真实无线网络中虚拟内存的分布式K-Backup布局及其应用
Distributed K-Backup Placement and Applications to Virtual Memory in Real-World Wireless Networks
摘要：
在$\mathcal{CONGEST}$分布式设置中的网络中的备份放置问题考虑网络图$G = (V,E)$，其中每个顶点$v \in V$的目标是选择邻居，使得$V$中选择相同顶点的顶点的最大数量被最小化[Halldorsson等人，2015年]。以往的备份放置算法忽略了实际异构无线网络中的主要因素。具体地，没有考虑节点的存储器和存储容量，并且没有参考节点具有不同能量容量的情况，因此可以在任何时间离开（或加入）网络。这些参数在无线网络中密切相关，因为网络不同部分的负载可能差异很大，因此需要更多的通信、能量、内存和存储。为了适应现实世界的无线网络的属性，这项工作解决了一个广义版本的原始问题，即$K$ -备份放置，其中每个顶点选择$K$邻居，为一个积极的参数$K$。我们的$K$ -备份放置算法仅在一轮内终止。此外，我们提出了两个互补的算法，采用$K$ -备份放置，以获得有效的虚拟内存计划的无线网络。第一个算法将每个节点的内存分成许多小部分。每个顶点都被分配了它的邻居的一个大子集的记忆。因此，更多的内存容量为更多的顶点获得，但有很多碎片。第二种算法需要更大的轮复杂度，但为每个顶点产生更大的虚拟内存而没有任何碎片。
英文摘要：
The Backup Placement problem in networks in the $\mathcal{CONGEST}$ distributed setting considers a network graph $G = (V,E)$, in which the goal of each vertex $v \in V$ is selecting a neighbor, such that the maximum number of vertices in $V$ that select the same vertex is minimized [Halldorsson et al., 2015]. Previous backup placement algorithms suffer from obliviousness to main factors of real-world heterogeneous wireless network. Specifically, there is no consideration of the nodes memory and storage capacities, and no reference to a case in which nodes have different energy capacity, and thus can leave (or join) the network at any time. These parameters are strongly correlated in wireless networks, as the load on different parts of the network can differ greatly, thus requiring more communication, energy, memory and storage. In order to fit the real-world attributes of wireless networks, this work addresses a generalized version of the original problem, namely $K$-Backup Placement, in which each vertex selects $K$ neighbors, for a positive parameter $K$. Our $K$-Backup Placement algorithm terminates within just one round. In addition we suggest two complementary algorithms which employ $K$-Backup-Placement to obtain efficient virtual memory schemes for wireless networks. The first algorithm divides the memory of each node to many small parts. Each vertex is assigned the memories of a large subset of its neighbors. Thus more memory capacity for more vertices is gained, but with much fragmentation. The second algorithm requires greater round-complexity, but produces larger virtual memory for each vertex without any fragmentation.
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