Social Distancing via Social Scheduling

Deepesh Kumar Lall, Garima Shakya, Swaprava Nath

Abstract: Motivated by the need for social distancing during a pandemic, we consider an approach to schedule the visitors of a facility (e.g., a general store). Our algorithms take input from the citizens and schedule the store's discrete time-slots based on their importance in visiting the facility. We consider indivisible customer job requests that take single or multiple slots to complete. The salient properties of our approach are: it (a) ensures social distancing by ensuring a maximum population in a given time-slot at the facility, (b) prioritizes individuals based on the importance of the jobs, (c) maintains truthfulness of the reported importance by adding a cooling-off period after their allocated time-slot, during which the individual cannot re-access the same facility, (d) guarantees voluntary participation of the citizens, and yet (e) is computationally tractable. The mechanisms we propose are prior-free. The problem is NP-complete for indivisible multi-slot jobs, and we provide a polynomial-time mechanism that is truthful, individually rational, and approximately optimal. Experiments with data collected from a store show that visitors with more important (single-slot) jobs are allocated more preferred slots, which comes at the cost of a longer cooling-off period and significantly reduces social congestion. For the multi-slot jobs, our mechanism yields reasonable approximation while reducing the computation time significantly. While our solutions are primarily motivated by the ongoing raging pandemic, our formulation naturally applies to a broad range of scheduling settings.