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Improved Approximation Algorithm for Maximum Balanced Biclique

Author Pasin Manurangsi

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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Discrete optimization
Keywords
  • Maximum Balanced Biclique
  • Approximation Algorithm
  • Semidefinite Programming

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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 (n/Ω̃((log n)³))-approximation algorithm for the problem, which improves upon an (n/Ω((log n)²))-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.

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Pasin Manurangsi. Improved Approximation Algorithm for Maximum Balanced Biclique. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 1:1-1:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.1

Author Details

Pasin Manurangsi
  • Google Research, Bangkok, Thailand

References

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