PTAS for the minimum weighted dominating set in growth bounded graphs

The minimum weighted dominating set (MWDS) problem is one of the classic NP‐hard optimization problems in graph theory with applications in many fields such as wireless communication networks. MWDS in general graphs has been showed not to have polynomial‐time constant‐approximation if $\mathrm{𝒩𝒫}\ne 𝒫$ . Recently, several polynomial‐time constant‐approximation SCHEMES have been designed for MWDS in unit disk graphs. In this paper, using the local neighborhood‐based scheme technique, we present a PTAS for MWDS in polynomial growth bounded graphs with bounded degree constraint.