A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem
The objective of this paper is to derive a tight and efficient lower bound for the minimum sum coloring problem. This NP-hard problem is a variant of the classical graph coloring problem where the objective is to minimize the sum of the colors. A column generation approach is proposed to solve the l...
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8990124/ |
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doaj-f76eab815869400eb0072a47fbbe84882021-03-30T03:17:33ZengIEEEIEEE Access2169-35362020-01-018578915790410.1109/ACCESS.2020.29731228990124A Column Generation-Based Lower Bound for the Minimum Sum Coloring ProblemMehdi Mrad0https://orcid.org/0000-0002-9482-5913Olfa Harrabi1https://orcid.org/0000-0002-8176-0698Jouhaina Chaouachi Siala2https://orcid.org/0000-0002-5240-7270Anis Gharbi3https://orcid.org/0000-0001-5658-7259Department of Industrial Engineering, College of Engineering, King Saud University, Riyadh, Saudi ArabiaHigher Institute of Management of Tunis, ISG Tunis, Tunis University, Bardo, TunisiaInstitute of Advanced Business Studies of Carthage, Carthage University, IHEC Carthage Presidency, Carthage, TunisiaDepartment of Industrial Engineering, College of Engineering, King Saud University, Riyadh, Saudi ArabiaThe objective of this paper is to derive a tight and efficient lower bound for the minimum sum coloring problem. This NP-hard problem is a variant of the classical graph coloring problem where the objective is to minimize the sum of the colors. A column generation approach is proposed to solve the linear relaxation of a set partition-based formulation. Various enhancements are proposed in order to efficiently obtain attractive columns while avoiding as much as possible the exact solution of the huge number of the NP-hard pricing problems. Experimental results conducted on 42 hard benchmark instances show an average reduction of 89.73% of the gap between the best known lower and upper bounds, including 14 new optimality results.https://ieeexplore.ieee.org/document/8990124/Chromatic sumgraph coloringcolumn generationlower bound |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mehdi Mrad Olfa Harrabi Jouhaina Chaouachi Siala Anis Gharbi |
| spellingShingle |
Mehdi Mrad Olfa Harrabi Jouhaina Chaouachi Siala Anis Gharbi A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem IEEE Access Chromatic sum graph coloring column generation lower bound |
| author_facet |
Mehdi Mrad Olfa Harrabi Jouhaina Chaouachi Siala Anis Gharbi |
| author_sort |
Mehdi Mrad |
| title |
A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem |
| title_short |
A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem |
| title_full |
A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem |
| title_fullStr |
A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem |
| title_full_unstemmed |
A Column Generation-Based Lower Bound for the Minimum Sum Coloring Problem |
| title_sort |
column generation-based lower bound for the minimum sum coloring problem |
| publisher |
IEEE |
| series |
IEEE Access |
| issn |
2169-3536 |
| publishDate |
2020-01-01 |
| description |
The objective of this paper is to derive a tight and efficient lower bound for the minimum sum coloring problem. This NP-hard problem is a variant of the classical graph coloring problem where the objective is to minimize the sum of the colors. A column generation approach is proposed to solve the linear relaxation of a set partition-based formulation. Various enhancements are proposed in order to efficiently obtain attractive columns while avoiding as much as possible the exact solution of the huge number of the NP-hard pricing problems. Experimental results conducted on 42 hard benchmark instances show an average reduction of 89.73% of the gap between the best known lower and upper bounds, including 14 new optimality results. |
| topic |
Chromatic sum graph coloring column generation lower bound |
| url |
https://ieeexplore.ieee.org/document/8990124/ |
| work_keys_str_mv |
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