Abstract
In this paper we study divisible loads scheduling in heterogeneous systems with high bandwidth. Divisible loads represent computations which can be arbitrarily divided into parts and performed independently in parallel. We propose fully polynomial time approximation schemes for two optimization problems. The first problem consists in finding the maximum load which can be processed in a given time. It turns out that this problem can be reduced to minimization of a half-product. The second problem is computing the minimum time required to process load of a given size. The FPTAS solving this problem uses a dual approximation algorithm approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agrawal, R., Jagadish, H.V.: Partitioning Techniques for Large-Grained Parallelism. IEEE Transactions on Computers 37(12), 1627–1634 (1988)
Badics, T., Boros, E.: Minimization of Half-products. Mathematics of Operations Research 23(3), 649–660 (1988)
Beaumont, O., Casanova, H., Legrand, A., Robert, Y., Yang, Y.: Scheduling Divisible Loads on Star and Tree Networks: Results and Open Problems. IEEE Transactions on Parallel and Distributed Systems 16(3), 207–218 (2005)
Bharadwaj, V., Ghose, D., Mani, V.: Optimal Sequencing and Arrangement in Single-Level Tree Networks with Communication Delays. IEEE Transactions on Parallel and Distributed Systems 5(9), 968–976 (1994)
Bharadwaj, V., Ghose, D., Mani, V., Robertazzi, T.G.: Scheduling Divisible Loads in Parallel and Distributed Systems. IEEE Computer Society Press, Los Alamitos (1996)
Blażewicz, J., Drozdowski, M.: Distributed Processing of Divisible Jobs with Communication Startup Costs. Discrete Applied Mathematics 76, 21–41 (1997)
Cheng, Y.-C., Robertazzi, T.G.: Distributed computation with communication delay. IEEE Transactions on Aerospace and Electronic Systems 24, 700–712 (1988)
Drozdowski, M., Lawenda, M.: The combinatorics in divisible load scheduling. Foundations of Computing and Decision Sciences 30(4), 297–308 (2005), http://www.cs.put.poznan.pl/mdrozdowski/txt/divBB2.pdf
Drozdowski, M., Wolniewicz, P.: Experiments with scheduling divisible tasks in clusters of workstations. In: Bode, A., Ludwig, T., Karl, W.C., Wismüller, R. (eds.) Euro-Par 2000. LNCS, vol. 1900, pp. 311–319. Springer, Heidelberg (2000)
Drozdowski, M., Wolniewicz, P.: Optimum divisible load scheduling on heterogeneous stars with limited memory. European Journal of Operational Research 172, 545–559 (2006)
Hochbaum, D., Shmoys, D.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the ACM 34(1), 144–162 (1987)
Li, X., Bharadwaj, V., Ko, C.C.: Distributed image processing on a network of workstations. International Journal of Computers and Applications 25(2), 1–10 (2003)
Lim, T., Robertazzi, T.G.: Efficient parallel video processing through concurrent communication on a multi-port star network. In: Proceedings of the 40th Conference on Information Sciences and Systems, Princeton, NJ, pp. 458–463 (2006)
Robertazzi, T.G.: Ten reasons to use divisible load theory. IEEE Computer 36, 63–68 (2003)
van der Raadt, K., Yang, Y., Casanova, H.: Practical divisible load scheduling on grid platforms with APST-DV. In: Proceedings of the 19th IPDPS 2005, p. 29b (2005)
Yang, Y., Casanova, H., Drozdowski, M., Lawenda, M., Legrand, A.: On the complexity of Multi-Round Divisible Load Scheduling. INRIA Rhône-Alpes, Research Report 6096 (2007)
Yu, D., Robertazzi, T.G.: Divisible load scheduling for grid computing. In: Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Systems, PDCS 2003 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Berlińska, J. (2010). Fully Polynomial Time Approximation Schemes for Scheduling Divisible Loads. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14403-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-14403-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14402-8
Online ISBN: 978-3-642-14403-5
eBook Packages: Computer ScienceComputer Science (R0)