Sum Multicoloring of Graphs
Scheduling dependent jobs on multiple machines is modeled by the graph multicoloring problem. In this paper we consider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring problem: Given a graph and the number of colors required by each vert...
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| Veröffentlicht in: | Journal of algorithms Jg. 37; H. 2; S. 422 - 450 |
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01.11.2000
Elsevier |
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| ISSN: | 0196-6774, 1090-2678 |
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| Abstract | Scheduling dependent jobs on multiple machines is modeled by the graph multicoloring problem. In this paper we consider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring problem: Given a graph and the number of colors required by each vertex, find a multicoloring which minimizes the sum of the largest colors assigned to the vertices. It reduces to the known sum coloring problem when each vertex requires exactly one color.
This paper reports a comprehensive study of the sum multicoloring problem, treating three models: with and without preemptions, as well as co-scheduling where jobs cannot start while others are running. We establish a linear relation between the approximability of the maximum independent set problem and the approximability of the sum multicoloring problem in all three models, via a link to the sum coloring problem. Thus, for classes of graphs for which the independent set problem is ρ-approximable, we obtain O(ρ)-approximations for preemptive and co-scheduling sum multicoloring and O(ρlogn)-approximation for nonpreemptive sum multicoloring. In addition, we give constant ratio approximations for a number of fundamental classes of graphs, including bipartite, line, bounded degree, and planar graphs. |
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| AbstractList | Scheduling dependent jobs on multiple machines is modeled by the graph multicoloring problem. In this paper we consider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring problem: Given a graph and the number of colors required by each vertex, find a multicoloring which minimizes the sum of the largest colors assigned to the vertices. It reduces to the known sum coloring problem when each vertex requires exactly one color.
This paper reports a comprehensive study of the sum multicoloring problem, treating three models: with and without preemptions, as well as co-scheduling where jobs cannot start while others are running. We establish a linear relation between the approximability of the maximum independent set problem and the approximability of the sum multicoloring problem in all three models, via a link to the sum coloring problem. Thus, for classes of graphs for which the independent set problem is ρ-approximable, we obtain O(ρ)-approximations for preemptive and co-scheduling sum multicoloring and O(ρlogn)-approximation for nonpreemptive sum multicoloring. In addition, we give constant ratio approximations for a number of fundamental classes of graphs, including bipartite, line, bounded degree, and planar graphs. |
| Author | Halldórsson, Magnús M. Kortsarz, Guy Shachnai, Hadas Salman, Ravit Bar-Noy, Amotz |
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| Keywords | chromatic sums scheduling dining philosophers graph coloring multicoloring dependent jobs sum coloring Starvation Operations research Dining philosopher Scheduling Graph theory Multicoloring Management Optimization Dependence Graph colouring Chromatic graph dependent job Chromatic sum |
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| SubjectTerms | Applied sciences chromatic sums Combinatorics Combinatorics. Ordered structures dependent jobs dining philosophers Exact sciences and technology graph coloring Graph theory Mathematics multicoloring Operational research and scientific management Operational research. Management science scheduling Scheduling, sequencing Sciences and techniques of general use sum coloring |
| Title | Sum Multicoloring of Graphs |
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