发表机构
American University of Beirut; University of Colorado Boulder（贝鲁特美国大学; 科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出利用k-核分解和子树计数技术加速网络模体发现中同构子图计数的算法，证明关键子程序为#P完全，并在11个真实网络上验证了性能提升。
AI 中文摘要
我们开发了一种新算法，用于计算网络中与给定查询图同构的子图数量（#子图同构问题），其动机源于网络模体搜索。真实世界网络中常见的高阶顶点（枢纽）会导致子图数量的组合爆炸，使得现有的模体搜索算法在多种感兴趣的网络中，对于大于约8的模体规模变得难以处理。我们的方法利用k-核分解和一种新颖的子树计数技术来快速扫描网络的边缘区域。这两项创新使得我们的算法在实践中显著加速其前代算法，尤其是因为大多数真实世界网络具有相对较大的边缘区域。我们证明了#根子树同构问题（我们算法中的一个关键子程序）通过从计数二分匹配问题归约而成为#P完全问题。我们提供了算法执行时间的解析上界，并在11个具有不同拓扑结构的真实世界网络上评估了其性能。
英文摘要
We develop a new algorithm for counting the number of subgraphs of a network isomorphic to a given query graph (#SubgraphIsomorphism), motivated by network motif search. High-degree vertices (hubs), common in real-world networks, contribute to a combinatorial explosion in the number of subgraphs, making existing motif search algorithms intractable for motif sizes greater than $\approx 8$ on a wide variety of networks of interest. Our procedure leverages the $k$-core decomposition and a novel subtree-counting technique to quickly scan the periphery of a network. These two innovations allow our algorithm to significantly speed up its predecessors in practice, especially as most real-world networks have a relatively large periphery. We prove that #RootedSubtreeIsomorphism, a key subroutine in our algorithm, is #P-complete via a reduction from counting bipartite matchings. We provide analytic upper bounds on our algorithm's execution time, and evaluate its performance on 11 real-world networks of varying topologies.
