<s>
In	O
mathematics	O
,	O
a	O
subadditive	B-Algorithm
set	I-Algorithm
function	I-Algorithm
is	O
a	O
set	O
function	O
whose	O
value	O
,	O
informally	O
,	O
has	O
the	O
property	O
that	O
the	O
value	O
of	O
function	O
on	O
the	O
union	O
of	O
two	O
sets	O
is	O
at	O
most	O
the	O
sum	O
of	O
values	O
of	O
the	O
function	O
on	O
each	O
of	O
the	O
sets	O
.	O
</s>
<s>
Every	O
non-negative	O
submodular	B-Algorithm
set	I-Algorithm
function	I-Algorithm
is	O
subadditive	O
(	O
the	O
family	O
of	O
non-negative	O
submodular	B-Algorithm
functions	I-Algorithm
is	O
strictly	O
contained	O
in	O
the	O
family	O
of	O
subadditive	O
functions	O
)	O
.	O
</s>
<s>
The	O
function	O
that	O
counts	O
the	O
number	O
of	O
sets	O
required	O
to	O
cover	B-Algorithm
a	O
given	O
set	O
is	O
subadditive	O
.	O
</s>
<s>
Define	O
as	O
the	O
minimum	O
number	O
of	O
subsets	O
required	O
to	O
cover	B-Algorithm
a	O
given	O
set	O
.	O
</s>
<s>
Then	O
is	O
a	O
subadditive	B-Algorithm
set	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Fractionally	O
subadditive	B-Algorithm
set	I-Algorithm
functions	I-Algorithm
are	O
a	O
generalization	O
of	O
submodular	B-Algorithm
functions	I-Algorithm
and	O
a	O
special	O
case	O
of	O
subadditive	O
functions	O
.	O
</s>
