Quasi-PTAS for Scheduling with Precedences using LP Hierarchies
A central problem in scheduling is to schedule n unit size jobs with precedence constraints on m identical machines so as to minimize the makespan. For m=3, it is not even known if the problem is NP-hard and this is one of the last open problems from the book of Garey and Johnson.
We show that for fixed m and epsilon, {polylog}(n) rounds of Sherali-Adams hierarchy applied to a natural LP of the problem provides a (1+epsilon)-approximation algorithm running in quasi-polynomial time. This improves over the recent result of Levey and Rothvoss, who used r=(log n)^{O(log log n)} rounds of Sherali-Adams in order to get a (1+epsilon)-approximation algorithm with a running time of n^O(r).
Approximation algorithms
hierarchies
scheduling
rounding techniques
Theory of computation~Scheduling algorithms
59:1-59:13
Regular Paper
https://arxiv.org/pdf/1708.04369.pdf
Shashwat
Garg
Shashwat Garg
Eindhoven University of Technology, Netherlands
Supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 022.005.025.
10.4230/LIPIcs.ICALP.2018.59
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Shashwat Garg
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