<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
charging	B-General_Concept
argument	I-General_Concept
is	O
used	O
to	O
compare	O
the	O
output	O
of	O
an	O
optimization	O
algorithm	O
to	O
an	O
optimal	O
solution	O
.	O
</s>
<s>
The	O
correctness	O
of	O
the	O
charging	B-General_Concept
argument	I-General_Concept
for	O
a	O
cost	O
minimization	O
problem	O
is	O
symmetric	O
.	O
</s>
<s>
Charging	B-General_Concept
arguments	I-General_Concept
can	O
also	O
be	O
used	O
to	O
show	O
approximation	O
results	O
.	O
</s>
<s>
Instead	O
of	O
showing	O
that	O
an	O
algorithm	O
produces	O
outputs	O
with	O
the	O
same	O
value	O
of	O
profit	O
or	O
cost	O
as	O
the	O
optimal	O
solution	O
,	O
show	O
that	O
it	O
attains	O
that	O
value	O
within	O
a	O
factor	O
of	O
n	O
.	O
Rather	O
than	O
proving	O
the	O
existence	O
of	O
a	O
one-to-one	O
function	O
,	O
the	O
charging	B-General_Concept
argument	I-General_Concept
focuses	O
on	O
proving	O
that	O
an	O
n-to-one	O
function	O
exists	O
in	O
order	O
to	O
prove	O
approximation	O
results	O
.	O
</s>
<s>
The	O
charging	B-General_Concept
argument	I-General_Concept
can	O
be	O
used	O
to	O
show	O
that	O
the	O
earliest	O
finish	O
time	O
algorithm	O
is	O
optimal	O
for	O
the	O
interval	O
scheduling	O
problem	O
.	O
</s>
<s>
To	O
show	O
that	O
the	O
earliest	O
finish	O
time	O
algorithm	O
is	O
optimal	O
using	O
the	O
charging	B-General_Concept
argument	I-General_Concept
,	O
h	O
must	O
be	O
shown	O
to	O
be	O
a	O
one-to-one	O
function	O
mapping	O
intervals	O
in	O
OPT(I )	O
to	O
those	O
in	O
EFT(I )	O
.	O
</s>
<s>
By	O
the	O
charging	B-General_Concept
argument	I-General_Concept
,	O
the	O
earliest	O
finishing	O
time	O
algorithm	O
is	O
optimal	O
.	O
</s>
<s>
After	O
modifying	O
the	O
definition	O
of	O
compatibility	O
in	O
the	O
algorithm	O
,	O
the	O
charging	B-General_Concept
argument	I-General_Concept
can	O
be	O
used	O
to	O
show	O
that	O
the	O
earliest	O
finish	O
time	O
algorithm	O
is	O
a	O
2-approximation	O
algorithm	O
for	O
the	O
job	O
interval	O
scheduling	O
problem	O
.	O
</s>
<s>
To	O
show	O
that	O
the	O
earliest	O
finish	O
time	O
algorithm	O
is	O
a	O
2-approximation	O
algorithm	O
using	O
the	O
charging	B-General_Concept
argument	I-General_Concept
,	O
h	O
must	O
be	O
shown	O
to	O
be	O
a	O
two-to-one	O
function	O
mapping	O
intervals	O
in	O
OPT(I )	O
to	O
those	O
in	O
EFT(I )	O
.	O
</s>
<s>
By	O
the	O
charging	B-General_Concept
argument	I-General_Concept
,	O
the	O
earliest	O
finishing	O
time	O
algorithm	O
is	O
a	O
two-approximation	O
algorithm	O
for	O
the	O
job	O
interval	O
scheduling	O
problem	O
.	O
</s>
