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1. Enumeration of Perfect Sequences of Chordal Graph

Author

Matsui, Yasuko, Uehara, Ryuhei, Uno, Takeaki, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Hong, Seok-Hee, editor, Nagamochi, Hiroshi, editor, and Fukunaga, Takuro, editor

Published
2008
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4. Enumeration of the perfect sequences of a chordal graph

Author

Matsui, Yasuko, Uehara, Ryuhei, and Uno, Takeaki

Subjects
*COMBINATORIAL enumeration problems, *MATHEMATICAL sequences, *TREE graphs, *COMPUTER algorithms, *POLYNOMIALS, *BOUNDARY value problems
Abstract

Abstract: 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 for each perfect sequence. [ABSTRACT FROM AUTHOR]

Published
2010
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