Wu et al. (2014) showed that under the small set expansion hypothesis (SSEH) there is no polynomial time approximation algorithm with any constant approximation factor for several graph width parameters, including tree-width, path-width, and cut-width (Wu et al. 2014). In this paper, we extend this line of research by exploring other graph width parameters: We obtain similar approximation hardness results under the SSEH for rank-width and maximum induced matching-width, while at the same time we show the approximation hardness of carving-width, clique-width, NLC-width, and boolean-width. We also give a simpler proof of the approximation hardness of tree-width, path-width, and cut-widththan that of Wu et al.
Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses
