Abstract
In this paper we propose a generalized Roman domination problem called connected strong k-Roman dominating set problem. It is NP-hard even in a unit ball graph. Unit ball graphs are the intersection graphs of equal sized balls in the three-dimensional space, they are widely used as a mathematical model for wireless sensor networks and some problems in computational geometry. This paper presents the first constant approximation algorithm with a guaranteed performance ratio at most \(6(k+2)\) in unit ball graphs, where k is a positive integer.
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The authors would like to thank the anonymous reviewers for their valuable suggestions and comments that have helped a lot to improve the quality of the paper.
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L. Wang: This author was partially supported by National Natural Science Foundation of China (61425024), the Jiangsu Province Double Innovation Talent Program and National Thousand Young Talents Program. Y. Shi: This author was partially supported by National Natural Science Foundation of China (11471003). Z. Zhang: This author was partially supported in part by NSFC (11771013, 11531011, 61751303) and the Zhejiang Provincial Natural Science Foundation of China (LD19A010001, LY19A010018). Z.-B. Zhang: This author was partially supported by the Natural Science Foundation of Guangdong Province (2016A030313829) and the Talent Project of Guangdong Industry Polytechnic (RC2016-004 and 2B141403). X. Zhang: This author was partially supported by National Natural Science Foundation of China (11871280, 11471003) and Qing Lan Project.
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Wang, L., Shi, Y., Zhang, Z. et al. Approximation algorithm for a generalized Roman domination problem in unit ball graphs. J Comb Optim 39, 138–148 (2020). https://doi.org/10.1007/s10878-019-00459-1
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DOI: https://doi.org/10.1007/s10878-019-00459-1