Math @ Duke

Publications [#235515] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Sharir, M; Welzl, E, Algorithms for center and Tverberg points,
ACM Transactions on Algorithms, vol. 5 no. 1
(2008), ISSN 15496325 [doi]
(last updated on 2017/12/13)
Abstract: Given a set S of n points in R3, a point x in R3 is called center point of S if every closed halfspace whose bounding hyperplane passes through x contains at least ⌈n/4⌉ points from S. We present a nearquadratic algorithm for computing the center region, that is the set of all center points, of a set of n points in R3. This is nearly tight in the worst case since the center region can have (n2) complexity. We then consider sets S of 3n points in the plane which are the union of three disjoint sets consisting respectively of n red, n blue, and n green points. A point x in R2 is called a colored Tverberg point of S if there is a partition of S into n triples with one point of each color, so that x lies in all triangles spanned by these triples. We present a first polynomialtime algorithm for recognizing whether a given point is a colored Tverberg point of such a 3colored set S. © 2008 ACM.


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