<s>
In	O
graph	O
theory	O
,	O
the	O
blossom	B-Algorithm
algorithm	I-Algorithm
is	O
an	O
algorithm	O
for	O
constructing	O
maximum	O
matchings	O
on	O
graphs	O
.	O
</s>
<s>
A	O
major	O
reason	O
that	O
the	O
blossom	B-Algorithm
algorithm	I-Algorithm
is	O
important	O
is	O
that	O
it	O
gave	O
the	O
first	O
proof	O
that	O
a	O
maximum-size	O
matching	O
could	O
be	O
found	O
using	O
a	O
polynomial	O
amount	O
of	O
computation	O
time	O
.	O
</s>
<s>
Another	O
reason	O
is	O
that	O
it	O
led	O
to	O
a	O
linear	B-Algorithm
programming	I-Algorithm
polyhedral	O
description	O
of	O
the	O
matching	O
polytope	O
,	O
yielding	O
an	O
algorithm	O
for	O
min-weight	O
matching	O
.	O
</s>
<s>
As	O
elaborated	O
by	O
Alexander	O
Schrijver	O
,	O
further	O
significance	O
of	O
the	O
result	O
comes	O
from	O
the	O
fact	O
that	O
this	O
was	O
the	O
first	O
polytope	O
whose	O
proof	O
of	O
integrality	O
"	O
does	O
not	O
simply	O
follow	O
just	O
from	O
total	B-Algorithm
unimodularity	I-Algorithm
,	O
and	O
its	O
description	O
was	O
a	O
breakthrough	O
in	O
polyhedral	O
combinatorics.	O
"	O
</s>
<s>
The	O
algorithm	O
thus	O
reduces	O
to	O
the	O
standard	O
algorithm	O
to	O
construct	O
maximum	O
cardinality	O
matchings	O
in	O
bipartite	O
graphs	O
where	O
we	O
repeatedly	O
search	O
for	O
an	O
augmenting	O
path	O
by	O
a	O
simple	O
graph	O
traversal	O
:	O
this	O
is	O
for	O
instance	O
the	O
case	O
of	O
the	O
Ford	B-Algorithm
–	I-Algorithm
Fulkerson	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
matching	O
problem	O
can	O
be	O
generalized	O
by	O
assigning	O
weights	O
to	O
edges	O
in	O
and	O
asking	O
for	O
a	O
set	O
that	O
produces	O
a	O
matching	O
of	O
maximum	O
(	O
minimum	O
)	O
total	O
weight	O
:	O
this	O
is	O
the	O
maximum	B-Algorithm
weight	I-Algorithm
matching	I-Algorithm
problem	O
.	O
</s>
