Abstract
Parallel jobs require more than one processor at the same time. We study speed scaling scheduling of parallel jobs with preemption. We propose “almost-exact” algorithms for problems with rigid jobs and single mode two-processor jobs. Based on configuration linear programs, our algorithms obtain an \(OPT + \varepsilon \) solution for any fixed \(\varepsilon > 0\).
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Albers, S., Antoniadis, A., Greiner, G.: On multi-processor speed scaling with migration: extended abstract. In: 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2011), pp. 279–288. ACM (2011)
Albers, S., Müller, F., Schmelzer, S.: Speed scaling on parallel processors. In: 19th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2007), pp. 289–298. ACM (2007)
Angel, E., Bampis, E., Kacem, F., Letsios, D.: Speed scaling on parallel processors with migration. In: Kaklamanis, C., Papatheodorou, T., Spirakis, P.G. (eds.) Euro-Par 2012. LNCS, vol. 7484, pp. 128–140. Springer, Heidelberg (2012)
Bampis, E., Kononov, A., Letsios, D., Lucarelli, G., Sviridenko, M.: Energy efficient scheduling and routing via randomized rounding. In: FSTTCS, pp. 449–460 (2013)
Bingham, B.D., Greenstreet, M.R.: Energy optimal scheduling on multiprocessors with migration. In: International Symposium on Parallel and Distributed Processing with Applications (ISPA 2008), pp. 153–161. IEEE (2008)
Cohen-Addad, V., Li, Z., Mathieu, C., Milis, I.: Energy-efficient algorithms for non-preemptive speed-scaling. In: Bampis, E., Svensson, O. (eds.) WAOA 2014. LNCS, vol. 8952, pp. 107–118. Springer, Heidelberg (2015)
Drozdowski, M.: On complexity of multiprocessor tasks scheduling. Bull. Pol. Acad. Sci. Tech. Sci. 43(3), 381–392 (1995)
Drozdowski, M.: Scheduling for Parallel Processing, p. 386. Springer, London (2009)
Gerards, M.E.T., Hurink, J.L., Hölzenspies, P.K.F.: A survey of offline algorithms for energy minimization under deadline constraints. J. Sched. 19, 3–19 (2016)
Greiner, G., Nonner, T., Souza, A.: The bell is ringing in speed-scaled multiprocessor scheduling. In: 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2009), pp. 11–18. ACM (2009)
Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimizations, 2nd, p. 362. Springer, Heidelberg (1993)
Jansen, K., Porkolab, L.: Preemptive parallel task scheduling in O(n)+poly(m) time. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 398–409. Springer, Heidelberg (2000)
Jansen, K., Porkolab, L.: Preemptive scheduling with dedicated processors: applications of fractional graph coloring. J. Sched. 7, 35–48 (2004)
Yao, F., Demers, A., Shenker, S.: A scheduling model for reduced CPU energy. In: 36th Annual Symposium on Foundation of Computer Science (FOCS 1995), pp. 374–382 (1995)
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This research is supported by the Russian Science Foundation grant 15-11-10009.
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Kononov, A., Kovalenko, Y. (2016). On Speed Scaling Scheduling of Parallel Jobs with Preemption. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_25
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