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The notion of a centerpoint of a finite set of points in two and higher dimensions is a generalisation of the concept of the median of a (finite) set of points on the real line. In this paper, we present an algorithm for computing a centerpoint of a set of n points in the plane. The algorithm has complexity O(n) which significantly improves the O(n log3 n) complexity of the previously best known algorithm. We use suitable modifications of the ham-sandwich-cut algorithm and the prune-and-search technique to achieve this improvement.

Article Optimal algorithms for some smallest intersection radius problems (extended abstract) Share on Authors: Binay K. Bhattacharya School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6 School of Computing Science, Simon Fraser University, Burnaby, B.C., Canada, V5A 1S6View Profile , Sreesh Jadhav Department of Computer Science, Indian Institute of Technology, Kanpur, India Department of Computer Science, Indian Institute of Technology, Kanpur, IndiaView Profile , Asish Mukhopadhayay Department of Computer Science, Indian Institute of Technology, Kanpur, India Department of Computer Science, Indian Institute of Technology, Kanpur, IndiaView Profile , Jean-Marc Robert School of Computer Science, McGill University, 3480 University St., Montreal, P.Q., Canada, H3A 2A7 School of Computer Science, McGill University, 3480 University St., Montreal, P.Q., Canada, H3A 2A7View Profile Authors Info & Claims SCG '91: Proceedings of the seventh annual symposium on Computational geometryJune 1991 Pages 81–88https://doi.org/10.1145/109648.109657Online:01 June 1991Publication History 1citation335DownloadsMetricsTotal Citations1Total Downloads335Last 12 Months2Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The polynomial Hensel code of a rational function a(x)/ b(x) ϵ F(x), F is a field, is the pair (c(x) d-1(x) mod Xr, n); r is a positive integer and a(x)/ b(x) = (c(x))xn such that c(x) and d(x) have nonzero constant terms. Such a representation scheme was proposed, in analogy with the Hensel code representations of rational numbers, to facilitate arithmetic operations on rational functions and control intermediate expressions well. The difficulty with this scheme was the conversion of such a code to rational function form. In this correspondence, we have given sufficient conditions under which this can be done and have described an algorithm for effecting the conversion. We have also discussed an application, namely, the reduction of a rational function to its simplest form.