Parameterized Complexity of Weighted Target Set Selection

• Item type: SIG Technical Reports(1)
• 公開日: 2024-01-13
• タイトル: Parameterized Complexity of Weighted Target Set Selection
• タイトル / 言語: en
• タイトル: Parameterized Complexity of Weighted Target Set Selection
• 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: Graduate School of Information Sciences, Tohoku University
• 著者所属: Graduate School of Information Sciences, Tohoku University
• 著者所属: Graduate School of Information Sciences, Tohoku University
• 著者所属: Graduate School of Information Sciences, Tohoku University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Sciences, Tohoku University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Sciences, Tohoku University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Sciences, Tohoku University
• 著者所属(英): en
• 著者所属(英): Graduate School of Information Sciences, Tohoku University
• 著者名: Takahiro, Suzuki; Akira, Suzuki; Yuma, Tamura; Xiao, Zhou
• 著者名(英): Takahiro, Suzuki; Akira, Suzuki; Yuma, Tamura; Xiao, Zhou
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Consider a graph G where each vertex has a threshold. A vertex v in G is activated if the number of active vertices adjacent to v is at least as many as its threshold. A vertex subset A0 of G is a target set if eventually all vertices in G are activated by initially activating vertices of A0. The Target Set Selection problem (TSS) involves finding the smallest target set of G with vertex thresholds. This problem has already been extensively studied and is known to be NP-hard even for very restricted conditions. In this paper, we analyze TSS and its weighted variant, called the Weighted Target Set Selection problem (WTSS) from the perspective of parameterized complexity. Let k be a solution size and l be the maximum threshold. We first show that TSS is W[1]-hard for split graphs when parameterized by k + l, and W[2]-hard for cographs when parameterized by k. We also prove that W[2]-hard for trivially perfect graphs when parameterized by k. On the other hand, we show that WTSS can be solved in O(n log n) time for complete graphs. Additionally, we design FPT algorithms for WTSS when parameterized by nd + l, tw + l, and ce, where nd is neighborhood diversity, tw is treewidth, and ce is cluster editing number.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Consider a graph G where each vertex has a threshold. A vertex v in G is activated if the number of active vertices adjacent to v is at least as many as its threshold. A vertex subset A0 of G is a target set if eventually all vertices in G are activated by initially activating vertices of A0. The Target Set Selection problem (TSS) involves finding the smallest target set of G with vertex thresholds. This problem has already been extensively studied and is known to be NP-hard even for very restricted conditions. In this paper, we analyze TSS and its weighted variant, called the Weighted Target Set Selection problem (WTSS) from the perspective of parameterized complexity. Let k be a solution size and l be the maximum threshold. We first show that TSS is W[1]-hard for split graphs when parameterized by k + l, and W[2]-hard for cographs when parameterized by k. We also prove that W[2]-hard for trivially perfect graphs when parameterized by k. On the other hand, we show that WTSS can be solved in O(n log n) time for complete graphs. Additionally, we design FPT algorithms for WTSS when parameterized by nd + l, tw + l, and ce, where nd is neighborhood diversity, tw is treewidth, and ce is cluster editing number.
• 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 2024-AL-196, 号 8, p. 1-6, 発行日 2024-01-13
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8566
• 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