Space-efficient algorithm for computing a centerpoint of a set of points in R2

We study a space-efficient algorithm for computing a centerpoint for a set P of n points in R2, where the points in P are given in a read-only array. We propose an algorithm that finds a centerpoint of P in O(T(n2)log3⁡n) time using O(S(n2)) extra space, where T(n) and S(n) are the time and extra sp...

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Bibliographic Details
Published in:Theoretical computer science Vol. 615; pp. 61 - 70
Main Authors: Bhattacharya, Binay K., Nandy, Subhas C., Roy, Sasanka
Format: Journal Article
Language:English
Published: Elsevier B.V 15.02.2016
Subjects:
Arrangement
Centerpoint
Duality
Prune-and-search
Space-efficient algorithm
Space-efficient algorithm
Duality
Prune-and-search
Centerpoint
Arrangement
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We study a space-efficient algorithm for computing a centerpoint for a set P of n points in R2, where the points in P are given in a read-only array. We propose an algorithm that finds a centerpoint of P in O(T(n2)log3⁡n) time using O(S(n2)) extra space, where T(n) and S(n) are the time and extra space complexities of computing the median among a set of n elements stored in a read-only array. We also present the applications of this algorithm for computing the Tukey depth and k-hull of a point set in R2.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.11.048