Fast Neighborhood Rendezvous
Ryota Eguchi, Naoki Kitamura, and Taisuke Izumi

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Abstract
In the rendezvous problem, two computing entities (called \emph{agents}) located at different vertices in a graph have to meet at the same vertex. In this paper, we consider the synchronous \emph{neighborhood rendezvous problem}, where the agents are initially located at two adjacent vertices. While this problem can be trivially solved in rounds ( is the maximum degree of the graph), it is highly challenging to reveal whether that problem can be solved in rounds, even assuming the rich computational capability of agents. The only known result is that the time complexity of rounds is achievable if the graph is complete and agents are probabilistic, asymmetric, and can use whiteboards placed at vertices. Our main contribution is to clarify the situation (with respect to computational models and graph classes) admitting such a sublinear-time…
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