Efficient Recognition Algorithms
Determining whether a given graph G = (V, E) is an interval graph can be done in O(|V|+|E|) time by seeking an ordering of the maximal cliques of G that is consecutive with respect to vertex inclusion.
The original linear time recognition algorithm of Booth & Lueker (1976) is based on their complex PQ tree data structure, but Habib et al. (2000) showed how to solve the problem more simply using lexicographic breadth-first search, based on the fact that a graph is an interval graph if and only if it is chordal and its complement is a comparability graph.
Read more about this topic: Interval Graph
Famous quotes containing the words efficient and/or recognition:
“The really efficient laborer will be found not to crowd his day with work, but will saunter to his task surrounded by a wide halo of ease and leisure.”
—Henry David Thoreau (1817–1862)
“That the world can be improved and yet must be celebrated as it is are contradictions. The beginning of maturity may be the recognition that both are true.”
—William Stott (b. 1940)