Correcting the algorithm for a minimum secure dominating set of proper interval graphs by Zou, Liu, Hsu and Wang
Zou et al. (2019) proposed an algorithm for calculating a minimum secure dominating set of a proper interval graph. However, we find a counterexample for which the algorithm outputs an incorrect subset of vertices. In this paper, we provide a modified algorithm and the proofs for the correctness.
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| Veröffentlicht in: | Discrete Applied Mathematics Jg. 334; S. 139 - 144 |
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Elsevier B.V
31.07.2023
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | Zou et al. (2019) proposed an algorithm for calculating a minimum secure dominating set of a proper interval graph. However, we find a counterexample for which the algorithm outputs an incorrect subset of vertices. In this paper, we provide a modified algorithm and the proofs for the correctness. |
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| AbstractList | Zou et al. (2019) proposed an algorithm for calculating a minimum secure dominating set of a proper interval graph. However, we find a counterexample for which the algorithm outputs an incorrect subset of vertices. In this paper, we provide a modified algorithm and the proofs for the correctness. |
| Author | Saito, Ryuya Araki, Toru |
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| Keywords | Domination Linear time algorithm Proper interval graphs Secure domination |
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| References | Klostermeyer, Mynhardt (b15) 2008; 28 Zou, Liu, Chang, Hsu (b19) 2022; 311 Jha, Pradhan, Banerjee (b13) 2019; 145 Zou, Liu, Hsu, Wang (b20) 2019; 260 Castillano, Ugbinada (b9) 2014; 8 Chartrand, Lesniak, Zhang (b10) 2011 Cockayne, Grobler, Gründlingh, Munganga, van Vuuren (b11) 2005; 67 Looges, Olariu (b17) 1993; 25 Arumugam, Ebadi, Manrique (b4) 2014 Golumbic (b12) 2004 Booth, Lueker (b5) 1976; 13 Burger, de Villiers, van Vuuren (b7) 2014; 171 Merouane, Chellali (b18) 2015; 115 Araki, Yumoto (b3) 2018; 236 Li, Shao, Xu (b16) 2017; 40 Araki, Miyazaki (b1) 2018; 247 Araki, Yamanaka (b2) 2019; 262 Burger, de Villiers, van Vuuren (b8) 2016; 39 Kišek, Klavžar (b14) 2021; 172 Burger, de Villiers, Vuuren (b6) 2013 Li (10.1016/j.dam.2023.04.002_b16) 2017; 40 Kišek (10.1016/j.dam.2023.04.002_b14) 2021; 172 Araki (10.1016/j.dam.2023.04.002_b1) 2018; 247 Merouane (10.1016/j.dam.2023.04.002_b18) 2015; 115 Araki (10.1016/j.dam.2023.04.002_b3) 2018; 236 Zou (10.1016/j.dam.2023.04.002_b20) 2019; 260 Golumbic (10.1016/j.dam.2023.04.002_b12) 2004 Chartrand (10.1016/j.dam.2023.04.002_b10) 2011 Burger (10.1016/j.dam.2023.04.002_b7) 2014; 171 Araki (10.1016/j.dam.2023.04.002_b2) 2019; 262 Klostermeyer (10.1016/j.dam.2023.04.002_b15) 2008; 28 Looges (10.1016/j.dam.2023.04.002_b17) 1993; 25 Burger (10.1016/j.dam.2023.04.002_b6) 2013 Arumugam (10.1016/j.dam.2023.04.002_b4) 2014 Booth (10.1016/j.dam.2023.04.002_b5) 1976; 13 Cockayne (10.1016/j.dam.2023.04.002_b11) 2005; 67 Burger (10.1016/j.dam.2023.04.002_b8) 2016; 39 Zou (10.1016/j.dam.2023.04.002_b19) 2022; 311 Castillano (10.1016/j.dam.2023.04.002_b9) 2014; 8 Jha (10.1016/j.dam.2023.04.002_b13) 2019; 145 |
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| SubjectTerms | Domination Linear time algorithm Proper interval graphs Secure domination |
| Title | Correcting the algorithm for a minimum secure dominating set of proper interval graphs by Zou, Liu, Hsu and Wang |
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