A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs

MIN CHIH LIN; FRANCISCO J. SOULIGNAC; JAYME L. SZWARCFITER

Gotenburgo, Suecia

Conferencia; SWAT'08 (11th Scandinavian Workshop on Algorithm Theory); 2008

Department of Computer Science and Engineering, Chalmers University of Technology , Sweden

A circular-arc model is a circle C together with a collection of arcs of C. If no arc is contained in any other then is a proper circular-arc model, and if some point of C is not covered by any arc then is an interval model. A (proper) (interval) circular-arc graph is the intersection graph of a (proper) (interval) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear time recognition algorithms have been described both for the general class and for some of its subclasses. For the isomorphism problem, there exists a polynomial time algorithm for the general case, and a linear time algorithm for interval graphs. In this work we develop a linear time algorithm for the isomorphism problem in proper circular-arc graphs, based on uniquely encoding a proper circular-arc model. Our method relies on results about uniqueness of certain PCA models, developed by Deng, Hell and Huang in [6]. The algorithm is easy to code and uses only basic tools available in almost every programming language.