分布式系统中信道分配和数据迁移的一种范例
A Paradigm for Channel Assignment and Data Migration in Distributed Systems
摘要：
在这篇手稿中，我们考虑在无线网络中的信道分配和异构存储系统中的数据迁移的问题。我们表明，软边着色的方法，这两个问题提供了严格的近似保证。在无线网络中出现的信道分配问题中，如果分配给它们的信道相同，则与顶点关联的一对边被称为冲突。我们的目标是分配通道（颜色边缘），以便最小化冲突的数量。该问题是NP-困难的减少边着色，我们提出了两种组合算法。第一个算法是基于分布式贪婪算法的，它给出的解最多比最优解有$2(1-\frac{1}{k})|E|$更多的冲突.第二个算法是$1 + \frac{|V|}{|E|}$，它给出了稠密图的（$1 + o(1)$）-因子，并且是最好的可能，除非P = NP.我们还考虑了异构存储系统中的数据迁移问题。在这样的系统中，可能需要随着时间的推移重新配置数据布局以用于负载均衡或者在系统故障/升级的情况下重新配置数据布局。将数据尽快迁移到目标位置以获得系统的最佳性能至关重要。以前的大多数数据迁移结果都假设每个存储节点一次只能执行一次数据传输。然而，存储设备往往具有异构能力，因为由于存储需求的增加，设备可能随着时间的推移而增加。我们开发的算法，以尽量减少数据迁移时间。我们表明，它是可能找到一个最佳的迁移时间表时，所有的$c_v$的甚至。此外，虽然该问题是NP-困难的一般情况下，我们给出了一个有效的软边着色算法，提供了严格的$(1 + o(1))$近似保证。
英文摘要：
In this manuscript, we consider the problems of channel assignment in wireless networks and data migration in heterogeneous storage systems. We show that a soft edge coloring approach to both problems gives rigorous approximation guarantees. In the channel assignment problem arising in wireless networks a pair of edges incident to a vertex are said to be conflicting if the channels assigned to them are the same. Our goal is to assign channels (color edges) so that the number of conflicts is minimized. The problem is NP-hard by a reduction from Edge coloring and we present two combinatorial algorithms for this case. The first algorithm is based on a distributed greedy method and gives a solution with at most $2(1-\frac{1}{k})|E|$ more conflicts than the optimal solution.The approximation ratio if the second algorithm is $1 + \frac{|V|}{|E|}$, which gives a ($1 + o(1)$)-factor for dense graphs and is the best possible unless P = NP. We also consider the data migration problem in heterogeneous storage systems. In such systems, data layouts may need to be reconfigured over time for load balancing or in the event of system failure/upgrades. It is critical to migrate data to their target locations as quickly as possible to obtain the best performance of the system. Most of the previous results on data migration assume that each storage node can perform only one data transfer at a time. However, storage devices tend to have heterogeneous capabilities as devices may be added over time due to storage demand increase. We develop algorithms to minimize the data migration time. We show that it is possible to find an optimal migration schedule when all $c_v$'s are even. Furthermore, though the problem is NP-hard in general, we give an efficient soft edge coloring algorithm that offers a rigorous $(1 + o(1))$-approximation guarantee.
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