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Scheduling to reduce close contacts: resolvable grid graph decomposition and packing

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Abstract

Motivated by the COVID-19 pandemic, we consider the scheduling of seating arrangement for an event that is divided into sessions, aiming at reducing the number of close contacts of participants, while the physical and temporal distancing rules are taken into consideration simultaneously. In this paper, we formalize the requirements as a resolvable graph decomposition or packing problem, and focus on the grid graphs defined over vertices that are arranged into arrays embedded in the Euclidean space. We provide explicit constructions of such arrangement, and particularly for those that reach or asymptotically reach the largest possible number of sessions.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and suggestions.

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Authors and Affiliations

  1. Industrial Systems Engineering and Management, National University of Singapore, Singapore, Singapore

    Yeow Meng Chee, Van Khu Vu & Hui Zhang

  2. Department of Computer Science, University of Vermont, Burlington, USA

    Alan Chi Hung Ling

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  1. Yeow Meng Chee
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  2. Alan Chi Hung Ling
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  3. Van Khu Vu
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  4. Hui Zhang
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Correspondence to Hui Zhang.

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Communicated by C. J. Colbourn.

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Chee, Y.M., Ling, A.C.H., Vu, V.K. et al. Scheduling to reduce close contacts: resolvable grid graph decomposition and packing. Des. Codes Cryptogr. 91, 4093–4106 (2023). https://doi.org/10.1007/s10623-023-01291-9

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