二部图的公平性最大二边圈计数
Fairness-aware Maximal Biclique Enumeration on Bipartite Graphs
摘要：
最大二部图计数是二部图数据分析中的一个基本问题。现有的二分图枚举方法主要针对无属性二分图，也忽略了图属性的\emph{fairness}。本文首次将公平性的概念引入到双团模型中，研究了公平性感知的双团枚举问题。具体来说，我们提出了两个公平感知的biclique模型，分别称为\nonesidebc ~和\ntwosidebc ~。为了有效地枚举所有{ \nonesidebc }，我们首先提出了两个非平凡的修剪技术，称为公平的$α$ - $β$核心修剪和丰富多彩的公平的$α$ - $β$核心修剪，以减少图的大小，而不损失准确性。然后，我们开发了一个分支定界算法，称为\onesideFBCEM，枚举所有的单边公平二分图的约简二分图。为了进一步提高效率，我们提出了一个有效的分支定界算法与精心设计的组合枚举技术。请注意，我们所有的技术也可以扩展到枚举所有双边公平bicliques。我们还通过限制每个属性的顶点数与顶点总数的比率来扩展这两个公平感知的biclique模型，并提出相应的枚举算法。在五个大型真实世界数据集上的大量实验结果证明了我们的方法的效率，有效性和可扩展性。
英文摘要：
Maximal biclique enumeration is a fundamental problem in bipartite graph data analysis. Existing biclique enumeration methods mainly focus on non-attributed bipartite graphs and also ignore the \emph{fairness} of graph attributes. In this paper, we introduce the concept of fairness into the biclique model for the first time and study the problem of fairness-aware biclique enumeration. Specifically, we propose two fairness-aware biclique models, called \nonesidebc~and \ntwosidebc~respectively. To efficiently enumerate all {\nonesidebc}s, we first present two non-trivial pruning techniques, called fair $α$-$β$ core pruning and colorful fair $α$-$β$ core pruning, to reduce the graph size without losing accuracy. Then, we develop a branch and bound algorithm, called \onesideFBCEM, to enumerate all single-side fair bicliques on the reduced bipartite graph. To further improve the efficiency, we propose an efficient branch and bound algorithm with a carefully-designed combinatorial enumeration technique. Note that all of our techniques can also be extended to enumerate all bi-side fair bicliques. We also extend the two fairness-aware biclique models by constraining the ratio of the number of vertices of each attribute to the total number of vertices and present corresponding enumeration algorithms. Extensive experimental results on five large real-world datasets demonstrate our methods' efficiency, effectiveness, and scalability.
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