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Algorithms 2018, 11(11), 173; https://doi.org/10.3390/a11110173

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

Division of Electronics and Informatics, Gunma University, Kiryu 376-8515, Japan
Received: 3 September 2018 / Revised: 23 October 2018 / Accepted: 30 October 2018 / Published: 31 October 2018
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Abstract

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. View Full-Text
Keywords: graph width parameter; inapproximability; small set expansion hypothesis graph width parameter; inapproximability; small set expansion hypothesis
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Yamazaki, K. Inapproximability of Rank, Clique, Boolean, and Maximum Induced Matching-Widths under Small Set Expansion Hypothesis. Algorithms 2018, 11, 173.

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