Abstract
We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed scalable processors in a fully heterogeneous setting. For both the preemptive-nonmigratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-nonmigratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.
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References
Agrawal, K., Li, J., Lu, K., & Moseley, B. (2016). Scheduling parallel DAG jobs online to minimize average flow time. In SODA, (pp. 176–189).
Albers, S. (2010). Energy-efficient algorithms. Communications of ACM, 53, 86–96.
Albers, S. (2011). Algorithms for dynamic speed scaling. In STACS, (pp. 1–11).
Albers, S., Antoniadis, A., & Greiner, G. (2011). On multi-processor speed scaling with migration: extended abstract. In SPAA (pp. 279–288). ACM
Albers, S., Müller, F., & Schmelzer, S. (2007). Speed scaling on parallel processors. In SPAA (pp. 289–298). ACM.
Andrews, M., Anta, A. F., Zhang, L., & Zhao, W. (2012). Routing for power minimization in the speed scaling model. IEEE/ACM Transaction on Networking, 20, 285–294.
Andrews, M., Antonakopoulos, S., & Zhang, L. (2010). Minimum-cost network design with (dis)economies of scale. In FOCS (pp. 585–592).
Angel, E., Bampis, E., Kacem, F., & Letsios, D. (2012). Speed scaling on parallel processors with migration. In Euro-Par, volume 7484 of LNCS, (pp. 128–140).
Antoniadis, A., Huang, C.-C. (2012). Non-preemptive speed scaling. In SWAT, volume 7357 of LNCS (pp. 249–260). Springer.
Antoniadis, A., Im, S., Krishnaswamy, R., Moseley, B., Nagarajan, V., Pruhs, K., & Stein, C. (2014). Hallucination helps: Energy efficient virtual circuit routing. In SODA (pp. 1141–1153).
Awerbuch, B., Kutten, S., & Peleg, D. (1992). Competitive distributed job scheduling (Extended abstract). In STOC (pp. 571–580).
Bampis, E., Chau, V., Letsios, D., Lucarelli, G., Milis, I., & Zois, G. (2014) Energy efficient scheduling of mapreduce jobs. In Euro-Par, volume 8632 of LNCS (pp. 198–209). Springer.
Bampis, E., Kononov, A., Letsios, D., Lucarelli, G., & Nemparis, I. (2015). From preemptive to non-preemptive speed-scaling scheduling. Discrete Applied Mathematics, 181, 11–20.
Bampis, E., Letsios, D., & Lucarelli, G. (2015). Green scheduling, flows and matchings. Theoretical Computer Science, 579, 126–136.
Bampis, E., Letsios, D., & Lucarelli, G. (2014). A note on multiprocessor speed scaling with precedence constraints. In SPAA (pp. 138–142). ACM
Baptiste, P., Carlier, J., Kononov, A., Queyranne, M., Sevastyanov, S., & Sviridenko, M. (2011). Properties of optimal schedules in preemptive shop scheduling. Discrete Applied Mathematics, 159(5), 272–280.
Berend, D., & Tassa, T. (2010). Improved bounds on Bell numbers and on moments of sums of random variables. Probability and Mathematical Statistics, 30, 185–205.
Bingham, B. D., & Greenstreet, M. R. (2008). Energy optimal scheduling on multiprocessors with migration. In ISPA (pp. 153–161). IEEE.
Brodtkorb, A. R., Dyken, C., Hagen, T. R., Hjelmervik, J. M., & Storaasli, O. O. (2010). State-of-the-art in heterogeneous computing. Scientific Programming, 18, 1–33.
Deng, X., Liu, H.-N., & Xiao, B. (1990). Deterministic load balancing in computer networks. In SPDP (pp. 50–57).
Gerards, M. E. T., Hurink, J. L., & Hölzenspies, P. K. F. (2016). A survey of offline algorithms for energy minimization under deadline constraints. Journal of Scheduling, 19, 3–19.
Greiner, G., Nonner, T., & Souza, A. (2009). The bell is ringing in speed-scaled multiprocessor scheduling. In SPAA (pp. 11–18). ACM.
Grötschel, M., Lovász, L., & Schrijver, A. (1993). Geometric algorithms and combinatorial optimizations (2nd ed.). Berlin: Springer.
Gupta, A., Im, S., Krishnaswamy, R., Moseley, B., & Pruhs, K. (2012). Scheduling heterogeneous processors isn’t as easy as you think. In SODA (pp. 1242–1253).
Gupta, A., Krishnaswamy, R., Pruhs, K. (2012). Online primal-dual for non-linear optimization with applications to speed scaling. In WAOA, volume 7846 of LNCS (pp. 173–186). Springer.
Hoeffding, W. (1956). On the distribution of the number of successes in independent trials. Annals of Mathematical Statistics, 27, 713–721.
Raghavan, P., & Thompson, C. D. (1991). Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica, 7, 365–374.
Svensson, O. (2011). Santa claus schedules jobs on unrelated machines. In STOC (pp. 617–626).
Wierman, A., Andrew, L. L. H., & Tang, A. (2009). Power-aware speed scaling in processor sharing systems. In INFOCOM (pp. 2007–2015).
Yao, F., Demers, A., & Shenker, S. (1995). A scheduling model for reduced CPU energy. In FOCS (pp. 374–382).
Acknowledgments
We would like to thank Oleg Pikhurko for providing the original proof of Part (b) of the Proposition 6.
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Bampis, E., Kononov, A., Letsios, D. et al. Energy-efficient scheduling and routing via randomized rounding. J Sched 21, 35–51 (2018). https://doi.org/10.1007/s10951-016-0500-2
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DOI: https://doi.org/10.1007/s10951-016-0500-2