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このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/3276
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| タイトル: | Linear-time counting algorithms for independent sets in chordal graphs |
| 著者: | Okamoto, Y
Uno, T
Uehara, R |
| キーワード: | chordal graph
counting
enumeration
independent set
NP-completeness
#P-completeness
polynomial time algorithm |
| 発行日: | 2005 |
| 出版者: | SPRINGER-VERLAG |
| 誌名: | Lecture Notes in Computer Science : including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics |
| 巻: | 3787 |
| 開始ページ: | 433 |
| 終了ページ: | 444 |
| DOI: | 10.1007/11604686_38 |
| 抄録: | 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: | This is the author-created version of Springer Berlin / Heidelberg, Yoshio Okamoto, Takeaki Uno and Ryuhei Uehara, Lecture Notes in Computer Science(Graph-Theoretic Concepts in Computer Science), 3787, 2005, 433-444. The original publication is available at www.springerlink.com, http://www.springerlink.com/content/768430570227u750 |
| URI: | http://hdl.handle.net/10119/3276 |
| 資料タイプ: | author |
| 出現コレクション: | f10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
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| S-49.pdf | | 83Kb | Adobe PDF | 見る/開く |
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