# Kolloquiumsvortrag: Dr. Lin Chen, TU Berlin

09.05.2014 von 13:45 bis 14:30

LMS2 Ü2/K

### On the optimality of the approximation schemes for the classical scheduling problem

Abstract:

We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH).

• The scheduling problem on a constant number m of identical machines, denoted as Pm||Cmax , is known to admit an FPTAS of running time O(n)+(1/ϵ)O(m) . We prove it is essentially the best possible in the sense that a (1/ϵ)O(m1δ)+nO(1) time FPTAS for any δ>0 implies that ETH fails.
• The scheduling problem on an arbitrary number of identical machines, denoted as P||Cmax , is known to admit a PTAS of running time 2O(1/ϵ2log3(1/ϵ))+nO(1) . We prove it is nearly optimal in the sense that a 2O((1/ϵ)1δ)+nO(1) time PTAS for any δ>0 implies that ETH fails.

We also obain lower bounds of exact algorithms for the scheduling problem that almost matches upper bounds.

This is joint work with K. Jansen and G. Zhang.