Wireless ATM layouts for chain networks

In this paper we consider the problem of constructing ATM layouts for wireless networks in which mobile users can move along a chain of base stations. We first show that deciding the existence of a layout with maximum hop count h, load l and channel distance d is NP-complete for every fixed value of d greater or equal to 1. We then provide optimal layout constructions for the case d less than or equal to 2. Finally, optimal layout constructions are obtained also for any d within the class of the so-called canonic layouts, that so far have always been shown to be the optimal ones.