Maximum weight independent set of circular-arc graph and its application

In this paper, an algorithm is designed to find a maximum weight independent set of a circular-arc graph withn vertices. The weights considered here are all non-negative real numbers and associated with each of the vertex of the graph. The proposed algorithm runs in timeO(n2). Here we shown that the program slots of television channels during 24 hours can be modeled as a circular-arc graph. Each program represents a vertex and number of viewers of that program represents the weight of the corresponding vertex. Two vertices are connected by an edge iff the corresponding program slots have a common program time, i.e., ifIi andIj are the program slots of two programsi andj then the corresponding verticesi andj are connected by an edge iffIi ∩ Ij 6⊋ Φ. We also shown that the non-overlapping program slots with maximum number of viewers can be selected by computing maximum weight independent set on the corresponding circular-arc graph.

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