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SS12 MINIMUM WEIGHTED
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Multiprocessor Scheduling
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SS10 MINIMUM MULTIPROCESSOR
-
I
NSTANCE
:
Set
T
of tasks, number
m
of identical processors, for each task
a release time
and a length
.
-
S
OLUTION
:
An
m
-processor schedule for
T
that obeys the resource constraints
and the release times, i.e., a function
such that, for all
and for each processor
i
, if
S(u,i)
is the set of tasks
t
for which
and
, then
|S(u,i)| = 1
and for each task
t
,
.
-
M
EASURE
:
The total flow time for the schedule, i.e.,
.
-
Good News:
Approximable within
where
n=|T|
[
252
].
-
Bad News:
Not approximable within
for any
[
252
].
-
Comment:
In the case
m=1
, it is approximable within
and it is not
approximable within
for any
[
213
]. In the preemptive case, that is, in the case a job
that is running can be preempted and continue later on any machine,
the problem is approximable within
and it is not
approximable within
where
[
252
].
Variation in which all speed factors are 1 and the load is measured using the
norm, i.e.
,
admits a PTAS for any
[
5
].
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997