Scheduling of a Smart Antenna: Capacitated Coloring of Unit Circular-Arc Graphs

We consider scheduling problems that are motivated by an optimization of the transmission schedule of a smart antenna. In these problems we are given a set of messages and a conflict graph that specifies which messages cannot be transmitted concurrently. In our model the conflict graph is a unit circular-arc graph. Two variants of the problem are considered: c-mbl and nu-c-mbl. In c-mbl, the messages have unit demands, whereas in nu-c-mbl demands are arbitrary. We present an optimal algorithm for c-mbl and a 3-approximation algorithm for nu-c-mbl.