Scheduling Meetings: Are the Odds in Your Favor?

Authors

Harsh Mathur, Case Western Reserve UniversityFollow

Document Type

Article

Publication Date

8-13-2024

Abstract

Abstract: Polling all the participants to find a time when everyone is available is the ubiquitous method of scheduling meetings nowadays. We examine the probability of a poll with m participants and ℓ possible meeting times succeeding, where each participant rejects r of the ℓ options. For large ℓ and fixed r/ℓ, we can carry out a saddle-point expansion and obtain analytical results for the probability of success. Despite the thermodynamic limit of large ℓ, the ‘microcanonical’ version of the problem where each participant rejects exactly r possible meeting times, and the ‘canonical’ version where each participant has a probability p=r/ℓ of rejecting any meeting time, only agree with each other if m→∞. For m→∞,ℓ has to be O(p^-m) for the poll to succeed, i.e., the number of meeting times that have to be polled increases exponentially with m. Equivalently, as a function of p, there is a discontinuous transition in the probability of success at p∼1/ℓ^1/m. If the participants’ availability is approximated as being unchanging from one week to another, i.e., ℓ is limited, a realistic example discussed in the text of the paper shows that the probability of success drops sharply if the number of participants is greater than approximately 4. Graphical abstract: (Figure presented.)

Language

English

Publication Title

European Physical Journal B

Rights

© The Author(s) 2024. This is an Open Access work distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Brown, K., Mathur, H. & Narayan, O. Scheduling meetings: are the odds in your favor?. Eur. Phys. J. B 97, 120 (2024). https://doi.org/10.1140/epjb/s10051-024-00742-z