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- Title
Scheduling meetings: are the odds in your favor?
- Authors
Brown, Katherine; Mathur, Harsh; Narayan, Onuttom
- 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.
- Subjects
PROBABILITY theory; SCHEDULING; SUCCESS; MEETINGS
- Publication
European Physical Journal B: Condensed Matter, 2024, Vol 97, Issue 8, p1
- ISSN
1434-6028
- Publication type
Article
- DOI
10.1140/epjb/s10051-024-00742-z