research-article

A Quasi-Polynomial Approximation for the Restricted Assignment Problem

Authors:

Klaus Jansen,

Lars RohwedderAuthors Info & Claims

SIAM Journal on Computing, Volume 49, Issue 6

Pages 1083 - 1108

https://doi.org/10.1137/19M128257X

Published: 01 January 2020 Publication History

Abstract

The Restricted Assignment problem is a prominent special case of Scheduling on Unrelated Parallel Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the nonconstructive bound on its integrality gap from 1.9412 to 1.8334 and significantly simplify the proof. Then we give a constructive variant, yielding a 1.8334-approximation in quasi-polynomial time. This is the first quasi-polynomial algorithm for this problem improving on the long-standing approximation rate of 2.

References

[1]

C. Annamalai, Lazy Local Search Meets Machine Scheduling, preprint, https://arxiv.org/abs/1611.07371, 2016.

Google Scholar

[2]

C. Annamalai, C. Kalaitzis, and O. Svensson, Combinatorial algorithm for restricted max-min fair allocation, ACM Trans. Algorithms, 13 (2017), 37, https://doi.org/10.1145/3070694.

Google Scholar

[3]

A. Asadpour, U. Feige, and A. Saberi, Santa Claus meets hypergraph matchings, ACM Trans. Algorithms, 8 (2012), 24, https://doi.org/10.1145/2229163.2229168.

Google Scholar

[4]

N. Bansal and M. Sviridenko, The Santa Claus problem, in Proceedings of the 38th Annual ACM Symposium on Theory of Computing, Seattle, WA, 2006, pp. 31--40, https://doi.org/10.1145/1132516.1132522.

Google Scholar

[5]

D. Chakrabarty, S. Khanna, and S. Li, 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), ACM, New York, SIAM, Philadelphia, 2015, pp. 1087--1101, https://doi.org/10.1137/1.9781611973730.73.

Google Scholar

[6]

S. Cheng and Y. Mao, Restricted max-min allocation: Approximation and integrality gap, in 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 (Patras, Greece), C. Baier, I. Chatzigiannakis, P. Flocchini, and S. Leonardi, eds., of LIPIcs. Leibniz Int. Proc. Inform. 132, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2019, 38, https://doi.org/10.4230/LIPIcs.ICALP.2019.38.

Google Scholar

[7]

S. Davies, T. Rothvoss, and Y. Zhang, A tale of Santa Claus, hypergraphs and matroids, in Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 (Salt Lake City, UT), S. Chawla, ed., ACM, New York, SIAM, Philadelphia, 2020, pp. 2748--2757, https://doi.org/10.1137/1.9781611975994.167.

Google Scholar

[8]

K. Jansen, K. Land, and M. Maack, Estimating the makespan of the two-valued restricted assignment problem, in 15th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2016 (Reykjavik, Iceland), 2016, 24, https://doi.org/10.4230/LIPIcs.SWAT.2016.24.

Google Scholar

[9]

J. K. Lenstra, D. B. Shmoys, and É. Tardos, Approximation algorithms for scheduling unrelated parallel machines, Math. Program., 46 (1990), pp. 259--271, https://doi.org/10.1007/BF01585745.

Google Scholar

[10]

L. Polácek and O. Svensson, Quasi-polynomial local search for restricted max-min fair allocation, ACM Trans. Algorithms, 12 (2016), 13, https://doi.org/10.1145/2818695.

Google Scholar

[11]

P. Schuurman and G. J. Woeginger, Polynomial time approximation algorithms for machine scheduling: Ten open problems, J. Scheduling, 2 (1999), pp. 203--213, https://doi.org/10.1002/(SICI)1099-1425(199909/10)2:5<203::AID-JOS26>3.0.CO;2-5.

Google Scholar

[12]

O. Svensson, Santa Claus schedules jobs on unrelated machines, SIAM J. Comput., 41 (2012), pp. 1318--1341, https://doi.org/10.1137/110851201.

Google Scholar

[13]

D. P. Williamson and D. B. Shmoys, The Design of Approximation Algorithms, Cambridge University Press, Cambridge, UK, 2011, https://doi.org/10.1017/CBO9780511921735.

Google Scholar

Cited By

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Bamas ÉRohwedder LSaha BServedio R(2023)Better Trees for Santa ClausProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585174(1862-1875)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585174
Karakostas GKolliopoulos S(2022)Resource Time-Sharing for IoT Applications with DeadlinesAlgorithmics of Wireless Networks10.1007/978-3-031-22050-0_7(91-107)Online publication date: 8-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-22050-0_7

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SIAM Journal on Computing Volume 49, Issue 6

ISSN:0097-5397

DOI:10.1137/smjcat.49.6

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2020

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Bamas ÉRohwedder LSaha BServedio R(2023)Better Trees for Santa ClausProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585174(1862-1875)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585174
Karakostas GKolliopoulos S(2022)Resource Time-Sharing for IoT Applications with DeadlinesAlgorithmics of Wireless Networks10.1007/978-3-031-22050-0_7(91-107)Online publication date: 8-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-22050-0_7

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On the configuration-LP of the restricted assignment problem

An EPTAS for Scheduling on Unrelated Machines of Few Different Types

Assigning sporadic tasks to unrelated machines

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