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.

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