任意有向无圈图网络上的在线能量收集问题
Online Energy Harvesting Problem Over An Arbitrary Directed Acyclic Graph Network
摘要：
被认为是一个通信网络建模的有向无环图（DAG），通过它的源希望发送指定数量的比特到目的地节点。DAG的每个节点由单独的可再生能源供电，并且所收集的能量用于促进源目的地数据流。这里的挑战是找到最佳的速率和功率分配跨时间的每个节点在其传出边缘，以便最大限度地减少的时间，目的地接收指定数量的比特。被认为是一个在线设置的算法只有因果信息的能量到达。利用竞争比作为性能度量，即在线算法和最优离线算法的成本之比，在所有输入上最大化，提出了一种对任意$δ>0$都具有竞争比为$2+δ$的{\it lazy}在线算法.顺便说一下，$2$也是这个问题的任何在线算法的竞争比的下界。我们的懒惰的在线算法描述和分析通过定义一个新的最大流问题的DAG，其中任何节点的外出边缘的子集上的速率是相关的/约束。还提供了一个最优算法来找到最大流与这些约束，这可能是独立的利益。
英文摘要：
A communication network modelled by a directed acyclic graph (DAG) is considered, over which a source wishes to send a specified number of bits to a destination node. Each node of the DAG is powered by a separate renewable energy source, and the harvested energy is used to facilitate the source destination data flow. The challenge here is to find the optimal rate and power allocations across time for each node on its outgoing edges so as to minimize the time by which the destination receives a specified number of bits. An online setting is considered where an algorithm only has causal information about the energy arrivals. Using the competitive ratio as the performance metric, i.e. the ratio of the cost of the online algorithm and the optimal offline algorithm, maximized over all inputs, a {\it lazy} online algorithm with a competitive ratio of $2+δ$ for any $δ>0$ is proposed. Incidentally, $2$ is also a lower bound to the competitive ratio of any online algorithm for this problem. Our lazy online algorithm is described and analyzed via defining a novel max-flow problem over a DAG, where the rate on the subset of outgoing edges of any node are related/constrained. An optimal algorithm to find max-flow with these constraints is also provided, which may be of independent interest.
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。
