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Approximating Minimum Sum Coloring with Bundles
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- Author / Creator
- Darbouy, Seyed Parsa
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In this thesis, we introduce a new problem called the Minimum Sum Coloring with Bundles. We are given an undirected graph and bundles which bundles are sets of nodes (not necessarily disjoint). The goal is to find a proper coloring of the graph with positive integers to minimize the weighted average/total completion time of all bundles, where the completion time of a bundle is the maximum integer assigned to one of its nodes. This can be viewed as a scheduling problem where nodes are jobs, edges represent constraints on processing jobs simultaneously, and bundles represent sets of jobs a customer wants to finish. We provide the first constant-factor approximation in perfect graphs and some more general graphs.
We then extend the problem to a more general model where bundles are disjoint, and we can only color/schedule a limited number of jobs from each bundle at a time. We achieve constant-factor approximations for this model for interval graphs and their generalizations.
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- Subjects / Keywords
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- Graduation date
- Fall 2024
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.