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arXiv 1409.0932cs.ITcs.NImath.IT
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随机图中贪婪极大调度的局部池因子的刻画

On Characterizing the Local Pooling Factor of Greedy Maximal Scheduling in Random Graphs

Jeffrey Wildman, Steven Weber

摘要:

无线通信网络中低复杂度贪婪调度技术的最优性研究是一个非常复杂的问题。局部池化(LoP)因子提供了一个单参数的手段来表达一个这样的方案,贪婪最大调度(GMS)的可实现的容量区域(和最优性)。任意网络图的精确LoP因子通常难以获得,但可以基于网络图的特定结构来评估或定界。在本文中,我们提供了严格的刻画的LoP因子的大型网络建模为Erdens-Rényi(ER)和随机几何(RG)图下的主要干扰模型。我们采用阈值函数来建立边缘概率或通信半径的临界值,以产生有用的范围和期望的LoP因子的网络增长大。对于足够密集的随机图,我们发现,LoP因子是1/2和2/3之间,而足够稀疏的随机图允许GMS最优性(LoP因子为1)的概率很高。然后,我们将LoP在一个更大的背景下,通常研究的随机图形属性围绕连通性。我们观察到,允许连通性的边缘密度一般承认循环子图,这形成了LoP因子上限为2/3的基础。最后,我们通过模拟来探索小型网络的机制,这表明ER或RG图满足LoP并连接的概率在网络大小上迅速衰减。

英文摘要:

The study of the optimality of low-complexity greedy scheduling techniques in wireless communications networks is a very complex problem. The Local Pooling (LoP) factor provides a single-parameter means of expressing the achievable capacity region (and optimality) of one such scheme, greedy maximal scheduling (GMS). The exact LoP factor for an arbitrary network graph is generally difficult to obtain, but may be evaluated or bounded based on the network graph's particular structure. In this paper, we provide rigorous characterizations of the LoP factor in large networks modeled as Erdős-Rényi (ER) and random geometric (RG) graphs under the primary interference model. We employ threshold functions to establish critical values for either the edge probability or communication radius to yield useful bounds on the range and expectation of the LoP factor as the network grows large. For sufficiently dense random graphs, we find that the LoP factor is between 1/2 and 2/3, while sufficiently sparse random graphs permit GMS optimality (the LoP factor is 1) with high probability. We then place LoP within a larger context of commonly studied random graph properties centered around connectedness. We observe that edge densities permitting connectivity generally admit cycle subgraphs which forms the basis for the LoP factor upper bound of 2/3. We conclude with simulations to explore the regime of small networks, which suggest the probability that an ER or RG graph satisfies LoP and is connected decays quickly in network size.

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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