 
Summary: Approximation Schemes for Scheduling
Noga Alon \Lambda Yossi Azar y Gerhard J. Woeginger z Tal Yadid x
Abstract
We consider the classic scheduling/load balancing problems
where there are m identical machines and n jobs, and each
job should be assigned to some machine. Traditionally, the
assignment of jobs to machines is measured by the makespan
(maximum load) i.e., the L1 norm of the assignment. An ffl
approximation scheme was given by Hochbaum and Shmoys
[10] for minimizing the L1 norm.
In several applications, such as in storage allocation, a
more appropriate measure is the sum of the squares of the
loads (which is equivalent to the L2 norm). This problem
was considered in [4, 5, 13] who showed how to approximate
the optimum value by a factor of about 1.04. In fact, a
more general measure, which is the Lp norm (for any p – 1)
can also be approximated to some constant (see Chandra
and Wong [4]) which may be as large as 3=2. We improve
these results by providing an fflapproximation scheme for the
general Lp norm (and in particular for the L2 norm). We
