Randomized approximation schemes for minimizing the weighted makespan on identical parallel machines

In this paper, we discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The objective is to minimize the weighted makespan of jobs, i.e., the maximum weighted completion time of jobs. This scheduling problem is a generalization of minimiz...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 47; no. 3; p. 34
Main Author: Sun, Ruiqing
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2024
Springer Nature B.V
Subjects:
Algorithms
Approximation
Combinatorics
Completion time
Convex and Discrete Geometry
Linear programming
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Scheduling
Theory of Computation
Fully polynomial time approximation scheme
Scheduling
Approximation algorithm
Weighted makespan
Efficient polynomial time approximation scheme
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:In this paper, we discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The objective is to minimize the weighted makespan of jobs, i.e., the maximum weighted completion time of jobs. This scheduling problem is a generalization of minimizing the makespan on parallel machine scheduling problem. We present a ( 2 - 1 m )-approximation algorithm and a randomized efficient polynomial time approximation scheme (EPTAS) for the problem. We also design a randomized fully polynomial time approximation scheme (FPTAS) for the special case when the number of machines is fixed.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-024-01118-w