# Towards Effective Exact Algorithms for the Maximum Balanced Biclique Problem

## TL;DR

This paper introduces novel exact algorithms for the NP-hard Maximum Balanced Biclique Problem, utilizing upper bound propagation, valid inequalities, and enumeration techniques to improve computational efficiency on large instances.

## Contribution

It presents new upper bound propagation methods, valid inequalities, and enumeration schemes that enhance the effectiveness of exact algorithms for MBBP.

## Key findings

- Algorithms outperform existing methods on random graphs
- Proposed formulations solve larger real-world instances
- Enhanced efficiency in solving MBBP problems

## Abstract

The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP. Firstly, we introduce an Upper Bound Propagation procedure to pre-compute an upper bound involving each vertex. Then we extend an existing branch-and-bound algorithm by integrating the pre-computed upper bounds. We also present a set of new valid inequalities induced from the upper bounds to tighten an existing mathematical formulation for MBBP. Lastly, we investigate another exact algorithm scheme which enumerates a subset of balanced bicliques based on our upper bounds. Experiments show that compared to existing approaches, the proposed algorithms and formulations are more efficient in solving a set of random graphs and large real-life instances.