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arXiv 1502.03517cs.ITcs.DMmath.IT
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协作数据交换中的最公平常数和速率传输:一种M-凸最小化方法

Fairest Constant Sum-rate Transmission for Cooperative Data Exchange: An M-convex Minimization Approach

Ni Ding, Rodney A. Kennedy, Parastoo Sadeghi

摘要:

我们考虑了一组无线客户端之间的协同数据交换(CDE)的公平性问题。在该系统中,每个客户端最初获得分组的子集。它们交换数据包,以便重建整个数据包集。我们研究的问题,如何找到一个传输策略,分配的通信负载最均匀的所有策略,具有相同的总和速率(传输的总次数),并实现普遍的恢复(当所有客户端恢复数据包集的情况)。我们将这个问题转化为一个离散的极小化问题,并证明了它的$M$ -凸性。我们表明,我们的结果也可以证明在以前的工作中所示的可行域的子模块性,并密切相关的子模块约束下的资源分配问题。为了解决这个问题,我们建议使用最速下降算法(SDA)的基础上$M$凸。通过改变客户端和数据包的数量,我们比较SDA与基于子模块的确定性算法(DA)的收敛性能和复杂度。结果表明,对于寻找最公平和最小总速率的CDE策略问题,当客户端数为5时,SDA比DA更有效。

英文摘要:

We consider the fairness in cooperative data exchange (CDE) problem among a set of wireless clients. In this system, each client initially obtains a subset of the packets. They exchange packets in order to reconstruct the entire packet set. We study the problem of how to find a transmission strategy that distributes the communication load most evenly in all strategies that have the same sum-rate (the total number of transmissions) and achieve universal recovery (the situation when all clients recover the packet set). We formulate this problem by a discrete minimization problem and prove its $M$-convexity. We show that our results can also be proved by the submodularity of the feasible region shown in previous works and are closely related to the resource allocation problems under submodular constraints. To solve this problem, we propose to use a steepest descent algorithm (SDA) based on $M$-convexity. By varying the number of clients and packets, we compare SDA with a deterministic algorithm (DA) based on submodularity in terms of convergence performance and complexity. The results show that for the problem of finding the fairest and minimum sum-rate strategy for the CDE problem SDA is more efficient than DA when the number of clients is up to five.

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