SIAM Journal on Computing, Ahead of Print.
We consider the problem of scheduling jobs on unrelated machines so as to minimize the sum of weighted completion times. Our main result is a $(\nicefrac{3}{2}-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of $\nicefrac{3}{2}$. To do this, we first introduce a new lift-and-project-based SDP relaxation for the problem. This is necessary, as the previous convex programming relaxations have an integrality gap of $\nicefrac{3}{2}$. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.

中文翻译：

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提升和绕行以提高无关机器上的加权完成时间

《 SIAM计算杂志》，预印本。
我们考虑在无关机器上调度作业的问题，以最大程度地减少加权完成时间的总和。我们的主要结果是对某些固定$ c> 0 $的$（\ nicefrac {3} {2} -c）$近似算法，改进了$ \ nicefrac {3} {2} $的长期边界。为此，我们首先针对该问题引入了基于提升和项目的新SDP松弛。这是必要的，因为先前的凸编程松弛具有$ \ nicefrac {3} {2} $的完整性缺口。其次，我们给出了一个新的一般二部舍入过程，该过程产生具有某些强负相关性的赋值。