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.
Bibliographical noteFunding Information:
*This work was first presented by the authors at the First International Japan Conference on Graph Theory and Applications, (Hakone, Japan), June 1986. +This research was sponsored in part by the U.S. Air Force Office of Scientific Research Grant AF 0271 and by the National Science Foundation Grant NSF ECS 8503212.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics