Profit-Driven Team Grouping in Social Networks

Abstract: In this paper, we investigate the profit-driven team grouping problem in social networks. We consider a setting in which people possess different skills, and the compatibility between these individuals is captured by a social network. Moreover, there is a collection of tasks, where each task requires a specific set of skills and yields a profit upon completion. Individuals may collaborate with each other as \emph{teams} to accomplish a set of tasks. We aim to find a group of teams to maximize the total profit of the tasks that they can complete. Any feasible grouping must satisfy the following conditions: (i) each team possesses all the skills required by the task assigned to it, (ii) individuals belonging to the same team are socially compatible, and (iii) no individual is overloaded. We refer to this as the \textsc{TeamGrouping} problem. We analyze the computational complexity of this problem and then propose a linear program-based approximation algorithm to address it and its variants. Although we focus on team grouping, our results apply to a broad range of optimization problems that can be formulated as cover decomposition problems.