An efficient polynomial time approximation scheme for load balancing on uniformly related machines

We consider basic problems of non-preemptive scheduling on uniformly related machines. For a given schedule, defined by a partition of the jobs into m subsets corresponding to the m machines, C i denotes the completion time of machine i . Our goal is to find a schedule that minimizes or maximizes ∑...

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Veröffentlicht in:Mathematical programming Jg. 147; H. 1-2; S. 1 - 23
Hauptverfasser: Epstein, Leah, Levin, Asaf
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
Springer Nature B.V
Schlagworte:
Algorithms
Analysis
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Completion time
Computer science
Dynamic programming
Employment
Full Length Paper
Intervals
Job shops
Load
Load balancing
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Partitions
Polynomials
Schedules
Scheduling
Studies
Theoretical
90C59 Approximation methods and heuristics
68W25 Approximation algorithms
90C27 Combinatorial optimization
Approximation algorithms
68W40 Analysis of algorithms
EPTAS
Scheduling
68Q25 Analysis of algorithms and problem complexity
Load balancing
ISSN:0025-5610, 1436-4646
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Beschreibung
Zusammenfassung:We consider basic problems of non-preemptive scheduling on uniformly related machines. For a given schedule, defined by a partition of the jobs into m subsets corresponding to the m machines, C i denotes the completion time of machine i . Our goal is to find a schedule that minimizes or maximizes ∑ i = 1 m C i p for a fixed value of p such that 0 < p < ∞ . For p > 1 the minimization problem is equivalent to the well-known problem of minimizing the ℓ p norm of the vector of the completion times of the machines, and for 0 < p < 1 , the maximization problem is of interest. Our main result is an efficient polynomial time approximation scheme (EPTAS) for each one of these problems. Our schemes use a non-standard application of the so-called shifting technique. We focus on the work (total size of jobs) assigned to each machine and introduce intervals of work that are forbidden. These intervals are defined so that the resulting effect on the goal function is sufficiently small. This allows the partition of the problem into sub-problems (with subsets of machines and jobs) whose solutions are combined into the final solution using dynamic programming. Our results are the first EPTAS’s for this natural class of load balancing problems.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0706-4