Power-aware scheduling for makespan and flow
- 173 Downloads
We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work.
For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor.
KeywordsPower-aware scheduling Dynamic voltage scaling Speed scaling Makespan Total flow
Unable to display preview. Download preview PDF.
- Advanced Micro Devices. (2004). AMD Athlon 64 processor power and thermal data sheet (version 3.43), October 2004. http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/30430.pdf.
- Albers, S., & Fujiwara, H. (2006). Energy-efficient algorithms for flow time minimization. In Proceedings of the 23rd international symposium on theoretical aspects of computer science (pp. 621–633). Google Scholar
- Albers, S., Müller, F., & Schmelzer, S. (2007). Speed scaling on parallel processors. In Proceedings of the 19th annual ACM symposium on parallelism in algorithms and architectures (pp. 289–298). Google Scholar
- Alon, N., Azar, Y., Woeginger, G. J., & Yadid, T. (1997). Approximation schemes for scheduling. In Proceedings of the 8th annual ACM-SIAM symposium on discrete algorithms (pp. 493–500). Google Scholar
- Bansal, N., Pruhs, K., & Stein, C. (2007). Speed scaling for weighted flow time. In Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms (pp. 805–813). Google Scholar
- Bunde, D. P. (2006). Power-aware scheduling for makespan and flow. In Proceedings of the 18th annual ACM symposium on parallelism in algorithms and architectures (pp. 190–196). Google Scholar
- Chen, J.-J., Kuo, T.-W., & Lu, H.-I. (2005). Power-saving scheduling for weakly dynamic voltage scaling devices. In Lecture notes in computer science: Vol. 3608. Proceedings of the 9th workshop on algorithms and data structures (pp. 338–349). Berlin: Springer. Google Scholar
- Chudak, F. A., & Shmoys, D. B. (1997). Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speeds. In Proceedings of the 8th annual ACM-SIAM symposium on discrete algorithms (pp. 581–590). Google Scholar
- Dummit, D. S., & Foote, R. M. (1991). Abstract algebra. Englewood Cliffs: Prentice-Hall. Google Scholar
- El Gamal, A., Nair, C., Prabhakar, B., Uysal-Biyikoglu, E., & Zahedi, S. (2002). Energy-efficient scheduling of packet transmissions over wireless networks. In Proceedings of the IEEE INFOCOM (pp. 1773–1782). Google Scholar
- GAP Group. (2006). GAP system for computational discrete algebra. http://turnbull.mcs.st-and.ac.uk/~gap/ (viewed January 2006).
- Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: Freeman. Google Scholar
- Keslassy, I., Kodialam, M., & Lakshman, T. V. (2003). Faster algorithms for minimum-energy scheduling of wireless data transmissions. In Proceedings of the modeling and optimization in mobile, ad hoc and wireless networks. Google Scholar
- Pinedo, M. L. (2005). Planning and scheduling in manufacturing and services. Springer series in operations research. New York: Springer. Google Scholar
- Pruhs, K., Uthaisombut, P., & Woeginger, G. (2004). Getting the best response for your erg. In Lecture notes in computer science: Vol. 3111. Proceedings of the 9th Scandinavian workshop on algorithm theory (pp. 14–25). Berlin: Springer. Google Scholar
- Rudin, W. (1987). Real and complex analysis (3rd ed.) New York: McGraw-Hill. Google Scholar
- Tiwari, V., Singh, D., Rajgopal, S., Mehta, G., Patel, R., & Baez, F. (1998). Reducing power in high-performance microprocessors. In Proceedings of the 35th ACM/IEEE design automation conference (pp. 732–737). Google Scholar
- Weiser, M., Welch, B., Demers, A., & Shenker, S. (1994). Scheduling for reduced CPU energy. In Proceedings of the 1st symposium on operating systems design and implementation (pp. 13–23). Google Scholar
- Xie, F., Martonosi, M., & Malik, S. (2003). Compile-time dynamic voltage scaling settings: Opportunities and limits. In Proceedings of the 2003 ACM SIGPLAN conference on programming language design and implementation (pp. 49–62). Google Scholar
- Yao, F., Demers, A., & Shenker, S. (1995). A scheduling model for reduced CPU energy. In Proceedings of the 36th symposium on foundations of computer science (pp. 374–382). Google Scholar