一种无线多跳网络的随机路由
Randomized Initialization of a Wireless Multihop Network
摘要：
地址自动配置是无线网络中自动设置节点IP地址所需的重要机制。地址自动配置，也称为初始化或命名，包括为一组$n$不可区分的节点提供范围从1到$n$的唯一标识符。我们考虑一个无线网络，其中$n$节点（处理器）被随机扔在一个正方形$X$，均匀和独立。我们假设网络是同步的，并且如果两个节点在彼此的最大$r$的距离内（$r$是发送/接收范围），则它们能够通信。本文的模型涉及没有冲突检测能力的节点：如果处理器$u$的两个或多个邻居在同一时间并发传输，那么$u$将不会接收到任何消息。我们还假设节点既不知道网络的拓扑结构，也不知道网络中节点的数量。此外，他们开始难以区分，匿名和无名。在这种极端的情况下，我们设计和分析了一个完全分布式的协议，以实现初始化任务的无线多跳网络的$n$节点均匀分散在一个正方形$X$。我们展示了部署的站的传输范围如何影响网络的度和直径等典型特征。通过允许节点在一个范围$r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{πn}}$（略大于一个需要有一个连接的网络）进行传输，我们展示了如何设计一个随机化的协议运行在预期的时间$O(n^{3/2} \log^2{n})$，以便分配一个唯一的数字范围从1到$n$的每个$n$参与节点。
英文摘要：
Address autoconfiguration is an important mechanism required to set the IP address of a node automatically in a wireless network. The address autoconfiguration, also known as initialization or naming, consists to give a unique identifier ranging from 1 to $n$ for a set of $n$ indistinguishable nodes. We consider a wireless network where $n$ nodes (processors) are randomly thrown in a square $X$, uniformly and independently. We assume that the network is synchronous and two nodes are able to communicate if they are within distance at most of $r$ of each other ($r$ is the transmitting/receiving range). The model of this paper concerns nodes without the collision detection ability: if two or more neighbors of a processor $u$ transmit concurrently at the same time, then $u$ would not receive either messages. We suppose also that nodes know neither the topology of the network nor the number of nodes in the network. Moreover, they start indistinguishable, anonymous and unnamed. Under this extremal scenario, we design and analyze a fully distributed protocol to achieve the initialization task for a wireless multihop network of $n$ nodes uniformly scattered in a square $X$. We show how the transmitting range of the deployed stations can affect the typical characteristics such as the degrees and the diameter of the network. By allowing the nodes to transmit at a range $r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{πn}}$ (slightly greater than the one required to have a connected network), we show how to design a randomized protocol running in expected time $O(n^{3/2} \log^2{n})$ in order to assign a unique number ranging from 1 to $n$ to each of the $n$ participating nodes.
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。
