The computational complexity of three graph problems for instances with bounded minors of constraint matrices

We consider boolean linear programming formulations of the independent set, the vertex and the edge dominating set problems and prove their polynomial-time solvability for classes of graphs with (augmented) constraint matrices having bounded minors in the absolute value.

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Published in:Discrete Applied Mathematics Vol. 227; pp. 13 - 20
Main Authors: Gribanov, D.V., Malyshev, D.S.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 20.08.2017
Elsevier BV
Subjects:
Boolean algebra
Boolean linear programming
Combinatorics
Dominating set problem
Efficient algorithm
Formulations
Graphs
Independent set problem
Linear programming
Mathematical analysis
Matrix
Matrix methods
Matrix minor
Dominating set problem
Boolean linear programming
Independent set problem
Matrix minor
Efficient algorithm
ISSN:0166-218X, 1872-6771
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Abstract We consider boolean linear programming formulations of the independent set, the vertex and the edge dominating set problems and prove their polynomial-time solvability for classes of graphs with (augmented) constraint matrices having bounded minors in the absolute value.
AbstractList We consider boolean linear programming formulations of the independent set, the vertex and the edge dominating set problems and prove their polynomial-time solvability for classes of graphs with (augmented) constraint matrices having bounded minors in the absolute value.
Author Gribanov, D.V.
Malyshev, D.S.
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  organization: National Research University Higher School of Economics, 25/12 Bolshaja Pecherskaja Ulitsa, Nizhny Novgorod, 603155, Russia
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10.1016/S0166-218X(02)00198-1
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10.1016/S0166-218X(02)00571-1
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10.1016/j.orl.2016.07.004
10.1007/BF02579150
10.1016/j.disc.2013.01.008
10.1561/0100000006
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Keywords Dominating set problem
Boolean linear programming
Independent set problem
Matrix minor
Efficient algorithm
Language English
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Snippet We consider boolean linear programming formulations of the independent set, the vertex and the edge dominating set problems and prove their polynomial-time...
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SubjectTerms Boolean algebra
Boolean linear programming
Combinatorics
Dominating set problem
Efficient algorithm
Formulations
Graphs
Independent set problem
Linear programming
Mathematical analysis
Matrix
Matrix methods
Matrix minor
Title The computational complexity of three graph problems for instances with bounded minors of constraint matrices
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