Faster Symmetric Rendezvous on Four or More Locations
arXiv:2604.02058v1 Announce Type: cross Abstract: In the symmetric rendezvous problem two players follow the same (randomized) strategy to visit one of $n$ locations in each time step $t=0,1,2,\dots$. Their goal is to minimize the expected time until they visit the same location and thus meet. Anderson and Weber [J. Appl. Prob., 1990] proposed a strategy that operates in rounds of $n-1$ steps: a player either remains in one location for $n-1$ steps or visits the other $n-1$ locations in random order; the choice between these two options is made with a probability that depends only on $n$. The strategy is known to be optimal for $n=2$ and $n=3$, and there is convincing evidence that it is not optimal for $n=4$. We show that it is not optimal for any $n\geq 4$, by constructing a strategy wit
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Abstract:In the symmetric rendezvous problem two players follow the same (randomized) strategy to visit one of $n$ locations in each time step $t=0,1,2,\dots$. Their goal is to minimize the expected time until they visit the same location and thus meet. Anderson and Weber [J. Appl. Prob., 1990] proposed a strategy that operates in rounds of $n-1$ steps: a player either remains in one location for $n-1$ steps or visits the other $n-1$ locations in random order; the choice between these two options is made with a probability that depends only on $n$. The strategy is known to be optimal for $n=2$ and $n=3$, and there is convincing evidence that it is not optimal for $n=4$. We show that it is not optimal for any $n\geq 4$, by constructing a strategy with a smaller expected meeting time.
Subjects:
Optimization and Control (math.OC); Computer Science and Game Theory (cs.GT)
Cite as: arXiv:2604.02058 [math.OC]
(or arXiv:2604.02058v1 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2604.02058
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Javier Cembrano [view email] [v1] Thu, 2 Apr 2026 13:55:56 UTC (46 KB)
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