<s>
In	O
computer	B-General_Concept
science	I-General_Concept
and	O
graph	O
theory	O
,	O
the	O
maximum	B-Algorithm
weight	I-Algorithm
matching	I-Algorithm
problem	O
is	O
the	O
problem	O
of	O
finding	O
,	O
in	O
a	O
weighted	O
graph	O
,	O
a	O
matching	O
in	O
which	O
the	O
sum	O
of	O
weights	O
is	O
maximized	O
.	O
</s>
<s>
A	O
special	O
case	O
of	O
it	O
is	O
the	O
assignment	B-Algorithm
problem	I-Algorithm
,	O
in	O
which	O
the	O
input	O
is	O
restricted	O
to	O
be	O
a	O
bipartite	O
graph	O
,	O
and	O
the	O
matching	O
constrained	O
to	O
be	O
have	O
cardinality	O
that	O
of	O
the	O
smaller	O
of	O
the	O
two	O
partitions	O
.	O
</s>
<s>
There	O
is	O
a	O
time	O
algorithm	O
to	O
find	O
a	O
maximum	O
matching	O
or	O
a	O
maximum	B-Algorithm
weight	I-Algorithm
matching	I-Algorithm
in	O
a	O
graph	O
that	O
is	O
not	O
bipartite	O
;	O
it	O
is	O
due	O
to	O
Jack	O
Edmonds	O
,	O
is	O
called	O
the	O
paths	O
,	O
trees	O
,	O
and	O
flowers	O
method	O
or	O
simply	O
Edmonds	B-Algorithm
 '	I-Algorithm
algorithm	I-Algorithm
,	O
and	O
uses	O
bidirected	O
edges	O
.	O
</s>
<s>
Their	O
work	O
proposes	O
an	O
approximation	B-Algorithm
algorithm	I-Algorithm
for	O
the	O
maximum	B-Algorithm
weight	I-Algorithm
matching	I-Algorithm
problem	O
,	O
which	O
runs	O
in	O
linear	O
time	O
for	O
any	O
fixed	O
error	O
bound	O
.	O
</s>
