Weighted target set selection on trees and cycles

Abstract

AbstractThere is significant interest in understanding the dynamics of influence diffusion on a social network. The weighted target set selection (WTSS) problem is a fundamental viral marketing problem arising on social networks. In this problem, the goal is to select a set of influential nodes to target (e.g., for promoting a new product) that can influence the rest of the network. The WTSS problem is APX‐hard. With the goal of generating insights to solve the WTSS problem on arbitrary graphs, we study in this paper the WTSS problem on trees and cycles. For trees, we propose a linear‐time dynamic programming algorithm and present a tight and compact extended formulation. Furthermore, we project the extended formulation onto the space of the natural node variables yielding the polytope of the WTSS problem on trees. This projection leads to an exponentially sized set of valid inequalities whose polynomial‐time separation is also discussed. Next, we focus on cycles: we describe a linear‐time algorithm and present the complete description of the polytope for the WTSS problem on cycles. Finally, we describe how these formulations can be applied to arbitrary graphs.