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arXiv 1406.3671cs.NIcs.DS
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能量收集网络中最大最小公平速率分配与路由的数学分析

Max-min Fair Rate Allocation and Routing in Energy Harvesting Networks: Algorithmic Analysis

Jelena Marasevic, Cliff Stein, Gil Zussman

摘要:

本文研究了能量收集网络中最大最小公平速率分配和路由问题,其中节点间和时隙间都需要公平性。与以往大多数工作的公平性,我们专注于多跳拓扑结构,并考虑不同的路由方法。我们假设一个可预测的能源配置文件,并专注于设计高效和最佳的算法,可以作为分布式和近似算法的基准。首先,我们开发了一种算法,获得一个最大最小的公平率分配任何给定的(时变或时不变)unsplittable路由或路由树。对于时间不变的unsplittable路由,我们还开发了一个算法,找到最大限度地提高分配给任何节点在任何时隙的最小速率的路由。对于分式路由,我们研究了联合路由和速率分配问题。我们开发了一个算法的时间不变的情况下,恒定的利率。我们表明,时间变量的情况下,至少是硬的2-商品可行流问题,并设计一个FPTAS打击高运行时间。最后,我们表明,找到一个不可分割的路由或路由树,提供字典最大速率分配(即,在最大-最小公平性项中是最好的)是NP难的,即使对于单个时隙的时间范围也是如此。我们的分析提供了深入的问题结构,并可以应用到其他相关的公平问题。

英文摘要:

This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms that can serve as benchmarks for distributed and approximate algorithms. We first develop an algorithm that obtains a max-min fair rate assignment for any given (time-variable or time-invariable) unsplittable routing or a routing tree. For time-invariable unsplittable routing, we also develop an algorithm that finds routes that maximize the minimum rate assigned to any node in any slot. For fractional routing, we study the joint routing and rate assignment problem. We develop an algorithm for the time-invariable case with constant rates. We show that the time-variable case is at least as hard as the 2-commodity feasible flow problem and design an FPTAS to combat the high running time. Finally, we show that finding an unsplittable routing or a routing tree that provides lexicographically maximum rate assignment (i.e., that is the best in the max-min fairness terms) is NP-hard, even for a time horizon of a single slot. Our analysis provides insights into the problem structure and can be applied to other related fairness problems.

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。

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