 
Summary: Approximation Schemes for
Scheduling on Parallel Machines
Noga Alon
Yossi Azar
Gerhard J. Woeginger
Tal Yadid §
Abstract
We discuss scheduling problems with m identical machines and n jobs where each job
has to be assigned to some machine. The goal is to optimize objective functions that
solely depend on the machine completion times.
As a main result, we identify some conditions on the objective function, under which
the resulting scheduling problems possess a polynomial time approximation scheme. Our
result contains, generalizes, improves, simplifies, and unifies many other results in this
area in a natural way.
Keywords: Scheduling theory, approximation algorithm, approximation scheme, worst
case ratio, combinatorial optimization.
1 Introduction
In this paper we consider scheduling problems with m identical machines Mi, 1 i m,
and n independent jobs Jj, 1 j n, where job Jj has processing time (or length) pj. A
schedule is an assignment of the n jobs to the m machines. For 1 i m, the completion
