An Optimal Algorithm for Finding a Maximum Independent Set of a Circular-Arc Graph

A new algorithm is presented for finding a maximum independent set of a circular-arc graph. When the graph is given in the form of a family of n arcs, our algorithm requires only $O(n \cdot \log n)$ time and $O(n)$ space. Furthermore, if the endpoints of the arcs are already sorted, it runs in $O(n)$ time. This algorithm is time- and space-optimal to within a constant factor.