A faster combinatorial approximation algorithm for scheduling unrelated parallel machines

We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time p i j on machine j , and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. T...

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Bibliographic Details
Published in:Theoretical computer science Vol. 380; no. 1; pp. 87 - 99
Main Authors: Gairing, Martin, Monien, Burkhard, Woclaw, Andreas
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 21.06.2007
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximation algorithms
Computer science; control theory; systems
Computer systems performance. Reliability
Exact sciences and technology
Miscellaneous
Scheduling
Software
Theoretical computing
Unrelated parallel machines
Unsplittable network flow
Approximation algorithms
Scheduling
Unrelated parallel machines
Unsplittable network flow
Costs
Approximation
Network flow
Computer theory
Solving
Combinatorial algorithm
Parallel machines
Processing time
Makespan
Approximation algorithm
Layer
Optimum
Relaxation
Network
Best approximation
Application
ISSN:0304-3975, 1879-2294
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Summary:We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time p i j on machine j , and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and then use rounding techniques to get an integral 2-approximation. In this paper we present a combinatorial approximation algorithm that matches this approximation quality. It is much simpler than the previously known algorithms and its running time is better. This is the first time that a combinatorial algorithm always beats the interior point approach for this problem. Our algorithm is a generic minimum cost flow algorithm, without any complex enhancements, tailored to handle unsplittable flow. It pushes unsplittable jobs through a two-layered bipartite generalized network defined by the scheduling problem. In our analysis, we take advantage from addressing the approximation problem directly. In particular, we replace the classical technique of solving the LP-relaxation and rounding afterwards by a completely integral approach. We feel that this approach will be helpful also for other applications.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2007.02.056