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arXiv 1502.03518cs.ITcs.DMmath.IT
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协同数据交换中最小和速率的估计

Estimating Minimum Sum-rate for Cooperative Data Exchange

Ni Ding, Rodney A. Kennedy, Parastoo Sadeghi

摘要:

研究如何准确估计最小和速率,以降低协同数据交换(CDE)问题求解的复杂度。CDE系统包含多个地理位置接近的客户端,这些客户端发送数据包以帮助其他客户端恢复整个数据包集。最小和速率是实现通用恢复(所有客户端恢复整个分组集的情况)的传输总数的最小值。基于超模基多面体非空的一个充分必要条件,我们证明了CDE系统的最小和率可以由客户集的所有可能分区的最大化来确定.由于解决这个最大化问题的复杂性很高,我们提出了一个确定性算法来近似最小和率的下限。我们通过实验表明,这个下限是严格得多,比那些在现有文献中得出的下限。我们还表明,确定性算法可以防止重复运行现有的算法解决CDE问题,使整体的复杂性可以相应地降低。

英文摘要:

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.

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