Scheduling jobs with communication delays: Using infeasible solutions for approximation
 Rolf H. Möhring,
 Markus W. Schäffter,
 Andreas S. Schulz
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Abstract
In the last few years, multiprocessor scheduling with interprocessor communication delays has received increasing attention. This is due to the more realistic constraints in modeling parallel processor systems.
Most research in this vein is concerned with the makespan criterion. We contribute to this work by presenting a new and simple (2−1/m)approximation algorithm for scheduling to minimize the makespan on identical parallel processors subject to seriesparallel precedence constraints and both unit processing times and communication delays. This meets the best known performance guarantee for the same problem but without communication delays. For the same problem but with (nontrivial) release dates, arbitrary precedence constraints, arbitrary processing times and “locally small” communication delays we obtain a simple 7/3approximation algorithm compared with the involved (7/3−4/3m)approximation algorithm by Hanen and Munier for the case with identical release dates.
Another quite important goal in realworld scheduling is to optimize average performance. Very recently, there have been significant developments in computing nearly optimal schedules for several classic processor scheduling models to minimize the average weighted completion time. In this paper, we study for the first time scheduling with communication delays to minimize the average weighted completion time. Specifically, based on an LP relaxation we give the first constantfactor polynomialtime approximation algorithm for scheduling identical parallel processors subject to release dates and locally small communication delays. Moreover, the optimal LP value provides a lower bound on the optimum with the same worstcase performance guarantee.
The common underlying idea of our algorithms is to compute first a schedule that regards all constraints except for the processor restrictions. This schedule is then used to construct a provable good feasible schedule for a given number of processors and as a tool in the analysis of our algorithms. Complementing our approximation results, we also show that minimizing the makespan on an unrestricted number of identical parallel processors subject to seriesparallel precedence constraints, unittime jobs, and zeroone communication delays is NPhard.
 P. Chrétienne and C. Picouleau, Scheduling with communication delays: a survey, Scheduling Theory and its Applications (P. Chrétienne, E. G. Coffman Jr, J. K. Lenstra, and Z. Liu, eds.), John Wiley & Sons, 1995, pp. 65–90.
 S. Chakrabarti, C. A. Phillips, A. S. Schulz, D. B. Shmoys, C. Stein, and J. Wein, Improved scheduling algorithms for minsum criteria, 1996, To appear in Springer Lecture Notes in Computer Science, Proceedings of the 23rd ICALP Conference.
 M. X. Goemans and J. Kleinberg, An improved approximation ratio for the minimum latency problem, Proceedings of the 7th ACMSIAM Symposium on Discrete Algorithms, 1996.
 Grötschel, M., Lovász, L., Schrijver, A. (1988) Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics, vol. 2. Springer, Berlin
 Graham, R. L. (1966) Bounds for certain multiprocessing anomalies. Bell System Tech. J. 45: pp. 15631581
 C. Hanen and A. Munier, An approximation algorithm for scheduling dependent tasks on m processors with small communication delays, Preprint, Laboratoire Informatique Théorique et Programmation, Institut Blaise Pascal, Université Pierre et Marie Curie, 1995.
 Hall, L. A., Schulz, A. S., Shmoys, D. B., Wein, J. (1996) Scheduling to minimize average completion time: Offline and online approximation algorithms. Preprint 516/1996. Department of Mathematics, University of Technology, Berlin, Germany
 L. A. Hall, D. B. Shmoys, and J. Wein, Scheduling to minimize average completion time: Offline and online algorithms, Proceedings of the 7th ACMSIAM Symposium on Discrete Algorithms, 1996, pp. 142–151.
 Hoogeveen, J. A., Veltman, B., Lenstra, J. K. (1994) Three, four, five, six, or the complexity of scheduling with communication delays. Operations Research Letters 16: pp. 129137
 E. L. Lawler, Scheduling trees on multiprocessors with unit communication delays, Presented at the First Workshop on Models and Algorithms for Planning and Scheduling Problems, unpublished manuscript, June 1993.
 Lenstra, J. K., Veldhorst, M., Veltman, B. (1996) The complexity of scheduling trees with communication delays. Journal of Algorithms 20: pp. 157173
 Munier, A., König, J.C. (1993) A heuristic for a scheduling problem with communication delays. Preprint 871. Laboratoire de Recherche en informatique, Université de Paris, France
 Möhring, R. H. Computationally tractable classes of ordered sets. In: Rival, I. eds. (1989) Algorithms and Order. D. Reidel Publishing Company, Dordrecht, pp. 105193
 Möhring, R. H., Schäffter, M. W. (1996) A simple approximation algorithm for scheduling forests with unit processing times and zeroone communication delays. Preprint No. 506/1996. University of Technology, Berlin
 Möhring, R. H., Schäffter, M. W., Schulz, A. S. (1996) Scheduling jobs with communication delays: Using infeasible solutions for approximation. Preprint 517/1996. Department of Mathematics, University of Technology, Berlin, Germany
 Picouleau, C. (1995) New complexity results on scheduling with small communication delays. Discrete Applied Mathematics 60: pp. 331342
 Phillips, C., Stein, C., Wein, J. (1995) Scheduling jobs that arrive over time. Lecture Notes in Computer Science, no. 955. Springer, Berlin, pp. 8697
 RaywardSmith, V. J. (1987) UET scheduling with unit interprocessor communication delays. Discrete Applied Math. 18: pp. 5571
 Schulz, A. S. (1995) Polytopes and scheduling. Ph.D. thesis. University of Technology, Berlin, Germany
 Schulz, A. S. Scheduling to minimize total weighted completion time: Performance guarantees of LPbased heuristics and lower bounds. In: Cunningham, W. H., McCormick, S. T., Queyranne, M. eds. (1996) Integer Programming and Combinatorial Optimization (Berlin). Springer, Berlin, pp. 301315
 J. Verriet, Scheduling UET, UCT dags with release dates and deadlines, Preprint No. UUCS199531, Utrecht University, Department of Computer Science, 1995.
 Veltman, B., Lageweg, B., Lenstra, J. K. (1990) Multiprocessor scheduling with commmunication delays. Parallel Computing 16: pp. 173182 CrossRef
 Title
 Scheduling jobs with communication delays: Using infeasible solutions for approximation
 Book Title
 Algorithms — ESA '96
 Book Subtitle
 Fourth Annual European Symposium Barcelona, Spain, September 25–27, 1996 Proceedings
 Pages
 pp 7690
 Copyright
 1996
 DOI
 10.1007/3540616802_48
 Print ISBN
 9783540616801
 Online ISBN
 9783540706670
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1136
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Authors

 Rolf H. Möhring ^{(1)}
 Markus W. Schäffter ^{(1)}
 Andreas S. Schulz ^{(1)}
 Author Affiliations

 1. Fachbereich Mathematik, Technische Universität Berlin, Sekr. MA 61, Straße des 17. Juni 136, 10623, Berlin, Germany
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