Abstract
We consider the problem of scheduling n jobs to m machines of different speeds s.t. the makespan is minimized (Q||C max). We provide a fast and simple, deterministic monotone 3-approximation algorithm for Q||C max Monotonicity is relevant in the context of truthful mechanisms: when each machine speed is only known to the machine itself, we need to motivate that machines declare their true speeds to the scheduling mechanism. As shown by Archer and Tardos, such motivation is possible only if the scheduling algorithm used by the mechanism is monotone. The best previous monotone algorithm that is polynomial in m, was a 5-approximation by Andelman et al. A randomized 2-approximation method, satisfying a weaker definition of truthfulness, is given by Archer. As a core result, we prove the conjecture of Auletta et al., that the greedy algorithm (Lpt) is monotone if machine speeds are all integer powers of 2.
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
Archer, A.: Mechanisms for Discrete Optimization with Rational Agents. PhD thesis, Cornell University (2004)
Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proc. 42nd IEEE Symp. on Found. of Comp. Sci (FOCS), pp. 482–491 (2001)
Hochbaum, D.S., Shmoys, D.B.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM J. Comp. 17(3), 539–551 (1988)
Horowitz, E., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23, 317–327 (1976)
Kovács, A.: Fast monotone 3-approximation algorithm for scheduling related machines, Extended version: http://www.mpi-sb.mpg.de/~panni/greedy.ps
Johnson, D.S., Garey, M.R.: Computers and Intractability; A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)
Azar, Y., Andelman, N., Sorani, M.: Truthful approximation mechanisms for scheduling selfish related machines. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 69–82. Springer, Heidelberg (2005)
Auletta, V., Ambrosio, P.: Deterministic monotone algorithms for scheduling on related machines. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 267–280. Springer, Heidelberg (2005)
Auletta, V., De Prisco, R., Penna, P., Persiano, G.: Deterministic truthful approximation mechanisms for scheduling related machines. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 608–619. Springer, Heidelberg (2004)
Ibarra, O.H., Gonzalez, T., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. Journal of the ACM 23, 317–327 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kovács, A. (2005). Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_55
Download citation
DOI: https://doi.org/10.1007/11561071_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29118-3
Online ISBN: 978-3-540-31951-1
eBook Packages: Computer ScienceComputer Science (R0)