Practical and Efficient Circle Graph Recognition

Circle graphs are the intersection graphs of chords in a circle. This paper presents the first sub-quadratic recognition algorithm for the class of circle graphs. Our algorithm is O ( n + m ) times the inverse Ackermann function, α ( n + m ), whose value is smaller than 4 for any practical graph. The algorithm is based on a new incremental Lexicographic Breadth-First Search characterization of circle graphs, and a new efficient data-structure for circle graphs, both developed in the paper. The algorithm is an extension of a Split Decomposition algorithm with the same running time developed by the authors in a companion paper.