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.


Line Segment Convex Hull Time Algorithm Colored Version Lower Envelope 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringPOSTECHPohangSouth Korea

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