Constrained k-Center Problem on a Convex Polygon
International Journal of Foundations of Computer Science
In this paper, we consider a restricted covering problem, in which a convex polygon P with n vertices and an integer k are given, the objective is to cover the entire region of P using k congruent disks of minimum radius ropt, centered on the boundary of P. For k ≥ 7 and any > 0, we propose an (1 + 7 k + 7 k + )-factor approximation algorithm for this problem, which runs in O((n + k)(|logropt| + logâ1 â) time. The best known approximation factor of the algorithm for the problem in the literature is 1.8841 [H. Du and Y. Xu: An approximation algorithm for k-center problem on a convex polygon, J. Comb. Optim. 27(3) (2014) 504-518].
Basappa, Manjanna; Jallu, Ramesh K.; and Das, Gautam K., "Constrained k-Center Problem on a Convex Polygon" (2020). Journal Articles. 400.