Approximation algorithm for a generalized Roman domination problem in unit ball graphs

  • Limin Wang
  • Yalin Shi
  • Zhao Zhang
  • Zan-Bo Zhang
  • Xiaoyan ZhangEmail author


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.


Connected 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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Authors and Affiliations

  1. 1.State Key Laboratory for Novel Software TechnologyNanjing UniversityNanjingChina
  2. 2.School of Mathematical Science and Institute of MathematicsNanjing Normal UniversityNanjingChina
  3. 3.College of Mathematics and Computer ScienceZhejiang Normal UniversityJinhuaChina
  4. 4.Institute of Artificial Intelligence and Deep Learning, and School of Statistics and MathematicsGuangdong University of Finance & EconomicsGuangzhouChina

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