Building bridges between convex regions

Abstract

In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in d-dimensional space, and we wish to find a minimum-cost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each region need to travel to meet the salesman. We show that constant-factor approximations to the TSBP and several similar problems can be obtained by visiting the centers of the smallest enclosing spheres of the regions. (C) 2002 Elsevier Science B.V. All rights reserved.