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arXiv · 1511.07826

Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines

Nikhil Bansal·Aravind Srinivasan·Ola Svensson
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Abstract

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 $(3/2-c)$-approximation algorithm for some fixed $c>0$, improving upon the long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM, 2001, and Sethuraman & Squillante, SODA, 1999). 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 $3/2$. Second, we give a new general bipartite-rounding procedure that produces an assignment with certain strong negative correlation properties.

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Nikhil Bansal, Aravind Srinivasan, Ola Svensson. 2015-12-01. Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines. https://arxiv.org/abs/1511.07826

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