Inapproximability of Rank, Clique, Boolean, and Maximum Induced Matching-Widths under Small Set Expansion Hypothesis

Inapproximability of Maximum Edge Biclique, Maximum Balanced Biclique and Minimum k-Cut from the Small Set Expansion Hypothesis

The Small Set Expansion Hypothesis (SSEH) is a conjecture which roughly states that it is NPhard to distinguish between a graph with a small set of vertices whose expansion is almost zero and one in which all small sets of vertices have expansion almost one. In this work, we prove conditional inapproximability results for the following graph problems based on this hypothesis: Maximum Edge Bicli...

Inapproximability of Maximum Biclique Problems, Minimum k-Cut and Densest At-Least-k-Subgraph from the Small Set Expansion Hypothesis

The Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose (edge) expansion is almost zero and one in which all small subsets of vertices have expansion almost one. In this work, we prove conditional inapproximability results with essentially optimal ratios for the following graph problems based...

Fixed parameter inapproximability for Clique and Set-Cover

A minimization (resp., maximization) problem is called fixed parameter (r, t)approximable for two functionsr, t if there exists an algorithm that given an integer k and a problem instance I with optimum value opt, finds either a feasible solution of value at most r(k) · k (resp., at least k/r(k)) or a certificate that k < opt (resp., k > opt), in time t(k) · |I|O(1). A problem is called fixed p...

Heuristics For Maximum Clique And Independent Set

Heuristics for Maximum Clique and Independent Set