Covering a simplex by spheres: complexity and algorithms - Zhang, Tongli; Xia, Yong (Journal of global optimization, 2022)
Simplex covering optimization problem (SCO) is modeled from the application of covering a simplex by m given balls. It contains the maximin dispersion problem as a special case. In this paper, we prove that (SCO) is NP-hard. We present an enumeration method (EM) to globally solve (SCO) and show that the complexity is strongly polynomial when m is fixed. Numerical experiments demonstrate that EM outperforms CPLEX when m is small. For larger m , we propose an efficient incomplete enumeration method based on linear programming relaxation.