eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
59:1
59:13
10.4230/LIPIcs.ICALP.2018.59
article
Quasi-PTAS for Scheduling with Precedences using LP Hierarchies
Garg, Shashwat
1
Eindhoven University of Technology, Netherlands
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).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.59/LIPIcs.ICALP.2018.59.pdf
Approximation algorithms
hierarchies
scheduling
rounding techniques