Data structures and network algorithms
Data structures and network algorithms
On generating all maximal independent sets
Information Processing Letters
Graph classes: a survey
Generating and characterizing the perfect elimination orderings of a chordal graph
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Dirac's theorem on chordal graphs and Alexander duality
European Journal of Combinatorics
Reduced clique graphs of chordal graphs
European Journal of Combinatorics
| Hi-index | 5.23 |
A graph is chordal if and only if it has no chordless cycle of length more than three. The set of maximal cliques in a chordal graph admits special tree structures called clique trees. A perfect sequence is a sequence of maximal cliques obtained by using the reverse order of repeatedly removing the leaves of a clique tree. This paper addresses the problem of enumerating all the perfect sequences. Although this problem has statistical applications, no efficient algorithm has been proposed. There are two difficulties with developing this type of algorithm. First, a chordal graph does not generally have a unique clique tree. Second, a perfect sequence can normally be generated by two or more distinct clique trees. Thus it is hard using a straightforward algorithm to generate perfect sequences from each possible clique tree. In this paper, we propose a method to enumerate perfect sequences without constructing clique trees. As a result, we have developed the first polynomial delay algorithm for dealing with this problem. In particular, the time complexity of the algorithm on average is O(1) for each perfect sequence.