We consider nite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the nite arrangements Cn such that conv Cn Cn + K, where Cn is a subset of a covering lattice for K (which satisses some natural conditions). We prove that for a xed lattice the optimal arrangement (measured with the parametric density) is either a sausage, a socalled double sausage ...

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been studied extensively in the context of crossing number problems. We consider a natural class of simple topological drawings of complete bipartite graphs, in ...

This article addresses a single row facility layout problem where the objective is to optimize the arrangement of some rectangular facilities with different dimensions on a line. Regarding the NP-Hard nature of the considered problem, a hybrid meta-heuristic algorithm based on simulated annealing has been proposed to obtain a near optimal solution. A number of test problems are randomly generat...

We consider an optimal design of composite hydrophones consisting of parallel piezoelectric PZT rods that are embedded in a porous polymer matrix. Given the material properties of the polymer and PZT ceramic, we have optimally designed the piezocomposite to maximize the hydrostatic coupling factor, hydrophone figure of merit, or electromechanical coupling factor, using the methods of homogeniza...

We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies (n!=(n ? k ? 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area (n!) 2 : This answers an open problem posed by Ak-ers, Harel and Krishnamurthy 1]. The method is also applied to the pancake graph. The results provide optimal upper and lower bounds for crossing numbers of t...

We provide new combinatorial bounds on the complexity of a face in an arrangement of segments in the plane. In particular, we show that the complexity of a single face in an arrangement of n line segments determined by h endpoints is O(h logh). While the previous upper bound, O(nn(n)), is tight for segments with distinct endpoints, it is far from being optimal when n = (h 2). Our result shows t...

A hyperplane arrangement is a polyhedral cell complex where the relative position of each cell of the arrangement and the composing hyperplanes are summarized by a sign vector computable in polynomial time. This tool from computational geometry enables the development of a fast and efficient algorithm that translates the composition of hybrid systems into a piecewise affine model. The tool prov...