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In this paper we consider the problem of locating an axis-parallel rectangle in the plane such that the sum of distances between the rectangle and a finite point set is minimized, where the distance is measured by the Manhattan norm ℓ1. In this way we solve an extension of the Weber problem to extensive facility location. As a model, our problem is appropriate for position sensing of rectangular...
In our paper we approximate a set of given points by a general circle. More precisely, given two norms k1 and k2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k1 such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k2. We present results...
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