2018
DOI: 10.3390/a11110173
|View full text |Cite
|
Sign up to set email alerts
|

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

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 appro… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
5
0

Year Published

2019
2019
2023
2023

Publication Types

Select...
2
1
1
1

Relationship

0
5

Authors

Journals

citations
Cited by 6 publications
(6 citation statements)
references
References 35 publications
(45 reference statements)
0
5
0
Order By: Relevance
“…pathwidth) of 3-manifolds (Corollary 14). This reduction, together with previous results [46,55,56], suggests that this problem may be computationally hard.…”
Section: Applicationsmentioning
confidence: 58%
See 1 more Smart Citation
“…pathwidth) of 3-manifolds (Corollary 14). This reduction, together with previous results [46,55,56], suggests that this problem may be computationally hard.…”
Section: Applicationsmentioning
confidence: 58%
“…Computing a constant-factor approximation of treewidth (resp. pathwidth) for arbitrary graphs is known to be conditionally NP-hard under the Small Set Expansion Hypothesis [46,55,56]. For proving Corollary 14, however, we rely on the assumption that the graph has bounded degree.…”
Section: Lemma 9 ([6 Lemma 46]mentioning
confidence: 99%
“…For many well-known graph classes a decomposition of bounded mim-width can be found in polynomial time. However, for general graphs it is known that computing mim-width is W[1]-hard and not in APX unless NP = ZPP [40], while Yamazaki [42] shows that under the small set expansion hypothesis it is not in APX unless P = NP. For dynamic programming algorithms as in this paper, to circumvent the assumption that we are given a decomposition, we want functions f , g and an algorithm that given a graph of mim-width OPT computes an f (O PT )-approximation to mim-width in time n g(O PT ) , i.e.…”
Section: Subset Odd Cycle Transveral (Soct)mentioning
confidence: 99%
“…The investigation of graph width parameters finds extensive applications across diverse fields, such as matroid theory, lattice theory, theoretical computer science, game theory, network theory, artificial intelligence, graph theory, and discrete mathematics, as evidenced by numerous studies (for example, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]22,[28][29][30][31][32][33]). These graph width parameters are frequently explored in conjunction with obstruction, contributing to a robust body of research.…”
Section: Introductionmentioning
confidence: 99%