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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Detalles Bibliográficos
Autores principales: Lin, M.C., Mestre, J., Vasiliev, S.
Formato: JOUR
Materias:
Approximation algorithms
Graph algorithms
Weighted neighborhood independent set
Computational complexity
Problem solving
Approximation ratios
Diamond-free graphs
General graph
Independent set
Maximum degree
Polynomially solvable
Regular graphs
Graph theory
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00200190_v130_n_p11_Lin
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
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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