Abstract
The spread of COVID-19 and similar viruses poses new challenges for our society. There is a strong incentive towards safety measures that help to mitigate the outbreaks. Many countries have imposed social distancing measures that require a minimum distance between people in given places, such as schools, restaurants, shops, etc. This in turn creates complications for these places, as their function is to serve as many people as they were originally designed for. In this article, we pose the problem of using the available space in a given place, such that the social distancing measures are satisfied, as a p-dispersion problem. We use recent algorithmic advancements, that were developed for the p-dispersion problem, and combine them with discretization schemes to find computationally attainable solutions to the p-dispersion problem and investigate the trade-off between the level of discretization and computational efforts on one side, and the value of the optimal solution on the other.
Highlights
The outbreak of the COVID-19 had an enormous impact on the world at large
As the social distancing measures do not have to be stable and can change over time, we will pose the problem of using the available space to its full extent in the following way: Given a fixed number p of people, fit them into a predefined space in such a way, that the minimum distance between any two persons is maximized
In this article we have studied the problem of locating persons in a given area, that should abide to social distancing measures such as those arising in the time of COVID-19 and similar viruses
Summary
The outbreak of the COVID-19 had an enormous impact on the world at large. To mitigate the spread of the virus, various technologies, such as Internet of Things, Unmanned Aerial Vehicles, blockchain, Artificial Intelligence, and 5G are already in use [1]. We devise a discretization scheme that is build on top of the decremental clustering to find computationally attainable solutions to the p-dispersion problem and investigate the trade-off between the level of discretization and computational efforts on one side, and the value of the optimal solution (the minimum distance between any two points) on the other. DEFINITION AND FORMULATIONS In the p-dispersion problem (pDP), we are given a set of n points, a dissimilarity (or distance) matrix. For k ∈ K , VOLUME 8, 2020 the binary variable zk indicates if the location decisions (the particular selection of p points) satisfy a minimum distance of at least Dk. The pure binary program is the following: max D0 + (Dk − Dk−1)zk (1). The formulation (1)-(6) can be further strengthen using clique-like inequalities and computation can be sped-up by exploiting valid lower and upper bounds [3]
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