In this paper, we consider the problem of optimally placing a given number of wavelength converters on a path to minimize the call blocking probability. Using a simple performance model, we first prove that uniform spacing of converters is optimal for the end-to-end performance when link loads are uniform and statistically independent. We then show that significant gains are achievable with opt...

In this paper we study the last round of the discrete Voronoi game in R, a problem which is also of independent interest in competitive facility location. The game consists of two players P1 and P2, and a finite set U of users in the plane. The players have already placed two disjoint sets of facilities F and S, respectively in the plane. The game begins with P1 placing a new facility followed ...

A well-known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain Ω, so as to maximize the torsional rigidity of the resulting rod; moreover, the proportion of these materials is prescribed. Such a problem may not have a classical solution as the optimal design may contain homogenization regions, where the two materials are...