A simple (2+ϵ)-approximation algorithm for Split Vertex Deletion
A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph G and weight function w:V(G)→Q≥0, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set of vertices X such that G−X is a split graph. It is easy to show that a graph is a sp...
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| Vydáno v: | European journal of combinatorics Ročník 121; s. 103844 |
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01.10.2024
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| ISSN: | 0195-6698, 1095-9971 |
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| Abstract | A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph G and weight function w:V(G)→Q≥0, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set of vertices X such that G−X is a split graph. It is easy to show that a graph is a split graph if and only if it does not contain a 4-cycle, 5-cycle, or a two edge matching as an induced subgraph. Therefore, SVD admits an easy 5-approximation algorithm. On the other hand, for every δ>0, SVD does not admit a (2−δ)-approximation algorithm, unless P=NP or the Unique Games Conjecture fails.
For every ϵ>0, Lokshtanov, Misra, Panolan, Philip, and Saurabh (Lokshtanov et al., 2020) recently gave a randomized(2+ϵ)-approximation algorithm for SVD. In this work we give an extremely simple deterministic (2+ϵ)-approximation algorithm for SVD. |
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| AbstractList | A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph G and weight function w:V(G)→Q≥0, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set of vertices X such that G−X is a split graph. It is easy to show that a graph is a split graph if and only if it does not contain a 4-cycle, 5-cycle, or a two edge matching as an induced subgraph. Therefore, SVD admits an easy 5-approximation algorithm. On the other hand, for every δ>0, SVD does not admit a (2−δ)-approximation algorithm, unless P=NP or the Unique Games Conjecture fails.
For every ϵ>0, Lokshtanov, Misra, Panolan, Philip, and Saurabh (Lokshtanov et al., 2020) recently gave a randomized(2+ϵ)-approximation algorithm for SVD. In this work we give an extremely simple deterministic (2+ϵ)-approximation algorithm for SVD. |
| ArticleNumber | 103844 |
| Author | Huynh, Tony Fiorini, Samuel Drescher, Matthew |
| Author_xml | – sequence: 1 givenname: Matthew surname: Drescher fullname: Drescher, Matthew email: knavely@gmail.com organization: Département de Mathématique, Université libre de Bruxelles, Boulevard du Triomphe, Brussels, B-1050, Belgium – sequence: 2 givenname: Samuel surname: Fiorini fullname: Fiorini, Samuel email: Samuel.Fiorini@ulb.be organization: Département de Mathématique, Université libre de Bruxelles, Boulevard du Triomphe, Brussels, B-1050, Belgium – sequence: 3 givenname: Tony surname: Huynh fullname: Huynh, Tony email: huynh@di.uniroma1.it organization: Dipartimento di Informatica, Sapienza Università di Roma, viale Regina Elena 295, Rome, 00198, Italy |
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| Cites_doi | 10.1016/j.jcss.2007.06.019 10.4007/annals.2006.164.51 10.1016/0012-365X(86)90076-2 10.1016/j.aim.2008.07.009 10.1016/j.jctb.2015.01.001 10.1016/j.ejc.2014.02.003 |
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| References | Bousquet, Lagoutte, Thomassé (b3) 2015; 113 Fox, Sudakov (b6) 2008; 219 Erdős, Hajnal (b5) 1989 Freund, Bar-Yehuda, Bendel (b7) 2005; 36 Lokshtanov, Misra, Mukherjee, Panolan, Philip, Saurabh (b9) 2020 Bar-Yehuda, Even (b1) 1985; vol. 109 Khot, Regev (b8) 2008; 74 Szemerédi (b12) 1978; vol. 260 Rödl (b11) 1986; 59 Bousquet, Lagoutte, Thomassé (b2) 2014; 40 Lokshtanov, Misra, Panolan, Philip, Saurabh (b10) 2020 Chudnovsky, Robertson, Seymour, Thomas (b4) 2006; 164 Chudnovsky (10.1016/j.ejc.2023.103844_b4) 2006; 164 Lokshtanov (10.1016/j.ejc.2023.103844_b9) 2020 Szemerédi (10.1016/j.ejc.2023.103844_b12) 1978; vol. 260 Bar-Yehuda (10.1016/j.ejc.2023.103844_b1) 1985; vol. 109 Khot (10.1016/j.ejc.2023.103844_b8) 2008; 74 Lokshtanov (10.1016/j.ejc.2023.103844_b10) 2020 Bousquet (10.1016/j.ejc.2023.103844_b2) 2014; 40 Bousquet (10.1016/j.ejc.2023.103844_b3) 2015; 113 Erdős (10.1016/j.ejc.2023.103844_b5) 1989 Fox (10.1016/j.ejc.2023.103844_b6) 2008; 219 Freund (10.1016/j.ejc.2023.103844_b7) 2005; 36 Rödl (10.1016/j.ejc.2023.103844_b11) 1986; 59 |
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