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Inter-Cluster Transmission Control Using Graph Modal Barriers
IEEE Transactions on Signal and Information Processing over Networks ( IF 3.2 ) Pub Date : 2021-04-07 , DOI: 10.1109/tsipn.2021.3071219
Leiming Zhang , Brian M. Sadler , Rick S. Blum , Subhrajit Bhattacharya

In this paper we consider the problem of transmission across a graph and develop a method for effectively controlling/restricting it with limited resources. Transmission can represent information transfer across a social network, spread of a malicious virus across a computer network, or spread of an infectious disease across communities. The key insight is to appropriately reduce the capacity for transmission on inter-cluster edges of the graph. To that end, the key contribution of the paper is to develop algorithms for computing a real, positive-valued distribution over the edges that gives a measure of the role each edge plays in being an inter-cluster edge. We refer to this distribution as the “ resistance ” and its computation is based on the eigenvectors of the graph Laplacian. Selectively reducing the weights (implying reduced transmission rate) on the critical edges based on this computed distribution helps establish barriers between the clusters ( modal barriers ) and thus limit the transmission from one cluster to another. Our proposed method for edge weight reduction for inter-cluster transmission control depends only on the graph topology and not on the exact model of the transmission dynamics. Unlike other work on graph partitioning and clustering, we completely circumvent the associated computational complexities by assigning real values to edges instead of performing discrete graph cuts. This allows us to provide strong theoretical results on our proposed methods. We also develop approximations that allow low complexity distributed computation of the barrier weights using only neighborhood communication.

中文翻译:

使用图模态障碍的集群间传输控制

在本文中,我们考虑了跨图传输的问题,并开发了一种在资源有限的情况下有效控制/限制图传输的方法。传输可以表示跨社交网络的信息传输,跨计算机网络的恶意病毒传播或跨社区的传染病传播。关键的见解是适当地减少图形在集群间边缘上的传输容量。为此,本文的主要贡献是开发了用于计算边缘上真实,正值分布的算法,该算法可以衡量每个边缘在集群间边缘中所扮演的角色。我们将此分布称为“ 抵抗性 ”,其计算基于图拉普拉斯算子的特征向量。根据此计算的分布,有选择地减少关键边缘的权重(暗示降低的传输速率)有助于在群集之间建立屏障( 模式障碍 ),从而限制了从一个群集到另一群集的传输。我们为集群间传输控制提出的减少边缘权重的方法仅取决于图拓扑,而不取决于传输动力学的精确模型。与其他有关图形分区和聚类的工作不同,我们通过为边缘分配实值而不是执行离散的图形切割来完全规避相关的计算复杂性。这使我们能够对我们提出的方法提供强有力的理论结果。我们还开发了一种近似方法,该方法允许仅使用邻域通信进行低复杂度的屏障权重分布式计算。
更新日期:2021-05-14
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