Improved Approximation Algorithm for Maximum Balanced Biclique

TL;DR

This paper presents a new polynomial-time approximation algorithm for the Maximum Balanced Biclique problem, achieving a ratio that improves previous results and aligns with the maximum clique problem approximation.

Contribution

The authors develop a polynomial-time approximation algorithm for MBB with a ratio that surpasses prior work and resolves an open question from Chalermsook et al. (2020).

Findings

Achieves an approximation ratio of n/˜Ω((log n)^3).

Improves upon previous n/Ω((log n)^2) ratio.

Matches the approximation ratio of the maximum clique problem up to O(log log n).

Abstract

We study the Maximum Balanced Biclique (MBB) problem: Given a bipartite graph $G$ with $n$ vertices on each side, find a balanced biclique in $G$ with maximum size. We give a polynomial-time $\left(\frac{n}{\widetilde{\Omega}\left((\log n)^3\right)}\right)$-approximation algorithm for the problem, which improves upon an $\left(\frac{n}{\Omega\left((\log n)^2\right)}\right)$-approximation by Chalermsook et al. (2020) and answers their open question. Furthermore, our approximation ratio matches that of the maximum clique problem by Feige (2004) up to an $O(\log \log n)$ factor.