In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for ”learning” piecewise linear scalar functions in two settings we term ”approximation” (where an ”oracle” outputs accurate functi...

If two sets of vectors (in Classification

We prove transversality theorems for piecewise linear manifolds, maps and polyhedra. Our main result is that given two closed manifolds contained in a third, then one can be ambient isotoped until it is transversal to the other. This result is then extended to maps and polyhedra. The transversality theory for smooth manifolds was initiated by Thorn in his classical paper [8], and has been exten...

The medial axis transform (or MAT) is a representation of an object as an in nite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a nite union of balls. Using this approximate MAT we de ne a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a suÆciently dense sam...

The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a sufficiently den...