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.

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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
Rieger ASegev D(2023)Quasi-polynomial time approximation schemes for assortment optimization under Mallows-based rankingsMathematical Programming: Series A and B10.1007/s10107-023-02033-4208:1-2(111-171)Online publication date: 11-Dec-2023
https://dl.acm.org/doi/10.1007/s10107-023-02033-4
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

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
Rieger ASegev D(2023)Quasi-polynomial time approximation schemes for assortment optimization under Mallows-based rankingsMathematical Programming: Series A and B10.1007/s10107-023-02033-4208:1-2(111-171)Online publication date: 11-Dec-2023
https://dl.acm.org/doi/10.1007/s10107-023-02033-4
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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