A subexponential-time algorithm for the Maximum Independent Set Problem in Pt-free graphs
The Maximum Independent Set Problem is known to be NP-hard in general. In the last decades lots of effort were spent to find polynomial-time algorithms for Pt-free graphs. A recent result presents such an algorithm for P5-free graphs. On the other hand, the complexity status for larger t is still un...
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| Vydáno v: | Discrete Applied Mathematics Ročník 231; s. 113 - 118 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
20.11.2017
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | The Maximum Independent Set Problem is known to be NP-hard in general. In the last decades lots of effort were spent to find polynomial-time algorithms for Pt-free graphs. A recent result presents such an algorithm for P5-free graphs. On the other hand, the complexity status for larger t is still unknown. In this paper we present a subexponential algorithm for the Maximum (Weighted) Independent Set Problem in Pt-free graphs. |
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| AbstractList | The Maximum Independent Set Problem is known to be NP-hard in general. In the last decades lots of effort were spent to find polynomial-time algorithms for Pt-free graphs. A recent result presents such an algorithm for P5-free graphs. On the other hand, the complexity status for larger t is still unknown. In this paper we present a subexponential algorithm for the Maximum (Weighted) Independent Set Problem in Pt-free graphs. |
| Author | Brause, Christoph |
| Author_xml | – sequence: 1 givenname: Christoph surname: Brause fullname: Brause, Christoph email: brause@math.tu-freiberg.de organization: Institute of Discrete Mathematics and Algebra, TU Bergakademie Freiberg, Freiberg, Germany |
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| Cites_doi | 10.1006/jcss.2000.1727 10.1016/j.dam.2010.01.007 10.1016/j.ipl.2003.07.004 10.1006/jcss.2001.1774 10.1016/j.dam.2008.08.025 10.1016/S0166-218X(99)00046-3 10.1016/S0166-218X(02)00290-1 10.1137/1.9781611973402.43 10.1137/1.9781611974331.ch124 |
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| References_xml | – year: 1979 ident: br000015 article-title: Computers and Intractability: A Guide to the Theory of NP-Completeness – volume: 62 start-page: 367 year: 2001 end-page: 375 ident: br000020 article-title: On the complexity of k-SAT publication-title: J. Comput. System Sci. – year: 1976 ident: br000055 publication-title: Principles of Mathematical Analysis – volume: 158 start-page: 731 year: 2010 end-page: 740 ident: br000060 article-title: A new characterization of publication-title: Discrete Appl. Math. – volume: 63 start-page: 512 year: 2001 end-page: 530 ident: br000025 article-title: Which problems have strongly exponential complexity? publication-title: J. Comput. System Sci. – reference: -free graphs, in: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, pp. 1784–1803. – start-page: 3 year: 1982 end-page: 13 ident: br000005 article-title: The effect of local constraints on the complexity of determination of the graph independence number publication-title: Combinatorial-Algebraic Methods in Applied Mathematics – volume: 158 start-page: 1041 year: 2010 end-page: 1044 ident: br000050 article-title: On maximum independent sets in publication-title: Discrete Appl. Math. – volume: 135 start-page: 3 year: 2004 end-page: 16 ident: br000010 article-title: Polynomial algorithm for finding the largest independent sets in graphs without forks publication-title: Discrete Appl. Math. – volume: 92 start-page: 177 year: 1999 end-page: 191 ident: br000045 article-title: Stable sets in certain publication-title: Discrete Appl. Math. – reference: D. Lokshantov, M. Vatshelle, Y. Villanger, Independent set in – reference: D. Lokshtanov, M. Pilipczuk, E.J. van Leeuwen, Independence and efficient domination on – reference: -free graphs in polynomial time, in: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 2014, pp. 570–581. – volume: 88 start-page: 167 year: 2003 end-page: 171 ident: br000040 article-title: Some results on graphs without long induced paths publication-title: Inform. Process. Lett. – volume: 62 start-page: 367 year: 2001 ident: 10.1016/j.dam.2016.06.016_br000020 article-title: On the complexity of k-SAT publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2000.1727 – volume: 158 start-page: 1041 year: 2010 ident: 10.1016/j.dam.2016.06.016_br000050 article-title: On maximum independent sets in P5-free graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2010.01.007 – volume: 88 start-page: 167 year: 2003 ident: 10.1016/j.dam.2016.06.016_br000040 article-title: Some results on graphs without long induced paths publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2003.07.004 – volume: 63 start-page: 512 year: 2001 ident: 10.1016/j.dam.2016.06.016_br000025 article-title: Which problems have strongly exponential complexity? publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2001.1774 – year: 1979 ident: 10.1016/j.dam.2016.06.016_br000015 – year: 1976 ident: 10.1016/j.dam.2016.06.016_br000055 – volume: 158 start-page: 731 year: 2010 ident: 10.1016/j.dam.2016.06.016_br000060 article-title: A new characterization of P6-free graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2008.08.025 – volume: 92 start-page: 177 year: 1999 ident: 10.1016/j.dam.2016.06.016_br000045 article-title: Stable sets in certain P6-free graphs publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(99)00046-3 – volume: 135 start-page: 3 year: 2004 ident: 10.1016/j.dam.2016.06.016_br000010 article-title: Polynomial algorithm for finding the largest independent sets in graphs without forks publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(02)00290-1 – ident: 10.1016/j.dam.2016.06.016_br000035 doi: 10.1137/1.9781611973402.43 – start-page: 3 year: 1982 ident: 10.1016/j.dam.2016.06.016_br000005 article-title: The effect of local constraints on the complexity of determination of the graph independence number – ident: 10.1016/j.dam.2016.06.016_br000030 doi: 10.1137/1.9781611974331.ch124 |
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| Title | A subexponential-time algorithm for the Maximum Independent Set Problem in Pt-free graphs |
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