Abstract
Malleable tasks are a way of modelling jobs that can be parallelized to get a (usually sublinear) speedup. The best currently known approximation algorithms for scheduling malleable tasks with precedence constraints are a) 2.62-approximation for certain classes of precedence constraints such as series-parallel graphs [1], and b) 4.72-approximation for general graphs via linear programming [2]. We show that these rates are tight, i.e. there exist instances that achieve the upper bounds.
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References
Lepère, R., Trystram, D., Woeginger, G.J.: Approximation algorithms for scheduling malleable tasks under precedence constraints. Int. J. Found. Comput. Sci. 13(4), 613–627 (2002)
Jansen, K., Zhang, H.: An approximation algorithm for scheduling malleable tasks under general precedence constraints. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 236–245. Springer, Heidelberg (2005)
Skutella, M.: Approximation algorithms for the discrete time-cost tradeoff problem. Technical Report 514/1996, Technische Universität Berlin (1996)
Du, J., Leung, J.Y.T.: Complexity of scheduling parallel task systems. SIAM J. Disc. Math. 2(4), 473–487 (1989)
Turek, J., Wolf, J.L., Yu, P.S.: Approximate algorithms scheduling parallelizable tasks. In: Proceedings of SPAA 1992, pp. 323–332 (1992)
Mounie, G., Rapine, C., Trystram, D.: A 3/2-approximation algorithm for scheduling independent monotonic malleable tasks. SIAM J. Comp. 37(2), 401–412 (2007)
Jansen, K.: Scheduling malleable parallel tasks: An asymptotic fully polynomial time approximation scheme. Algorithmica 39(1), 59–81 (2004)
Dutot, P.F.: Hierarchical scheduling for moldable tasks. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 302–311. Springer, Heidelberg (2005)
Leung, J.Y.T. (ed.): Handbook of Scheduling. CRC Press, Boca Raton (2004)
Gonzalez, T.F. (ed.): Handbook of Approximation Algorithms and Metaheuristics. Chapman & Hall/CRC, Boca Raton (2007)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5 (1979)
Grigoriev, A., Woeginger, G.J.: Project scheduling with irregular costs: complexity, approximability, and algorithms. Acta Informatica 41(2–3), 83–97 (2004)
Schwarz, U.M.: Design and analysis of approximation algorithms for certain scheduling problems. Diploma thesis, University of Kiel (2006)
Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell Systems Tech. J. 45, 1563–1581 (1966)
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Schwarz, U.M. (2008). Tightness Results for Malleable Task Scheduling Algorithms. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_112
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DOI: https://doi.org/10.1007/978-3-540-68111-3_112
Publisher Name: Springer, Berlin, Heidelberg
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