醒来，加入我！无线网络中一种能量有效的最大匹配算法
Wake Up and Join Me! An Energy-Efficient Algorithm for Maximal Matching in Radio Networks
摘要：
我们考虑的是小型自主设备的网络，这些设备相互无线通信。最大限度地减少能源使用是设计此类网络算法的重要考虑因素，因为电池寿命是一个关键而有限的资源。工作在一个模型中，发送和监听消息消耗能量，我们考虑的问题，找到一个最大匹配的节点在任意和未知的拓扑结构的无线电网络。我们提出了一个分布式的随机算法，产生，具有很高的概率，一个最大的匹配。每个节点的最大能量成本是$O(\log^2 n)$，其中$n$是网络的大小。我们的算法的总延迟是$O(n \log n)$时间步长。我们观察到，存在家庭的网络拓扑结构，这两个界限是同时最佳的polylog因素，所以任何显着的改善将需要额外的假设网络拓扑结构。我们还考虑了相关的分配问题，为网络中的每个节点，邻居备份其数据的情况下，节点故障。这里，一个关键目标是最小化最大负载，最大负载定义为分配给单个节点的节点数量。我们提出了一个分散的低能量算法，找到一个邻居分配的最大负载是最多的polylog（$n$）的因素大于最佳。
英文摘要：
We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is $O(\log^2 n)$, where $n$ is the size of the network. The total latency of our algorithm is $O(n \log n)$ time steps. We observe that there exist families of network topologies for which both of these bounds are simultaneously optimal up to polylog factors, so any significant improvement will require additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present a decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog($n$) factor bigger that the optimum.
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