Approximability of average completion time scheduling on unrelated machines

We show that minimizing the average job completion time on unrelated machines is APX -hard if preemption of jobs is allowed. This provides one of the last missing pieces in the complexity classification of machine scheduling with (weighted) sum of completion times objective. The proof is based on a...

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Bibliographic Details
Published in:Mathematical programming Vol. 161; no. 1-2; pp. 135 - 158
Main Author: Sitters, René
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2017
Springer Nature B.V
Subjects:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Classification
Combinatorics
Completion time
Employment
Full Length Paper
Job shops
Linear programming
Lower bounds
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mixed integer
Numerical Analysis
Preemption
Quadratic programming
Scheduling
Studies
Texts
Theoretical
hardness
68W25 Approximation algorithms
Approximation algorithms
90B35 Scheduling theory, deterministic
Scheduling
68Q25 Analysis of algorithms and problem complexity
Quadratic programming
Average completion time
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We show that minimizing the average job completion time on unrelated machines is APX -hard if preemption of jobs is allowed. This provides one of the last missing pieces in the complexity classification of machine scheduling with (weighted) sum of completion times objective. The proof is based on a mixed integer linear program. This means that verification of the reduction is partly done by an ILP-solver. This gives a concise proof which is easy to verify. In addition, we give a deterministic 1.698-approximation algorithm for the weighted version of the problem. The improvement is made by modifying and combining known algorithms and by the use of new lower bounds. These results improve on the known NP -hardness and 2-approximability.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1004-8