Computing the Center Region and Its Variants

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10167)


We present an \(O(n^2\log ^4 n)\)-time algorithm for computing the center region of a set of n points in the three-dimensional Euclidean space. This improves the previously best known algorithm by Agarwal, Sharir and Welzl, which takes \(O(n^{2+\epsilon })\) time for any \(\epsilon > 0\). It is known that the complexity of the center region is \(\varOmega (n^2)\), thus our algorithm is almost tight.

The second problem we consider is computing a colored version of the center region in the two-dimensional Euclidean space. We present an \(O(n\log ^4 n)\)-time algorithm for this problem.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringPOSTECHPohangSouth Korea

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