Abstract
For the Restricted Assignment Problem the best known polynomial algorithm is a 2-approximation by Lenstra, Shmoys and Tardos [7]. Even for the case with only two different processing times the ratio above has merely been improved by a tiny margin [2].
In some cases where the restrictions on one or both job sizes are somewhat structured, simple combinatorial algorithms are known that provide better approximation ratios than the algorithm above.
In this paper we study two classes of structured restrictions, that we refer to as the Inclusion Chain Class and the Two Partition Class. We present a 1.5-approximation for each of them.
Research was in part supported by German Research Foundation (DFG) project JA 612/15-1.
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References
Chakrabarty, D., Khanna, S.: A special case of restricted assignment makespan minimization. In: 11th Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP) (2013)
Chakrabarty, D., Khanna, S., Li, S.: On \((1, \epsilon )\)-restricted assignment makespan minimization. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, pp. 1087–1101. SIAM (2015). http://dl.acm.org/citation.cfm?id=2722129.2722202
Ebenlendr, T., Krčál, M., Sgall, J.: Graph balancing: a special case of scheduling unrelated parallel machines. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pp. 483–490 (2008). http://dl.acm.org/citation.cfm?id=1347082.1347135
Huang, C., Ott, S.: A combinatorial approximation algorithm for graph balancing with light hyper edges. In: 24th Annual European Symposium on Algorithms, ESA 2016, 22–24 August 2016, pp. 49:1–49:15, Aarhus, Denmark (2016). http://dx.doi.org/10.4230/LIPIcs.ESA.2016.49
Jansen, K., Land, K., Maack, M.: Estimating the makespan of the two-valued restricted assignment problem. In: 15th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2016, 22–24 June 2016, Reykjavik, Iceland, pp. 24:1–24:13 (2016). http://dx.doi.org/10.4230/LIPIcs.SWAT.2016.24
Jansen, K., Rohwedder, L.: On the configuration-LP of the restricted assignment problem. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, 16–19 January 2017 (2017, to appear)
Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(3), 259–271 (1990). http://dx.doi.org/10.1007/BF01585745
Svensson, O.: Santa claus schedules jobs on unrelated machines. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 617–626. ACM, New York (2011). http://doi.acm.org/10.1145/1993636.1993718
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Jansen, K., Rohwedder, L. (2017). Structured Instances of Restricted Assignment with Two Processing Times. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_21
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DOI: https://doi.org/10.1007/978-3-319-53007-9_21
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