A Lasserre-Based (1+epsilon)-Approximation for Makespan Scheduling with Precedence Constraints


February 8, 2016


Thomas Rothvoss


University of Washington


In a classical problem in scheduling, one has n unit size jobs with a precedence order and the goal is to find a schedule of those jobs on m identical machines as to minimize the makespan. It is one of the remaining four open problems from the book of Garey and Johnson whether or not this problem is NP-hard for m=3. We prove that for any fixed epsilon and m, a Sherali-Adams / Lasserre lift of the time-index LP with slightly super poly-logarithmic number of rounds provides a (1+epsilon)-approximation.

The previously best approximation algorithms guarantee a 2-7/(3m+1)-approximation in polynomial time for m>=4 and 4/3 for m=3. Our algorithm is based on a recursive scheduling approach where in each step we reduce the correlation in form of long chains. Our method adds to the rather short list of examples where hierarchies are actually useful to obtain better approximation algorithms.

This is joint work with Elaine Levey.


Thomas Rothvoss

Thomas Rothvoss is Assistant Professor in the Department of Mathematics as well as in the Department of Computer Science and Engineering at the University of Washington. He completed his PhD in Mathematics in 2009 at EPFL under Friedrich Eisenbrand, followed by a PostDoc at MIT with Michel Goemans. His work received best paper awards at STOC 2010, SODA 2014 and STOC 2014. He was a recipient of a 2015 Alfred P. Sloan Research Fellowship.