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All-Norm Approximation for Scheduling on Identical Machines

Summary: All-Norm Approximation for Scheduling on
Identical Machines
Yossi Azar  Shai Taub y
We consider the problem of assigning jobs to m identical machines. The load of a
machine is the sum of the weights of jobs assigned to it. The goal is to minimize the norm
of the resulting load vector. It is known that for any xed norm there is a PTAS. On
the other hand, it is also known that there is no single assignment which is optimal for
all norms. We show that there exists one assignment which simultaneously guarantees
a 1.388-approximation of the optimal assignments for all norms. This improves the 1.5
approximation given by Chandra and Wong in 1975.
1 Introduction
The problem of machine scheduling is one of the most researched problems in the area of
approximation algorithms. The identical machines model is de ned by m parallel machines
and n independent jobs, where each job j has a non-negative weight w j . Each job should
be assigned to one of the machines, and the load of each machine i, l i , is de ned as the
sum of weights of all jobs assigned to it. The goal of the problem is to get the best assign-
ment. For each speci c norm ` p (p > 1), this is de ned as the assignment that minimizes
k(l 1 ; : : : ; l m )k p = (
P m


Source: Azar, Yossi - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences