On greedy approximation algorithm for the minimum resolving dominating set problem

In this paper, we investigate the minimum resolving dominating set problem which is a emerging combinatorial optimization problem in general graphs. We prove that the resolving dominating set problem is NP-hard and propose a greedy algorithm with an approximation ratio of (1+2lnn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 + 2\ln n$$\end{document}) by establishing a submodular potential function, where n is the node number of the input graph.