Submodularity in Team Formation Problem

We consider the team formation problem where the goal is to find a team of experts for a specific project. In the past, several attempts have been made to formulate this problem and each formulation focuses only on a subset of design criteria such as skill coverage, social compatibility, economy, skill redundancy, etc. In this paper, for the first time, we show that most of the important design criteria for this problem can be fully modeled within one single formulation as an unconstrained submodular function maximization problem. In our formulation, the submodular function turns out to be non-negative and non-monotone. The maximization of this class of submodular function is much less explored than its monotone constrained counterpart. A few recent works [7] [4] have come up with a simulated annealing based randomized approximation scheme for this problem with an approximation ratio of 0.41. In this paper, we customize this algorithm to our formulation and conduct an extensive set of experiments to show its efficacy. Our proposed formulation offers several advantageous features over the existing formulations including skill cover softening, better team communication, and connectivity relaxation. Unlike previous formulations, the skill cover softening feature allows a designer to specify Must Have and Should Have skills. Similarly, through better team communication, we avoid the restriction that all the communication among team members should pass through only the team members and not the outsiders. Finally, connectivity relaxation feature alleviates the constraint of whole team being connected and thereby, lowering the cost.