工作时睡觉：无线电网络的节能广播
Sleeping on the Job: Energy-Efficient Broadcast for Radio Networks
摘要：
我们解决的问题，最小化功耗时，在无线电网络上执行可靠的广播在以下流行的模型。网络中的每个节点都位于二维的网格中的一个点上，并且每当节点发送消息时，距离r内的所有唤醒节点都接收该消息。在广播问题中，一些节点希望成功地将消息发送到网络中的所有其他节点，即使每个邻域内的节点的1/2分数可以被对手删除。删除节点的集合是由对手精心选择的，以挫败我们的算法，而且，删除节点的集合可能会周期性地变化。这模拟了由于移动节点、静态节点失去功率或仅仅是网格中的某些点未被占用而导致的最坏情况行为。一个平凡的解决方案要求网络中的每个节点大约在1/2的时间内处于唤醒状态，而一个平凡的下限表明每个节点必须在至少1/n的时间内处于唤醒状态。我们的第一个结果是一个算法，它要求每个节点只在预期时间的1/sqrt（n）部分内保持清醒。我们的算法实现了这一点，同时确保概率为1的正确性，并保持其他资源成本（如延迟和发送的消息数量）的最佳值。我们给出了一个下界，表明这种降低功耗是渐近最优的延迟和发送的消息的数量必须是最佳的。如果我们可以增加延迟和发送的消息，只有一个log*n的因素，我们给出了拉斯维加斯算法，要求每个节点只唤醒一个（log*n）/n预期的时间分数;我们给出了一个下限，表明第二个算法是接近最优的。最后，我们展示了如何确保在拜占庭故障的存在下的节能广播。
英文摘要：
We address the problem of minimizing power consumption when performing reliable broadcast on a radio network under the following popular model. Each node in the network is located on a point in a two dimensional grid, and whenever a node sends a message, all awake nodes within distance r receive the message. In the broadcast problem, some node wants to successfully send a message to all other nodes in the network even when up to a 1/2 fraction of the nodes within every neighborhood can be deleted by an adversary. The set of deleted nodes is carefully chosen by the adversary to foil our algorithm and moreover, the set of deleted nodes may change periodically. This models worst-case behavior due to mobile nodes, static nodes losing power or simply some points in the grid being unoccupied. A trivial solution requires each node in the network to be awake roughly 1/2 the time, and a trivial lower bound shows that each node must be awake for at least a 1/n fraction of the time. Our first result is an algorithm that requires each node to be awake for only a 1/sqrt(n) fraction of the time in expectation. Our algorithm achieves this while ensuring correctness with probability 1, and keeping optimal values for other resource costs such as latency and number of messages sent. We give a lower-bound that shows that this reduction in power consumption is asymptotically optimal when latency and number of messages sent must be optimal. If we can increase the latency and messages sent by only a log*n factor we give a Las Vegas algorithm that requires each node to be awake for only a (log*n)/n expected fraction of the time; we give a lower-bound showing that this second algorithm is near optimal. Finally, we show how to ensure energy-efficient broadcast in the presence of Byzantine faults.
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