An Incremental Linear-Time Algorithm for Recognizing Interval Graphs

Abstract

The fastest-known algorithm for recognizing interval graphs [S. Booth and S. Lucker, J. Comput. System Sci., 13 (1976), pp. 335–379] iteratively manipulates the system of all maximal cliques of the given graph in a rather complicated way in order to construct a consecutive arrangement (more precisely, a tree representation of all possible consecutive arrangements). This paper presents a much simpler algorithm using a related, but much more informative tree representation of interval graphs. This tree is constructed in an incremental fashion by adding vertices to the graph in a predefined order such that adding a vertex u takes $O(|{\operatorname{Adj}}(u)| + 1)$ amortized time.