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 \(O\big ((\log n)(\log \Delta )\big ),\) and the time complexity is \(O(\Delta \log n)\). Here n is any upper bound on the number of nodes, and \(\Delta \) is any upper bound on the maximum degree; n and \(\Delta \) are parameters of our algorithm that we assume are known a priori to all the processors. We note that there exist families of graphs for which our bounds on energy cost and time complexity are simultaneously optimal up to polylog factors, so any significant improvement would need 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 eventual 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 an efficient decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog (n) factor bigger that the optimum.

我们考虑以无线方式相互通信的小型自主设备网络。在为此类网络设计算法时，尽量减少能源使用是一个重要的考虑因素，因为电池寿命是一项至关重要且有限的资源。在发送和收听消息都消耗能量的模型中工作，我们考虑在任意和未知拓扑的无线电网络中找到节点的最大匹配的问题。我们提出了一种分布式随机算法，该算法以高概率产生最大匹配。每个节点的最大能量成本为\(O\big ((\log n)(\log \Delta )\big ),\)，时间复杂度为\(O(\Delta \log n)\)。这里n是节点数的任何上限，并且\(\Delta \)是最大度数的任何上限；n和\(\Delta \)是我们算法的参数，我们假设所有处理器都先验地知道这些参数。我们注意到存在图族，我们对能量成本和时间复杂度的限制同时对于多对数因子是最优的，因此任何显着的改进都需要对网络拓扑结构进行额外的假设。我们还考虑了为网络中的每个节点分配一个邻居来备份其数据以防最终节点故障的相关问题。在这里，一个关键目标是最小化最大负载，定义为分配给单个节点的节点数。我们提出了一种有效的分散式低能量算法，该算法可以找到最大负载最多为大于最优值 的 polylog ( n ) 因子的邻居分配。