SINR模型下的无线网络多跳路由与调度
Multi-Hop Routing and Scheduling in Wireless Networks in the SINR model
摘要：
我们提出了一个多跳路由和调度的请求在无线网络中的\sinr模型的算法。我们的算法的目标是最大化的吞吐量或最大化的流量和需求之间的最小比率。我们的算法将链接划分为桶。每个桶由一组具有几乎相等的接收功率的链路组成。我们用$\sigdiv$表示非空桶的数量。我们的算法获得了一个近似比$O(\sigdiv \cdot \log n)$，其中$n$表示的节点数。对于线性幂$\sigdiv =1$的情况，因此算法的近似比为$O(\log n)$。这是线性幂的第一个实用近似算法，近似比仅取决于$n$（而不是最大与最小距离比）。如果每条链路的传输功率是输入的一部分（并且是任意的），则为$\sigdiv = O(\logΓ+ \log Δ)$，其中$Γ$表示最大功率与最小功率之比，$Δ$表示最大距离与最小距离之比。因此，近似比是$O(\log n \cdot (\logΓ+ \log Δ))$。最后，我们考虑的情况下，该算法需要分配功率的范围$[\pmin,\pmax]$的每个链路。这种情况下的算法的扩展实现了$O[(\log n + \log \log Γ) \cdot (\logΓ+ \log Δ)]$的近似比。
英文摘要：
We present an algorithm for multi-hop routing and scheduling of requests in wireless networks in the \sinr\ model. The goal of our algorithm is to maximize the throughput or maximize the minimum ratio between the flow and the demand. Our algorithm partitions the links into buckets. Every bucket consists of a set of links that have nearly equivalent reception powers. We denote the number of nonempty buckets by $\sigdiv$. Our algorithm obtains an approximation ratio of $O(\sigdiv \cdot \log n)$, where $n$ denotes the number of nodes. For the case of linear powers $\sigdiv =1$, hence the approximation ratio of the algorithm is $O(\log n)$. This is the first practical approximation algorithm for linear powers with an approximation ratio that depends only on $n$ (and not on the max-to-min distance ratio). If the transmission power of each link is part of the input (and arbitrary), then $\sigdiv = O(\logΓ+ \log Δ)$, where $Γ$ denotes the ratio of the max-to-min power, and $Δ$ denotes the ratio of the max-to-min distance. Hence, the approximation ratio is $O(\log n \cdot (\logΓ+ \log Δ))$. Finally, we consider the case that the algorithm needs to assign powers to each link in a range $[\pmin,\pmax]$. An extension of the algorithm to this case achieves an approximation ratio of $O[(\log n + \log \log Γ) \cdot (\logΓ+ \log Δ)]$.
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