Social Distancing via Social Scheduling

Abstract: Motivated by the need of {\em 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 to visit the facility. Naturally, the formulation applies to several similar problems. We consider {\em indivisible} 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)~aims to prioritize individuals based on the importance of the jobs, (c)~maintains truthfulness of the reported importance by adding a {\em 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. We show that the problem becomes NP-complete for indivisible multi-slot demands, and 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.