大型图中稀疏子图和稠密子图的快速识别算法
Identifying sparse and dense sub-graphs in large graphs with a fast algorithm
摘要：
在没有先验信息的情况下，如何识别小的子图的节点是一个困难的问题。在这项工作中，我们希望找到一个稀疏的子图嵌入在动态和静态的背景图，平均度较大的每个节点。我们发现，利用可求和性超过几个背景实现的埃斯特拉达-Benzi通信和Krylov近似的矩阵指数，它是可能的，以恢复子图的快速算法与计算复杂性O（N n）。将问题放宽到完全子图，在单个背景下获得相同的性能。最坏情况下的复杂度为O（n log（n））。
英文摘要：
Identifying the nodes of small sub-graphs with no a priori information is a hard problem. In this work, we want to find each node of a sparse sub-graph embedded in both dynamic and static background graphs, of larger average degree. We show that exploiting the summability over several background realizations of the Estrada-Benzi communicability and the Krylov approximation of the matrix exponential, it is possible to recover the sub-graph with a fast algorithm with computational complexity O(N n). Relaxing the problem to complete sub-graphs, the same performance is obtained with a single background. The worst case complexity for the single background is O(n log(n)).
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