带足迹的匿名智能体的通用会合算法
Universal Rendezvous of Anonymous Agents with Footprints
AI总结：
本文针对带足迹模型中所有连通（有限或可数无限）底层图的会合实例，提出通用会合算法，解决了Das和Pelc提出的开放问题，给出该模型所有实例存在通用算法的肯定答案。
AI中文摘要：
针对匿名连通图中两个匿名移动智能体从不同节点同步出发的确定性会合问题，要求它们在某个节点相遇。会合问题的一个实例是底层图加上两个不同的初始节点位置，若存在确定性算法保证会合则该实例可行，仅针对该实例的算法为专用算法；若某算法能保证某类实例中所有可行实例都能会合，则称其为该类实例的通用算法。本文研究带足迹模型：智能体访问未标记节点时会留下永久且完全相同的足迹。本文旨在解决Das和Pelc（SPAA 2026）论文中提出的开放问题：带足迹模型的所有实例是否存在通用会合算法？我们针对带足迹模型中所有底层图为连通（有限或可数无限）的实例，提出了一种通用会合算法，证明了带足迹模型所有实例类存在通用算法，对该开放问题给出了肯定回答。
英文摘要：
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.
