Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs

• Item type: SIG Technical Reports(1)
• 公開日: 2014-02-24
• タイトル: Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs
• タイトル / 言語: en
• タイトル: Polynomial-Time Algorithms for Subgraph Isomorphism in Small Graph Classes of Perfect Graphs
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: School of Information Science, Japan Advanced Institute of Science and Technology
• 著者所属: School of Information Science, Japan Advanced Institute of Science and Technology
• 著者所属: School of Information Science, Japan Advanced Institute of Science and Technology
• 著者所属(英): en
• 著者所属(英): School of Information Science, Japan Advanced Institute of Science and Technology
• 著者所属(英): en
• 著者所属(英): School of Information Science, Japan Advanced Institute of Science and Technology
• 著者所属(英): en
• 著者所属(英): School of Information Science, Japan Advanced Institute of Science and Technology
• 著者名: Matsuo, Konagaya; Yota, Otachi; Ryuhei, Uehara
• 著者名(英): Matsuo, Konagaya; Yota, Otachi; Ryuhei, Uehara
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Given two graphs, Subgraph Isomorphism is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second graph (the pattern graph). This problem is NP-complete for very restricted graph classes such as connected proper interval graphs. Only a few cases are known to be polynomial-time solvable even if we restrict the graphs to be perfect. For example, if both graphs are co-chain graphs, then the problem can be solved in linear time. In this paper, we present a polynomial-time algorithm for the case where the base graphs are chordal graphs and the pattern graphs are co-chain graphs. We also present a linear-time algorithm for the case where the base graphs are trivially perfect graphs and the pattern graphs are threshold graphs. These results answer some of the open questions of Kijima et al. [Discrete Math. 312, pp. 3164-3173, 2012]. To present a complexity contrast, we then show that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Given two graphs, Subgraph Isomorphism is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second graph (the pattern graph). This problem is NP-complete for very restricted graph classes such as connected proper interval graphs. Only a few cases are known to be polynomial-time solvable even if we restrict the graphs to be perfect. For example, if both graphs are co-chain graphs, then the problem can be solved in linear time. In this paper, we present a polynomial-time algorithm for the case where the base graphs are chordal graphs and the pattern graphs are co-chain graphs. We also present a linear-time algorithm for the case where the base graphs are trivially perfect graphs and the pattern graphs are threshold graphs. These results answer some of the open questions of Kijima et al. [Discrete Math. 312, pp. 3164-3173, 2012]. To present a complexity contrast, we then show that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN1009593X
• 書誌情報: 研究報告アルゴリズム（AL）; 巻 2014-AL-147, 号 12, p. 1-6, 発行日 2014-02-24
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会