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SS10 MINIMUM MULTIPROCESSOR
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Multiprocessor Scheduling
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SS8 MINIMUM RESOURCE
-
I
NSTANCE
:
Set
C
of compilers, set
T
of tasks, number
m
of
processors, length
and compiler
for each
,
set-up time
for each
.
-
S
OLUTION
:
An
m
-processor preemptive schedule for
T
, i.e., for
each
, a partition of
t
into any number of subtasks
such that
and an assignment
that assigns to each subtask
of
t
a pair of nonnegative integers
such that
and, for
,
.
Such a schedule must satisfy the following additional constraint:
Whenever two subtasks
of
t
and
of
t'
with
are
scheduled consecutively on the same machine (i.e.,
and no other subtask
has
and
),
then
if they have the same
compiler (i.e.,
c(t) = c(t')
) and
if they have different compilers.
-
M
EASURE
:
The overall completion time, i.e., the maximum over all subtasks of
.
-
Good News:
Approximable within
[
66
].
-
Comment:
If all set-up times are equal, then the problem is approximable within
3/2-1/2m
for
and admits an FPTAS for
m=2
[
346
].
-
Garey and Johnson:
SS6 and SS12
Viggo Kann
Mon Apr 21 13:07:14 MET DST 1997