Approximating weighted neighborhood independent sets
A neighborhood independent set (NI-set) is a subset of edges in a graph such that the closed neighborhood of any vertex contains at most one edge of the subset. Finding a maximum cardinality NI-set is an NP-complete problem. We consider the weighted version of this problem. For general graphs we giv...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00200190_v130_n_p11_Lin |
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todo:paper_00200190_v130_n_p11_Lin2023-10-03T14:16:41Z Approximating weighted neighborhood independent sets Lin, M.C. Mestre, J. Vasiliev, S. Approximation algorithms Graph algorithms Weighted neighborhood independent set Approximation algorithms Computational complexity Problem solving Approximation ratios Diamond-free graphs General graph Graph algorithms Independent set Maximum degree Polynomially solvable Regular graphs Graph theory A neighborhood independent set (NI-set) is a subset of edges in a graph such that the closed neighborhood of any vertex contains at most one edge of the subset. Finding a maximum cardinality NI-set is an NP-complete problem. We consider the weighted version of this problem. For general graphs we give an algorithm with approximation ratio Δ, and for diamond-free graphs we give a ratio Δ/2+1, where Δ is the maximum degree of the input graph. Furthermore, we show that the problem is polynomially solvable on cographs. Finally, we give a tight upper bound on the cardinality of a NI-set on regular graphs. © 2017 JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00200190_v130_n_p11_Lin |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Approximation algorithms Graph algorithms Weighted neighborhood independent set Approximation algorithms Computational complexity Problem solving Approximation ratios Diamond-free graphs General graph Graph algorithms Independent set Maximum degree Polynomially solvable Regular graphs Graph theory |
| spellingShingle |
Approximation algorithms Graph algorithms Weighted neighborhood independent set Approximation algorithms Computational complexity Problem solving Approximation ratios Diamond-free graphs General graph Graph algorithms Independent set Maximum degree Polynomially solvable Regular graphs Graph theory Lin, M.C. Mestre, J. Vasiliev, S. Approximating weighted neighborhood independent sets |
| topic_facet |
Approximation algorithms Graph algorithms Weighted neighborhood independent set Approximation algorithms Computational complexity Problem solving Approximation ratios Diamond-free graphs General graph Graph algorithms Independent set Maximum degree Polynomially solvable Regular graphs Graph theory |
| description |
A neighborhood independent set (NI-set) is a subset of edges in a graph such that the closed neighborhood of any vertex contains at most one edge of the subset. Finding a maximum cardinality NI-set is an NP-complete problem. We consider the weighted version of this problem. For general graphs we give an algorithm with approximation ratio Δ, and for diamond-free graphs we give a ratio Δ/2+1, where Δ is the maximum degree of the input graph. Furthermore, we show that the problem is polynomially solvable on cographs. Finally, we give a tight upper bound on the cardinality of a NI-set on regular graphs. © 2017 |
| format |
JOUR |
| author |
Lin, M.C. Mestre, J. Vasiliev, S. |
| author_facet |
Lin, M.C. Mestre, J. Vasiliev, S. |
| author_sort |
Lin, M.C. |
| title |
Approximating weighted neighborhood independent sets |
| title_short |
Approximating weighted neighborhood independent sets |
| title_full |
Approximating weighted neighborhood independent sets |
| title_fullStr |
Approximating weighted neighborhood independent sets |
| title_full_unstemmed |
Approximating weighted neighborhood independent sets |
| title_sort |
approximating weighted neighborhood independent sets |
| url |
http://hdl.handle.net/20.500.12110/paper_00200190_v130_n_p11_Lin |
| work_keys_str_mv |
AT linmc approximatingweightedneighborhoodindependentsets AT mestrej approximatingweightedneighborhoodindependentsets AT vasilievs approximatingweightedneighborhoodindependentsets |
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1807315924283293696 |