Efficient Top-k s-Biplexes Search over Large Bipartite Graphs

• URL: http://arxiv.org/abs/2409.18473v1
• Date: Fri, 27 Sep 2024 06:23:29 GMT
• Title: Efficient Top-k s-Biplexes Search over Large Bipartite Graphs
• Authors: Zhenxiang Xu, Yiping Liu, Yi Zhou, Yimin Hao, Zhengren Wang,
• Abstract summary: In bipartite graph analysis, enumeration of $s$-biplexes is a fundamental problem. In real-world data engineering, finding all $s-biplexes is neither necessary nor computationally affordable. We propose MVBP, that breaks the simple $2n enumeration algorithm. FastMVBP outperforms the benchmark algorithms by up to three orders of magnitude in several instances.
• Score: 4.507351209412066
• License:
• Abstract: In a bipartite graph, a subgraph is an $s$-biplex if each vertex of the subgraph is adjacent to all but at most $s$ vertices on the opposite set. The enumeration of $s$-biplexes from a given graph is a fundamental problem in bipartite graph analysis. However, in real-world data engineering, finding all $s$-biplexes is neither necessary nor computationally affordable. A more realistic problem is to identify some of the largest $s$-biplexes from the large input graph. We formulate the problem as the {\em top-$k$ $s$-biplex search (TBS) problem}, which aims to find the top-$k$ maximal $s$-biplexes with the most vertices, where $k$ is an input parameter. We prove that the TBS problem is NP-hard for any fixed $k\ge 1$. Then, we propose a branching algorithm, named MVBP, that breaks the simple $2^n$ enumeration algorithm. Furthermore, from a practical perspective, we investigate three techniques to improve the performance of MVBP: 2-hop decomposition, single-side bounds, and progressive search. Complexity analysis shows that the improved algorithm, named FastMVBP, has a running time $O^*(\gamma_s^{d_2})$, where $\gamma_s<2$, and $d_2$ is a parameter much smaller than the number of vertex in the sparse real-world graphs, e.g. $d_2$ is only $67$ in the AmazonRatings dataset which has more than $3$ million vertices. Finally, we conducted extensive experiments on eight real-world and synthetic datasets to demonstrate the empirical efficiency of the proposed algorithms. In particular, FastMVBP outperforms the benchmark algorithms by up to three orders of magnitude in several instances.

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