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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Bibliographic Details
Published in:	Discrete Applied Mathematics Vol. 334; pp. 139 - 144
Main Authors:	Araki, Toru, Saito, Ryuya
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 31.07.2023
Subjects:	Domination Linear time algorithm Proper interval graphs Secure domination Domination Linear time algorithm Proper interval graphs Secure domination
ISSN:	0166-218X, 1872-6771
Online Access:	Get full text
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Description
Summary:	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.
ISSN:	0166-218X 1872-6771
DOI:	10.1016/j.dam.2023.04.002