无线电网络上的简单随机游动（超图上的简单随机游动）
Simple Random Walks on Radio Networks (Simple Random Walks on Hyper-Graphs)
摘要：
近年来，基于图上随机游动性质的协议在无线网络、对等网络和Web等通信和信息网络中得到了广泛的应用。对于无线网络（和其他网络），图实际上不是正确的通信模型;相反，超图更好地捕捉无线共享信道上的通信。受这个例子的启发，本文研究超图上的随机游动。首先，我们形式化超图上的随机游走过程，并从图上的随机游走中推广关键概念。然后，我们给出了无线电覆盖时间的新定义，即随机游走被所有节点听到（而不是访问）的预期时间。然后，我们给出了无线覆盖的一些基本界，特别地，我们证明了在图上无线覆盖时间为O（mn），在超图中无线覆盖时间为O（mnr），其中n，m和r分别是超图的节点数，边数和秩.此外，我们定义了无线电击中时间，并给出了一个多项式算法来计算它们。我们得出结论，在一个和两个维度的无线网络模型的具体超图的结果。
英文摘要：
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless networks (and other networks), graphs are actually not the correct model of the communication; instead hyper-graphs better capture the communication over a wireless shared channel. Motivated by this example, we study in this paper random walks on hyper-graphs. First, we formalize the random walk process on hyper-graphs and generalize key notions from random walks on graphs. We then give the novel definition of radio cover time, namely, the expected time of a random walk to be heard (as opposed to visit) by all nodes. We then provide some basic bounds on the radio cover, in particular, we show that while on graphs the radio cover time is O(mn), in hyper-graphs it is O(mnr) where n, m and r are the number of nodes, the number of edges and the rank of the hyper-graph, respectively. In addition, we define radio hitting times and give a polynomial algorithm to compute them. We conclude the paper with results on specific hyper-graphs that model wireless networks in one and two dimensions.
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。
