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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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00200190_v130_n_p11_Lin http://hdl.handle.net/20.500.12110/paper_00200190_v130_n_p11_Lin |
| Aporte de: |
| Sumario: | 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 |
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