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A long line of literature has focused on the problem of selecting a team ofindividuals from a large pool of candidates, such that certain constraints arerespected, and a given objective function is maximized. Even though extantresearch has successfully considered diverse families of objective functionsand constraints, one of the most common limitations is the focus on thesingle-team paradigm. Despite its well-documented applications in multipledomains, this paradigm is not appropriate when the team-builder needs topartition the entire population into multiple teams. Team-partitioning tasksare very common in an educational setting, in which the teacher has topartition the students in her class into teams for collaborative projects. Thetask also emerges in the context of organizations, when managers need topartition the workforce into teams with specific properties to tackle relevantprojects. In this work, we extend the team formation literature by introducingthe Guided Team-Partitioning (GTP) problem, which asks for the partitioning ofa population into teams such that the centroid of each team is as close aspossible to a given target vector. As we describe in detail in our work, thisformulation allows the team-builder to control the composition of the producedteams and has natural applications in practical settings. Algorithms for theGTP need to simultaneously consider the composition of multiple non-overlappingteams that compete for the same population of candidates. This makes theproblem considerably more challenging than formulations that focus on theoptimization of a single team. In fact, we prove that GTP is NP-hard to solveand even to approximate. The complexity of the problem motivates us to considerefficient algorithmic heuristics, which we evaluate via experiments on bothreal and synthetic datasets.

The Guided Team-Partitioning Problem: Definition, Complexity, and Algorithm