文章基本信息

标题：Neighborhood Inclusions for Minimal Dominating Sets Enumeration: Linear and Polynomial Delay Algorithms in P_7 - Free and P_8 - Free Chordal Graphs
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作者：defrain_et_al:LIPIcs: : , author {Oscar Defrain ; Lhouari Nourine
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：149
页码：1-16
DOI：10.4230/LIPIcs.ISAAC.2019.63
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In [M. M. KantÃ©, V. Limouzy, A. Mary, and L. Nourine. On the enumeration of minimal dominating sets and related notions. SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014.] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-free chordal graphs. In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k. In particular, we give O(n+m) and O(n^3 * m) delays algorithms in the classes of P_7-free and P_8-free chordal graphs. As for P_k-free chordal graphs for k >= 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.
关键词：Minimal dominating sets; enumeration algorithms; linear delay enumeration; chordal graphs; forbidden induced paths