  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.
