SIAM Journal on Computing, Volume 49, Issue 6, Page 1083-1108, January 2020.
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.

中文翻译：

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约束分配问题的拟多项式逼近

SIAM计算杂志，第49卷，第6期，第1083-1108页，2020年1月
。受限分配问题是不相关并行机上调度的一个突出特殊情况。对于已知的最强线性规划松弛（配置LP），我们将其完整性缺口的非构造界线从1.9412改进为1.8334，并显着简化了证明。然后，我们给出一个构造变量，在准多项式时间内得出1.8334的近似值。这是针对此问题的第一种拟多项式算法，它对长期逼近率2进行了改进。