Searching Personalized $k$k-Wing in Bipartite Graphs

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 personalized
$k$
-wing search problem. We study the
$k$
-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.,
$k$k-wing equivalence class
, forming an efficient and wing number conserving index called
EquiWing-Graph
. Further, we propose a more compact index,
EquiWing-Tree
, which is achieved by using our proposed
$k$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-world graphs to validate the efficiency and effectiveness of
EquiWing-Graph
and
EquiWing-Tree
compared to the baseline.