Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut

We consider the Minimum Linear Arrangement problem and the (Uniform) Sparsest Cut problem. So far, these two notorious NP-hard graph problems have resisted all attempts to prove inapproximability results. We show that they have no polynomial time approximation scheme, unless NP-complete problems can be solved in randomized subexponential time. Furthermore, we show that the same techniques can be used for the Maximum Edge Biclique problem, for which we obtain a hardness factor similar to previous results but under a more standard assumption. Key words. hardness of approximation, graph theory AMS subject classifications. 68Q17, 68Q25 DOI. 10.1137/080729256

• Type: Journal
• Year: 2011
• Where: SIAMCOMP
• Authors: Christoph Ambühl, Monaldo Mastrolilli, Ola Svensson
• Keywords: Formal Methods, Linear Arrangement Problem, Polynomial Time Approximation, SIAMCOMP 2011, Time Approximation Scheme