In this paper, we introduce and study the Non-Uniform k-Center (NUkC) problem. Given a finite metric space (X, d) and a collection of balls of radii {r1 ≥ · · · ≥ rk}, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation α, such that the union of balls of radius α · ri around the ith center covers all the points in X . This problem naturally...

Goodman, J.E. and R. Pollack, The complexity of point configurations, Discrete Applied Mathematics 31 (1991) 167-180. There are several natural ways to extend the notion of the order of points on a line to higher dimensions. This article focuses on three of them-combinatorial type, order type, and isotopy class-and surveys work done in recent years on the efficient encoding of order types and o...

The light-harvesting apparatus of the purple bacterial photosynthetic unit consists of a pool of peripheral light-harvesting complexes that transfer excitation energy to a reaction center (RC) via the surrounding pigment-protein complex LH1. Recent electron microscopy and atomic force microscopy studies have revealed that RC-LH1 units of Rhodobacter sphaeroides form membrane-bending dimeric com...

We consider the k-Center problem and some generalizations. For k-Center a set of k center vertices needs to be found in a graph G with edge lengths, such that the distance from any vertex of G to its nearest center is minimized. This problem naturally occurs in transportation networks, and therefore we model the inputs as graphs with bounded highway dimension, as proposed by Abraham et al. [SOD...

We study the LowerBoundedCenter (LBC) problem, which is a clustering problem that can be viewed as a variant of the k-Center problem. In the LBC problem, we are given a set of points P in a metric space and a lower bound λ, and the goal is to select a set C ⊆ P of centers and an assignment that maps each point in P to a center of C such that each center of C is assigned at least λ points. The p...

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