On positive-influence target-domination

Consider a graph G = (V, E) and a vertex subset A ⊆ V . A vertex v is positive-influence dominated by A if either v is in A or at least half the number of neighbors of v belong to A. For a target vertex subset S ⊆ V , a vertex subset A is a positive-influence target-dominating set for target set S if every vertex in S is positive-influence dominated by A. Given a graph G and a target vertex subset S, the positive-influence target-dominating set (PITD) problem is to find the minimum positive-influence dominating set for target S. In this paper, we show two results: (1) The PITD problem has a polynomial-time (1 + log 3 2 )-approximation in general graphs where is the maximum vertex-degree of the input graph. (2) For target set S with |S| = (|V |), the PITD problem has a polynomial-time O(1)-approximation in power-law graphs. B Ding-Zhu Du [email protected]; [email protected] Guangmo Tong [email protected] Weili Wu [email protected] Panos M. Pardalos [email protected] 1 Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA 2 Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA 3 Laboratory of Algorithms and Technologies for Networks Analysis (LATNA), National Research University, Higher School of Economics, 20 Myasnitskaya st., Moscow 101000, Russia 4 Division of Algorithms and Technologies for Networks Analysis, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam