 
Summary: Approximation schemes for covering and
scheduling on related machines
Yossi Azar 1 ,Leah Epstein 2
1 Dept. of Computer Science, TelAviv University. ???
2 Dept. of Computer Science, TelAviv University. y
Abstract. We consider the problem of assigning a set of jobs to m par
allel related machines so as to maximize the minimum load over the
machines. This situation corresponds to a case that a system which con
sists of the m machines is alive (i.e. productive) only when all machines
are alive, and the system should be maintained alive as long as possible.
The above problem is called related machines covering problem and is dif
ferent from the related machines scheduling problem in which the goal is
to minimize the maximum load. Our main result is a polynomial approx
imation scheme for this covering problem. To the best of our knowledge
the previous best approximation algorithm has a performance ratio of 2.
Also, an approximation scheme for the special case of identical machines
was given by [14].
Some of our techniques are built on ideas of Hochbaum and Shmoys
[12]. They provided an approximation scheme for the well known related
machines scheduling. In fact, our algorithm can be adapted to provide
