Social Distancing via Social Scheduling

TL;DR

This paper proposes a social scheduling mechanism for managing visitor flow during a pandemic, ensuring social distancing, prioritizing important visits, and maintaining truthfulness and computational efficiency.

Contribution

It introduces a novel, prior-free scheduling mechanism that handles indivisible job requests, guarantees social distancing, and is computationally tractable, with proven theoretical properties.

Findings

Visitors with more important jobs get preferred slots.

The mechanism reduces social congestion effectively.

It provides a reasonable approximation for multi-slot jobs.

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.