish Mukhopadhyay
Affiliations:
NIMC, Alipore, Calcutta, India;School of Computer Science, University of Windsor, Windsor, Canada
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Year:
2003

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Abstract

Given a set S of n points in Ed (d ≥ 3), we consider the problem of computing a closest point to a query hyperplane Q. For d = 3, we report an algorithm whose preprocessing time is in O(n1+Ɛ), space complexity is in O(n log n) and query time is in O(n2/3+Ɛ). For d 3, we adopt a different approach and propose an algorithm which has a query time in O(d log n), in an amortized sense, under a rather strong assumption that we explain in the paper, with O(nd+κ) preprocessing space and, O(nd+1+κ) preprocessing time, both in an expected sense, for some κ 0.