There are extensive studies focusing on the application scenario that all the bipartite cohesive subgraphs need to be discovered in a bipartite graph. However, we observe that, for some applications, one is interested in finding bipartite cohesive subgraphs containing a specific vertex. In this paper, we study a new query dependent bipartite cohesive subgraph search problem based on $k$-wing model, named as the personalized $k$-wing search problem. We introduce a $k$-wing equivalence relationship to summarize the edges of a bipartite graph $G$ into groups. Therefore, all the edges of $G$ are segregated into different groups, i.e. $k$-wing equivalence class, forming an efficient and wing number conserving index called EquiWing. Further, we propose a more compact version of EquiWing, EquiWing-Comp, which is achieved by integrating our proposed $k$-butterfly loose approach and discovered hierarchy properties. These indices are used to expedite the personalized $k$-wing search with a non-repetitive access to $G$, which leads to linear algorithms for searching the personalized $k$-wing. Moreover, we conduct a thorough study on the maintenance of the proposed indices for evolving bipartite graphs. We discover novel properties that help us localize the scope of the maintenance at a low cost. By exploiting the discoveries, we propose novel algorithms for maintaining the two indices, which substantially reduces the cost of maintenance. We perform extensive experimental studies in real, large-scale graphs to validate the efficiency and effectiveness of EquiWing and EquiWing-Comp compared to the baseline.

中文翻译：

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在大型和动态二分图中搜索个性化的$ k $ -wing

有广泛的研究集中于需要在二分图中发现所有二分内聚子图的应用场景。但是，我们观察到，对于某些应用程序，人们感兴趣的是寻找包含特定顶点的二分内聚子图。在本文中，我们研究了一种基于$ k $ -wing模型的新的依赖于查询的二元内聚子图搜索问题，称为个性化$ k $ -wing搜索问题。我们引入了$ k $ -wing等价关系，以将二分图$ G $的边缘归纳成组。因此，$ G $的所有边都被分为不同的组，即$ k $ -wing等价类，形成了一个称为EquiWing的高效且保留翼数的索引。此外，我们提出了更紧凑的EquiWing，EquiWing-Comp，这是通过整合我们提出的$ k $ -butterfly宽松方法和发现的层次结构属性来实现的。这些索引用于通过非重复访问$ G $来加速个性化$ k $ -wing的搜索，这导致了搜索个性化$ k $ -wing的线性算法。此外，我们对演化的二部图的拟议指标的维护进行了深入研究。我们发现了新颖的特性，可帮助我们以低成本定位维护范围。通过利用这些发现，我们提出了用于维护两个索引的新颖算法，从而大大降低了维护成本。我们在真实的大型图形中进行了广泛的实验研究，以验证EquiWing和EquiWing-Comp与基线相比的效率和有效性。