AAA 2 1 Introduction

In this short note we give a characterization of the support map from classical convexity. We show it is the unique additive transformation from the class of closed convex sets in Rn which include 0 to the class of positive 1-homogeneous functions on Rn. This will be a consequence of a theorem about transforms from the class of convex sets to itself which preserve Minkowski addition. © 2009 Els...

Given a disk O in the plane called the objective, we want to find n small disks P1, . . . , Pn called the pupils such that ⋃n i,j=1 Pi ⊖ Pj ⊇ O, where ⊖ denotes the Minkowski difference operator, while minimizing the number of pupils, the sum of the radii or the total area of the pupils. This problem is motivated by the construction of very large telescopes from several smaller ones by so-calle...

We consider here a variation of Vector Addition Systems where one counter can be tested for zero. We extend the reachability proof for Vector Addition System recently published by Leroux to this model. This provides an alternate, more conceptual proof of the reachability problem that was originally proved by Reinhardt.

We consider the problem of listing faces of the Minkowski sum of several V-polytopes in R. An algorithm for listing all faces of dimension up to j is presented, for any given 0 ≤ j ≤ d − 1. It runs in time polynomial in the sizes of input and output.

Minkowski sums of simplices in Rn form an interesting class of polytopes that seem to emerge in various situations. In this paper we discuss the Minkowski sum of the simplices ∆k−1 in Rn where k and n are fixed, their flags and some of their face lattice structure. In particular, we derive a closed formula for their exponential generating flag function. These polytopes are simple, include both ...

AAA 2

We consider the problem of traveling the contour of the set of all points that are within distance 1 of a connected planar curve arrangement P, forming an embedding of the graph G. We show that if the overall length of P is L, there is a closed roundtrip that visits all points of the contour and has length no longer than 2L + 2. This result carries over in a more general setting: if R is a comp...