Approximation algorithm for a generalized Roman domination problem in unit ball graphs
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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.
KeywordsConnected strong k-Roman dominating set Constant approximation algorithm Unit ball graph
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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