K-核最小化：一种博弈论方法
K-Core Minimization: A Game Theoretic Approach
摘要：
K-核是所有顶点的度至少为k的最大诱导子图。这些密集模式在社区发现、网络可视化和蛋白质功能预测等方面具有应用价值。然而，k核对于网络修改可能非常不稳定，这引发了一个问题：网络（如Web或Facebook）的k核结构对边删除的弹性如何？我们从算法的角度来研究这个问题。更具体地说，我们研究的问题，计算一个小的一组边缘的删除最小化的$k$核心结构的网络。本文给出了k-核极小化问题（KCM）的难性的一个全面的刻画，包括不可逼近性和固定参数难处理性。出于这样的挑战，在算法设计方面，我们提出了一种新的算法的启发Shapley值-合作博弈论的概念-这是能够利用强相互依赖的边缘去除的影响，在搜索空间。由于计算Shapley值也是NP难的，我们使用具有概率保证的随机算法有效地近似它们。我们的实验，使用几个真实的数据集，表明该算法优于竞争的解决方案，在k-核心最小化，同时能够处理大型图形。此外，我们说明了如何KCM可以应用于网络的k-核心弹性的分析。
英文摘要：
K-cores are maximal induced subgraphs where all vertices have degree at least k. These dense patterns have applications in community detection, network visualization and protein function prediction. However, k-cores can be quite unstable to network modifications, which motivates the question: How resilient is the k-core structure of a network, such as the Web or Facebook, to edge deletions? We investigate this question from an algorithmic perspective. More specifically, we study the problem of computing a small set of edges for which the removal minimizes the $k$-core structure of a network. This paper provides a comprehensive characterization of the hardness of the k-core minimization problem (KCM), including innaproximability and fixed-parameter intractability. Motivated by such a challenge in terms of algorithm design, we propose a novel algorithm inspired by Shapley value -- a cooperative game-theoretic concept -- that is able to leverage the strong interdependencies in the effects of edge removals in the search space. As computing Shapley values is also NP-hard, we efficiently approximate them using a randomized algorithm with probabilistic guarantees. Our experiments, using several real datasets, show that the proposed algorithm outperforms competing solutions in terms of k-core minimization while being able to handle large graphs. Moreover, we illustrate how KCM can be applied in the analysis of the k-core resilience of networks.
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。
