Abstract
We study the problem of simultaneously minimizing the makespan and the average weighted completion time for the precedence multiprocessor constrained scheduling problem with unit execution times and unit communication delays, known as the UET–UCT problem (Munier and König, Operations Research, 45(1), 145–148 (1997)). We propose a simple (16/9, 16/9)-approximation algorithm for the problem with an unrestricted number of machines. We improve our algorithm by adapting a technique first introduced by Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999) and provide a (1.745, 1.745)-approximate solution. For the considered scheduling problem, we prove the existence of a (1.445, 1.445)-approximate solution, improving the generic existence result of Aslam et al. (Proceedings of ACM-SODA, pp. 846–847, 1999). Also notice that our results for the case of an unrestricted number of processors hold for the more general scheduling problem with small communication delays (SCT problem), and for two other classical optimality criteria: maximum lateness and weighted lateness. Finally, we propose an approximation algorithm for the UET–UCT problem with a restricted number of processors.
Similar content being viewed by others
References
Angel, E., E. Bampis, and A. Kononov, “A FPTAS for approximating the unrelated parallel machines scheduling problem with costs,” in Proceedings of ESA′2001, 2001, pp. 194–205.
Aslam, J., A. Rasala, C. Stein, and N. Young, “Improved bicriteria existence theorems for scheduling,” in Proceedings of ACM-SODA ′ 1999, pp. 846–847.
Chen, B., C. N. Potts, and G. J. Woeginger, “A review of machine scheduling: Complexity, algorithms and approximability,” Technical Report Woe-29, TU Graz, 1998.
Ergott, M., Multicriteria Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 491, 2000.
Erlebach, H., H. Kellerer, and U. Pferschy, “Approximating multi-objective Knapsack problems,” in Proceedings of the Seventh International Workshop on Algorithms and Data Structures (WADS 2001) LNCS 2125, Springer Verlag, 2001, pp. 210–221.
Graham, R. L., E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan, “Optimization and approximation in deterministic sequencing and scheduling theory: A survey,” Annals of Discrete Mathematics, 5, 287–326 (1979).
Hanen, C. and D. S. A. Munier, “An approximation algorithm for scheduling dependent tasks on m processors with small communication delays,” in IEEE Symposium on Emerging Technologies and Factory Automation, September 1995.
Hoogeveen, J. A., J. K. Lenstra, and B. Veltman, “Three, four, five, six, or the complexity of scheduling with communication delays,” Operations Research Letters, 16(3), 129–137 (1994).
Möhring, R. H., M. W. Schäfter, and A. S. Schulz, “Scheduling jobs with communication delays—Using infeasible solutions for approximation,” in Proceedings of the Fourth European Symposium on Algorithms, Lecture Notes in Computer Science, 1136, Springer Verlag, 1996, pp. 76–90.
Munier, A. and J. C. König, “A heuristic for a scheduling problem with communication delays,” Operations Research, 45(1), 145–148 (1997).
Papadimitriou, C. H. and M. Yannakakis, “On the approximability of trade-offs and optimal access of web sources,” in Proceedings of FOCS’2000, 2000, pp. 86–92.
Rasala, A., “Existence theorems for scheduling to meet two objectives,” Department of Computer Science, Dartmouth College, Technical Report PCS-TR 99–347, 1999.
Rasala, A., C. Stein, E. Tomg, and P. Uthaisom, “Existence theorems, lower bounds and algorithms for scheduling to meet two objectives,” in Proceedings of ACM-SODA, 2002, pp. 723–731.
Schulz, A. S., “Polytopes and scheduling,” PhD thesis, Technical University of Berlin, Berlin, Germany, 1995.
Schulz, A. S., “Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bounds,” in LNCS 1084, Proceedings of the 5th International IPCO Conference, 1996, pp. 301–315.
Stein, C. and J. Wein, “On the existence of schedules that are near-optimal for both makespan and total weighted completion time,” Operations Research Letters, 21(3), 115–122 (1997).
Author information
Authors and Affiliations
Corresponding author
Additional information
Research partially supported by the thematic network APPOL II (IST 2001-32007) of the European Union, the ACI-GRID2 project of the French government, and the MULT-APPROX project of the France-Berkeley Fund.
Rights and permissions
About this article
Cite this article
Bampis, E., Kononov, A. Bicriteria approximation algorithms for scheduling problems with communications delays. J Sched 8, 281–294 (2005). https://doi.org/10.1007/s10951-005-1637-6
Issue Date:
DOI: https://doi.org/10.1007/s10951-005-1637-6