# Faster Biclique Mining in Near-Bipartite Graphs

## TL;DR

This paper presents two optimized algorithms for enumerating maximal induced bicliques and bicliques in near-bipartite graphs, demonstrating improved practical performance over previous methods through extensive experiments.

## Contribution

Introduces two new algorithms for biclique enumeration in near-bipartite graphs, with improved theoretical complexity and practical efficiency over prior approaches.

## Key findings

- Algorithms outperform previous methods on diverse graph datasets.
- OCT-based algorithms are faster in practice.
- Effective for graphs with various sizes, densities, and OCT decompositions.

## Abstract

Identifying dense bipartite subgraphs is a common graph data mining task. Many applications focus on the enumeration of all maximal bicliques (MBs), though sometimes the stricter variant of maximal induced bicliques (MIBs) is of interest. Recent work of Kloster et al. introduced a MIB-enumeration approach designed for "near-bipartite" graphs, where the runtime is parameterized by the size k of an odd cycle transversal (OCT), a vertex set whose deletion results in a bipartite graph. Their algorithm was shown to outperform the previously best known algorithm even when k was logarithmic in |V|. In this paper, we introduce two new algorithms optimized for near-bipartite graphs - one which enumerates MIBs in time O(M_I |V||E| k), and another based on the approach of Alexe et al. which enumerates MBs in time O(M_B |V||E| k), where M_I and M_B denote the number of MIBs and MBs in the graph, respectively. We implement all of our algorithms in open-source C++ code and experimentally verify that the OCT-based approaches are faster in practice than the previously existing algorithms on graphs with a wide variety of sizes, densities, and OCT decompositions.