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arXiv · 2608.08981

Universal Rendezvous of Anonymous Agents with Footprints

Bibhuti Das
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Abstract

Deterministic rendezvous for two anonymous mobile agents starting simultaneously from two distinct nodes of an anonymous connected graph and navigating synchronously in the graph requires that they meet at some node. An instance of the rendezvous problem is the underlying graph, together with two distinct nodes that are the initial positions of the agents. Such an instance is said to be feasible if there is a deterministic algorithm guaranteeing rendezvous, possibly valid only for this instance. A rendezvous algorithm is said to be universal for a class of instances if it guarantees rendezvous for all feasible instances from this class. We consider the model with footprints: whenever an agent visits an unmarked node, it leaves a permanent footprint on it, and all footprints are identical. This paper aims at answering the open problem from the paper by Das and Pelc (SPAA 2026), asking whether there exists a universal rendezvous algorithm for the class of all instances in the model with footprints. We propose a universal rendezvous algorithm for the class of all instances where the underlying graph is connected (finite or countably infinite) in the model with footprints. This shows the existence of a universal algorithm for the class of all instances in the model with footprints, which is an affirmative answer to the open problem.

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Bibhuti Das. 2026-08-10. Universal Rendezvous of Anonymous Agents with Footprints. https://arxiv.org/abs/2608.08981

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