<s>
In	O
mathematics	O
and	O
computer	O
science	O
,	O
the	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
problem	O
is	O
a	O
problem	O
in	O
real-time	B-Algorithm
scheduling	I-Algorithm
with	O
repeating	O
tasks	O
of	O
unit	O
length	O
and	O
hard	O
constraints	O
on	O
the	O
time	O
between	O
repetitions	O
.	O
</s>
<s>
The	O
input	O
to	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
consists	O
of	O
a	O
list	O
of	O
tasks	O
,	O
each	O
of	O
which	O
is	O
assumed	O
to	O
take	O
unit	O
time	O
per	O
instantiation	O
.	O
</s>
<s>
Then	O
the	O
density	O
of	O
a	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
problem	O
is	O
.	O
</s>
<s>
Every	O
instance	O
of	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
with	O
density	O
at	O
most	O
has	O
a	O
solution	O
,	O
and	O
it	O
has	O
been	O
conjectured	O
that	O
every	O
instance	O
with	O
density	O
at	O
most	O
has	O
a	O
solution	O
.	O
</s>
<s>
With	O
a	O
compact	O
input	O
representation	O
that	O
specifies	O
,	O
for	O
each	O
distinct	O
repeat	O
time	O
,	O
the	O
number	O
of	O
objects	O
that	O
have	O
that	O
repeat	O
time	O
,	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
is	O
NP-hard	O
.	O
</s>
<s>
Applications	O
of	O
pinwheel	B-Operating_System
scheduling	I-Operating_System
include	O
scheduling	O
communications	O
between	O
satellites	O
and	O
a	O
ground	O
station	O
,	O
scheduling	O
maintenance	O
of	O
a	O
collection	O
of	O
objects	O
(	O
such	O
as	O
oil	O
changes	O
for	O
automobiles	O
)	O
,	O
computer	O
processing	O
of	O
multimedia	O
data	O
,	O
and	O
contention	O
resolution	O
in	O
real-time	O
wireless	O
computer	O
networks	O
.	O
</s>
