Integer linear programming formulations for double roman domination problem

For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then vertex v must have at least one neighbour u with . In this paper, we consider the do...

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Published inOptimization methods & software Vol. 37; no. 1; pp. 1 - 22
Main Authors Cai, Qingqiong, Fan, Neng, Shi, Yongtang, Yao, Shunyu
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2022
Taylor & Francis Ltd
Subjects
Algorithms
Approximation
approximation algorithm
Double roman domination
integer linear programming
Integer programming
Linear programming
Mathematical functions
Mixed integer
Optimization
Polynomials
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Abstract For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then vertex v must have at least one neighbour u with . In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance.
AbstractList For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then vertex v must have at least one neighbour u with . In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance.
For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with , and if , then vertex v must have at least one neighbour u with . In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance.
Author Yao, Shunyu
Fan, Neng
Shi, Yongtang
Cai, Qingqiong
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Snippet For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2...
For a graph , a double Roman dominating function (DRDF) is a function having the property that if , then vertex v must have at least two neighbours assigned 2...
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SubjectTerms Algorithms
Approximation
approximation algorithm
Double roman domination
integer linear programming
Integer programming
Linear programming
Mathematical functions
Mixed integer
Optimization
Polynomials
Title Integer linear programming formulations for double roman domination problem
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Volume 37
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