Hardness of approximation of the Balanced Complete Bipartite Subgraph problem

We prove that the Maximum Balanced Complete Bipartite Subgraph (BCBS) problem is hard to approximate within a factor of 2 n) δ for some δ > 0 under the plausible assumption that 3-SAT ∈ DTIME ( 2 3/4+ ) for some > 0. We also show that it is NP -hard to approximate the BCBS problem within a constant factor under the assumption that it is NP -hard to approximate the maximum clique problem within a factor of n/2 √ lg n for some small enough c > 0. Furthermore we show that the same hardness of approximation results holds for the Maximum Edge Biclique problem.

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