Methods in Constrained Community Detection: An Integer Optimization Model and Heuristic Approach for Cohort Creation

As a result of the COVID-19 pandemic, many organizations and schools have switched to a virtual environ-ment. Recently, as vaccines have become more readily available, organizations and educational institutions have started shifting from virtual environments to physical office spaces and schools. For the highest level of safety and caution with respect to the containment of COVID-19, the shift to in-person interaction requires a thoughtful approach. With the help of an Integer Programming (IP) Optimization model, it is possible to formulate the objective function and constraints to determine a safe way of returning to the office through cohort development. In addition to our IP formulation, we developed a heuristic approximation method. Starting with an initial contact matrix, these methods aim to reduce additional contacts introduced by subgraphs representing the cohorts. These formulations can be generalized to other applications that benefit from constrained community detection.