Linear-time generation of random chordal graphs

Abstract

Chordal graphs form one of the most well studied graph classes. Several graph problems that are NP-hard in general become solv-able in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the latter, approxima-tion algorithms, parameterized algorithms, and algorithms with moder-ately exponential or sub-exponential running time have been designed. Chordal graphs have also gained increasing interest during the recent years in the area of enumeration algorithms. Being able to test these algorithms on instances of chordal graphs is crucial for understanding the concepts of tractability of hard problems on graph classes. Unfortu-nately, only few published papers give algorithms for generating chordal graphs. Even in these papers, only very few methods aim for generating a large variety of chordal graphs. Surprisingly, none of these methods is based on the “intersection of subtrees of a tree” characterization of chordal graphs. In this paper, we give an algorithm for generating chordal graphs, based on the characterization that a graph is chordal if and only if it is the intersection graph of subtrees of a tree. The complexity of our algorithm is linear in the size of the produced graph. We give test results to show the variety of chordal graphs that are produced, and we compare these results to existing results.