通过边增强提高网络鲁棒性同时保持强结构可控性
Improving Network Robustness through Edge Augmentation While Preserving Strong Structural Controllability
摘要：
在本文中，我们考虑了一个网络的代理与拉普拉斯动力学，并研究了提高网络的鲁棒性的问题，增加了最大数量的边缘内的网络，同时保持其强结构可控性（SSC）的下限。边缘增强增强了网络对噪声和结构变化的鲁棒性，但它也可能恶化网络的可控性。因此，通过利用网络可控性和图中节点之间的距离之间的关系，我们制定了一个边增强问题的约束，以保持某些节点对之间的距离，这反过来又保证了SSC的下限，即使在添加边缘。在这个方向上，首先我们选择一个节点对，并在保持所选节点之间距离的同时最大限度地添加边。我们表明，最佳的解决方案属于一类图称为团链。然后，我们提出了一个算法，添加边，同时保持一定的节点集合之间的距离。此外，我们提出了一个随机算法，保证了所需的近似比与高概率解决边缘增强问题。最后，我们评估了我们在各种网络上的结果。
英文摘要：
In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding a maximum number of edges within the network while preserving a lower bound on its strong structural controllability (SSC) at the same time. Edge augmentation increases network's robustness to noise and structural changes, however, it could also deteriorate network controllability. Thus, by exploiting relationship between network controllability and distances between nodes in graphs, we formulate an edge augmentation problem with a constraint to preserve distances between certain node pairs, which in turn guarantees that a lower bound on SSC is maintained even after adding edges. In this direction, first we choose a node pair and maximally add edges while maintaining the distance between selected nodes. We show that an optimal solution belongs to a certain class of graphs called clique chains. Then, we present an algorithm to add edges while preserving distances between a certain collection of nodes. Further, we present a randomized algorithm that guarantees a desired approximation ratio with high probability to solve the edge augmentation problem. Finally, we evaluate our results on various networks.
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