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:
“An efficient and valuable man does what he can, whether the community pay him for it or not. The inefficient offer their inefficiency to the highest bidder, and are forever expecting to be put into office. One would suppose that they were rarely disappointed.”
—Henry David Thoreau (1817–1862)
“Tragedy, as you know, is always a fait accompli, whereas terror always has to do with anticipation, with man’s recognition of his own negative potential—with his sense of what he is capable of.”
—Joseph Brodsky (b. 1940)