Abstract
We study the problem of scheduling on k identical machines a set of parallel tasks with release dates and deadlines in order to maximize simultaneously two criteria, namely the Size (number of scheduled tasks) and the Weight (sum of the weights of scheduled tasks). If no task requires more than half of the machines, we construct schedules that are simultaneously approximations for the Size and the Weight by combining two approximate schedules, one for each parameter. We obtain existence results and polynomial time bicriteria approximation algorithms in contiguous and non contiguous models.
Similar content being viewed by others
References
Arkin, E., & Silverberg, B. (1987). Scheduling jobs with fixed start and end times. Discrete Applied Mathematics, 18, 1–8.
Baille, F., Bampis, E., & Laforest, C. (2004a). Maximization of the size and the weight of schedules of degradable intervals. In K.-Y. Chwa & I. Munro (Eds.), LNCS: Vol. 3106. Proceedings of COCOON’04 (pp. 219–228). Berlin: Springer.
Baille, F., Bampis, E., & Laforest, C. (2004b). A note on bicriteria schedules with optimal approximation ratios. Parallel Processing Letters, 14, 315–323.
Bar-Noy, A., Guha, S., Naor, J., & Schieber, B. (1999). Approximating the throughput of multiple machines under real-time scheduling. In STOCS 99 (pp. 622–631).
Bar-Noy, A., Bar-Yehuda, R., Freund, A., Seffi Naor, J., & Schieber, B. (2001). A unified approach to approximating resource allocation and scheduling. Journal of the ACM, 48(5), 1069–1090.
Calinescu, G., Amit, C., Karloff, H., & Rabani, Y. (2002). Improved approximation algorithms for resource allocation. In LNCS: Vol. 2337. Proceedings of IPCO ’02 combinatorial optimization (pp. 401–414). Berlin: Springer.
Carlisle, M. C., & Lloyd, E. L. (1995). On the k-coloring of intervals. Discrete Applied Mathematics, 59, 225–235.
Chen, B., Hassin, R., & Tzur, M. (2002). Allocation of bandwidth and storage. IIE Transactions, 34, 501–507.
Faigle, U., & Nawijn, W. (1991). Greedy decomposition of intervals order. In Proceedings of 2nd Twente workshop on graphs and combinatorial optimisation (pp. 53–56). Department of Applied Mathematics, University of Twente.
Faigle, U., & Nawijn, M. (1995). Note on scheduling intervals on-line. Discrete Applied Mathematics, 58, 13–17.
Mounie, G., Rapine, C., & Trystram, D. (1999). Efficient approximation algorithms for scheduling malleable tasks. In SPAA ’99: Proceedings of the eleventh annual ACM symposium on parallel algorithms and architectures (pp. 23–32). New York: ACM Press.
Spieksma, F. (1999). On the approximability of an interval scheduling problem. Journal of Scheduling, 2, 215–227.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baille, F., Bampis, E., Laforest, C. et al. Bicriteria scheduling for contiguous and non contiguous parallel tasks. Ann Oper Res 159, 97–106 (2008). https://doi.org/10.1007/s10479-007-0282-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-007-0282-1