Abstract
Scheduling jobs on unrelated machines and minimizing the makespan is a classical problem in combinatorial optimization. A job j has a processing time \(p_{ij}\) for every machine i. The best polynomial algorithm known for this problem goes back to Lenstra et al. and has an approximation ratio of 2. In this paper we study the Restricted Assignment problem, which is the special case where \(p_{ij}\in \{p_j,\infty \}\). We present an algorithm for this problem with an approximation ratio of \(11/6 + \epsilon \) and quasi-polynomial running time \(n^{\mathcal O(1/\epsilon \log (n))}\) for every \(\epsilon > 0\). This closes the gap to the best estimation algorithm known for the problem with regard to quasi-polynomial running time.
Research supported by German Research Foundation (DFG) project JA 612/15-1.
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References
Annamalai, C.: Lazy local search meets machine scheduling. CoRR abs/1611.07371 (2016). http://arxiv.org/abs/1611.07371
Annamalai, C., Kalaitzis, C., Svensson, O.: Combinatorial algorithm for restricted max-min fair allocation. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, 4–6 January 2015, pp. 1357–1372 (2015). doi:10.1137/1.9781611973730.90
Bansal, N., Sviridenko, M.: The santa claus problem. In: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, USA, 21–23 May 2006, pp. 31–40 (2006). doi:10.1145/1132516.1132522
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, San Diego, CA, USA, 4–6 January 2015, pp. 1087–1101 (2015). doi:10.1137/1.9781611973730.73
Jansen, K., Land, F., Land, K.: Bounding the running time of algorithms for scheduling and packing problems. SIAM J. Discrete Math. 30(1), 343–366 (2016). doi:10.1137/140952636
Jansen, K., Land, K., Maack, M.: Estimating the makespan of the two-valued restricted assignment problem. In: Proceedings of the 15th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2016, Reykjavik, Iceland, 22–24 June 2016, pp. 24:1–24:13 (2016). doi: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, Hotel Porta Fira, 16–19 January, pp. 2670–2678 (2017). doi:10.1137/1.9781611974782.176
Lenstra, J.K., Shmoys, D.B., Tardos, E.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46(3), 259–271 (1990). doi:10.1007/BF01585745
Polácek, L., Svensson, O.: Quasi-polynomial local search for restricted max-min fair allocation. ACM Trans. Algorithms 12(2), 13 (2016). doi:10.1145/2818695
Svensson, O.: Santa claus schedules jobs on unrelated machines. SIAM J. Comput. 41(5), 1318–1341 (2012). doi:10.1137/110851201
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Jansen, K., Rohwedder, L. (2017). A Quasi-Polynomial Approximation for the Restricted Assignment Problem. In: Eisenbrand, F., Koenemann, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2017. Lecture Notes in Computer Science(), vol 10328. Springer, Cham. https://doi.org/10.1007/978-3-319-59250-3_25
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