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http://hdl.handle.net/10119/7872
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| 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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