Prior-free Strategic Multiagent Scheduling with focus on Social Distancing

Motivated by the need for social distancing during a pandemic, we consider an approach to schedule the visitors of a facility. The algorithm takes input from citizens and schedules the store's time-slots based on their importance to visit the facility (e.g., a general store). Naturally, the formulation applies to several similar problems. We consider the single slot and multiple slot demands of the requests. 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 users' 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. We show that the problem becomes NP-complete as soon as the multi-slot demands are indivisible and provide a polynomial-time mechanism that is truthful, individually rational, and approximately optimal. Experiments show that visitors with more important jobs are allocated more preferred slots, which comes at the cost of a longer delay to re-access the store. We show that it reduces the social congestion significantly using users' visit data from a store. For the multi-slot indivisible jobs, our approximately optimal mechanism performs well in practice.