Stability in circular arc graphs

An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(nlogn) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in O(n + δe) time where n, e, and δ are the number of vertices, edges, and minimum vertex degree, respectively. Our algorithms are based on a simple neighborhood reduction theorem which allows one to reduce any circular arc graph to a special canonical form. © 1988.