如何异步（几乎）到处见面
How to meet asynchronously (almost) everywhere
摘要：
两个具有不同标签的移动代理（机器人）必须在一个任意的，可能是无限的，未知的连接图或平面上的未知连接地形中相遇。智能体被建模为点，每个智能体的路径仅取决于其标签和未知环境。每个代理的实际行走还取决于异步对手，其可以任意改变代理的速度，停止它，或者甚至来回移动它，只要代理在其路线的每个段中的行走是连续的，不离开它并且覆盖它的全部。在图中相遇意味着两个代理必须同时在图的边缘内的某个节点或某个点中，而在地形中相遇意味着两个代理必须同时处于地形的某个点。是否存在一种确定性算法，允许任何两个代理人在任何未知的环境中，尽管这个非常强大的对手？我们给出了确定性会合算法的代理开始于任意节点的任何匿名连接图（有限或无限）和代理开始于任何内部点的合理坐标在任何封闭区域的平面与路径连接的内部。当我们的算法在一个非常普遍的环境中工作时？事实上，代理人几乎可以在任何地方见面？我们表明，上述对环境施加的几个限制都不能消除。另一方面，我们的算法还保证了以下近似会合的代理开始在任意内部点的地形如上：代理最终将在一个任意小的正距离彼此。
英文摘要：
Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent in each segment of its route is continuous, does not leave it and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerfull adversary? We give deterministic rendezvous algorithms for agents starting at arbitrary nodes of any anonymous connected graph (finite or infinite) and for agents starting at any interior points with rational coordinates in any closed region of the plane with path-connected interior. While our algorithms work in a very general setting ? agents can, indeed, meet almost everywhere ? we show that none of the above few limitations imposed on the environment can be removed. On the other hand, our algorithm also guarantees the following approximate rendezvous for agents starting at arbitrary interior points of a terrain as above: agents will eventually get at an arbitrarily small positive distance from each other.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
