Parameterized complexity of team formation in social networks

Given a task that requires some skills and a social network of individuals with different skills, the Team Formation problem asks to find a team of individuals that together can perform the task, while minimizing communication costs. Since the problem is NP-hard, we identify the source of intractability by analyzing its parameterized complexity with respect to parameters such as the total number of skills k, the team size l, the communication cost budget b, and the maximum vertex degree \(\varDelta \). We show that the computational complexity strongly depends on the communication cost measure: when using the weight of a minimum spanning tree of the subgraph formed by the selected team, we obtain fixed-parameter tractability for example with respect to the parameter k. In contrast, when using the diameter as measure, the problem is intractable with respect to any single parameter; however, combining \(\varDelta \) with either b or l yields fixed-parameter tractability.