Silent Robots的协作分散
Collaborative Dispersion by Silent Robots
摘要：
在分散问题中，一组$k$协同定位的移动机器人必须重新定位在一个未知的网络中的不同节点。网络被建模为匿名图$G=(V,E)$，其中图的节点未被标记。关联到具有度$d$的节点$v$的边用在$v$处的范围$0,1, \cdots, d-1$中的端口号来标记。机器人具有在范围$[0,L]$中的唯一ID，其中$L \ge k$，并且最初被放置在源节点$s$处。每个机器人只知道自己的id，但不知道其他机器人的id或$L,k$的值。分散的任务传统上是通过两种类型的通信能力的假设来实现的：（a）当一些机器人在同一个节点上时，它们可以通过在它们之间交换消息来进行通信（b）网络中的任何两个机器人都可以在它们之间交换消息。在本文中，我们问这种能力的协同定位的机器人之间的通信是必要的，以实现分散。我们表明，即使通信的能力是不可用的，一组移动机器人的分散的任务可以实现在一个弱得多的模型，其中一个机器人在节点$v$有以下非常有限的信息，在任何一轮的开始访问：（1）我独自在$v$？(2)与上一轮相比，$v$的机器人数量增加还是减少？我们提出了一个确定性的算法，实现分散在任何给定的图$G=(V,E)$在时间$O\left( k\log L+k^2 \log Δ\right)$，其中$Δ$是在$G$节点的最大程度。每个机器人使用$O(\log L+ \log Δ)$附加内存。我们还证明了分散的任务不能实现由一组移动机器人与$o(\log L + \log Δ)$额外的内存。
英文摘要：
In the dispersion problem, a set of $k$ co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph $G=(V,E)$, where the nodes of the graph are not labeled. The edges incident to a node $v$ with degree $d$ are labeled with port numbers in the range $0,1, \cdots, d-1$ at $v$. The robots have unique ids in the range $[0,L]$, where $L \ge k$, and are initially placed at a source node $s$. Each robot knows only its own id but does not know the ids of the other robots or the values of $L,k$. The task of dispersion was traditionally achieved with the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them (b) any two robots in the network can exchange messages between them. In this paper, we ask whether this ability of communication among co-located robots is necessary to achieve dispersion. We show that even if the ability of communication is not available, the task of dispersion by a set of mobile robots can be achieved in a much weaker model where a robot at a node $v$ has the access of following very restricted information at the beginning of any round: (1) am I alone at $v$? (2) the number of robots at $v$ increased or decreased compare to the previous round? We propose a deterministic algorithm that achieves dispersion on any given graph $G=(V,E)$ in time $O\left( k\log L+k^2 \log Δ\right)$, where $Δ$ is the maximum degree of a node in $G$. Each robot uses $O(\log L+ \log Δ)$ additional memory. We also prove that the task of dispersion cannot be achieved by a set of mobile robots with $o(\log L + \log Δ)$ additional memory.
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。
