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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/7872

Title: Counting the number of independent sets in chordal graphs
Authors: Okamoto, Yoshio
Uno, Takeaki
Uehara, Ryuhei
Keywords: Chordal graph
counting
enumeration
independent set
NP-completeness
#P-completeness
polynomial time algorithm
Issue Date: 2008-06
Publisher: Elsevier
Magazine name: Journal of Discrete Algorithms
Volume: 6
Number: 2
Start page: 229
End page: 242
DOI: 10.1016/j.jda.2006.07.006
Abstract: We study some counting and enumeration problems for chordal graphs, especially concerning independent sets. We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (2) a linear-time algorithm for counting the number of maximum independent sets; (3) a polynomial-time algorithm for counting the number of independent sets of a fixed size. With similar ideas, we show that enumeration (namely, listing) of the independent sets, the maximum independent sets, and the independent sets of a fixed size in a chordal graph can be done in constant amortized time per output. On the other hand, we prove that the following problems for a chordal graph are #P-complete: (1) counting the number of maximal independent sets; (2) counting the number of minimum maximal independent sets. With similar ideas, we also show that finding a minimum weighted maximal independent set in a chordal graph is NP-hard, and even hard to approximate.
Rights: NOTICE: This is the author's version of a work accepted for publication by Elsevier. Yoshio Okamoto, Takeaki Uno, Ryuhei Uehara, Journal of Discrete Algorithms, 6(2), 2008, 229-242, http://dx.doi.org/10.1016/j.jda.2006.07.006
URI: http://hdl.handle.net/10119/7872
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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