保护多边形而不失去接触
Guarding a Polygon Without Losing Touch
摘要：
我们从移动多智能体的角度研究了Klee在1973年首次提出的经典画廊问题。具体来说，我们需要一个最佳的小数量的代理（也称为警卫），以导航和定位自己在一个未知的简单多边形的内部与$n$顶点，使所有代理的集体视图覆盖多边形。我们认为，明显连接设置代理必须保持连接，通过视线链接-一个要求，特别是相关的多代理系统。我们首先提供了一个集中式算法的可视连接设置，运行在时间$O(n)$，这当然是最佳的。然后，我们提供了两种不同的分布式设置的算法。在第一种设置中，智能体只能感知相对接近度（即，可以分辨出一对物体中的哪一个更近），而在第二种设置中，它们可以感知精确的距离。尽管代理没有多边形的先验知识，但我们的分布式算法仍有效。此外，我们提供的下界表明，我们的分布式算法是接近最优的。我们的可视连接保护确保（i）保护形成连接的网络，（ii）多边形被完全保护。因此，这种保护提供了分布式基础设施来执行针对该多边形的任何几何算法。
英文摘要：
We study the classical Art Gallery Problem first proposed by Klee in 1973 from a mobile multi-agents perspective. Specifically, we require an optimally small number of agents (also called guards) to navigate and position themselves in the interior of an unknown simple polygon with $n$ vertices such that the collective view of all the agents covers the polygon. We consider the visibly connected setting wherein agents must remain connected through line of sight links -- a requirement particularly relevant to multi-agent systems. We first provide a centralized algorithm for the visibly connected setting that runs in time $O(n)$, which is of course optimal. We then provide algorithms for two different distributed settings. In the first setting, agents can only perceive relative proximity (i.e., can tell which of a pair of objects is closer) whereas they can perceive exact distances in the second setting. Our distributed algorithms work despite agents having no prior knowledge of the polygon. Furthermore, we provide lower bounds to show that our distributed algorithms are near-optimal. Our visibly connected guarding ensures that (i) the guards form a connected network and (ii) the polygon is fully guarded. Consequently, this guarding provides the distributed infrastructure to execute any geometric algorithm for this polygon.
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。
