<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
specifically	O
in	O
algorithms	O
related	O
to	O
pathfinding	B-Algorithm
,	O
a	O
heuristic	B-Algorithm
function	I-Algorithm
is	O
said	O
to	O
be	O
admissible	O
if	O
it	O
never	O
overestimates	O
the	O
cost	O
of	O
reaching	O
the	O
goal	O
,	O
i.e.	O
</s>
<s>
It	O
is	O
related	O
to	O
the	O
concept	O
of	O
consistent	O
heuristics	B-Algorithm
.	O
</s>
<s>
While	O
all	O
consistent	O
heuristics	B-Algorithm
are	O
admissible	O
,	O
not	O
all	O
admissible	B-General_Concept
heuristics	I-General_Concept
are	O
consistent	O
.	O
</s>
<s>
An	O
admissible	B-General_Concept
heuristic	I-General_Concept
is	O
used	O
to	O
estimate	O
the	O
cost	O
of	O
reaching	O
the	O
goal	O
state	O
in	O
an	O
informed	O
search	B-Application
algorithm	I-Application
.	O
</s>
<s>
version	O
of	O
the	O
problem	O
,	O
or	O
by	O
information	O
from	O
pattern	O
databases	O
that	O
store	O
exact	O
solutions	O
to	O
subproblems	O
of	O
the	O
problem	O
,	O
or	O
by	O
using	O
inductive	B-General_Concept
learning	I-General_Concept
methods	O
.	O
</s>
<s>
Two	O
different	O
examples	O
of	O
admissible	B-General_Concept
heuristics	I-General_Concept
apply	O
to	O
the	O
fifteen	O
puzzle	O
problem	O
:	O
</s>
<s>
It	O
is	O
clear	O
that	O
this	O
heuristic	B-Algorithm
is	O
admissible	O
since	O
the	O
total	O
number	O
of	O
moves	O
to	O
order	O
the	O
tiles	O
correctly	O
is	O
at	O
least	O
the	O
number	O
of	O
misplaced	O
tiles	O
(	O
each	O
tile	O
not	O
in	O
place	O
must	O
be	O
moved	O
at	O
least	O
once	O
)	O
.	O
</s>
<s>
The	O
Manhattan	O
distance	O
is	O
an	O
admissible	B-General_Concept
heuristic	I-General_Concept
in	O
this	O
case	O
because	O
every	O
tile	O
will	O
have	O
to	O
be	O
moved	O
at	O
least	O
the	O
number	O
of	O
spots	O
in	O
between	O
itself	O
and	O
its	O
correct	O
position	O
.	O
</s>
<s>
If	O
an	O
admissible	B-General_Concept
heuristic	I-General_Concept
is	O
used	O
in	O
an	O
algorithm	O
that	O
,	O
per	O
iteration	O
,	O
progresses	O
only	O
the	O
path	O
of	O
lowest	O
evaluation	O
(	O
current	O
cost	O
+	O
heuristic	B-Algorithm
)	O
of	O
several	O
candidate	O
paths	O
,	O
terminates	O
the	O
moment	O
its	O
exploration	O
reaches	O
the	O
goal	O
and	O
,	O
crucially	O
,	O
never	O
closes	O
all	O
optimal	O
paths	O
before	O
terminating	O
(	O
something	O
that	O
's	O
possible	O
with	O
A*	B-Protocol
search	I-Protocol
algorithm	I-Protocol
if	O
special	O
care	O
is	O
n't	O
taken	O
)	O
,	O
then	O
this	O
algorithm	O
can	O
only	O
terminate	O
on	O
an	O
optimal	O
path	O
.	O
</s>
<s>
If	O
our	O
heuristic	B-Algorithm
is	O
admissible	O
it	O
follows	O
that	O
at	O
this	O
penultimate	O
step	O
Teval	O
=	O
Ttrue	O
because	O
any	O
increase	O
on	O
the	O
true	O
cost	O
by	O
the	O
heuristic	B-Algorithm
on	O
T	O
would	O
be	O
inadmissible	O
and	O
the	O
heuristic	B-Algorithm
cannot	O
be	O
negative	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
an	O
admissible	B-General_Concept
heuristic	I-General_Concept
would	O
require	O
that	O
Seval	O
≤	O
Strue	O
which	O
combined	O
with	O
the	O
above	O
inequalities	O
gives	O
us	O
Teval	O
<	O
Ttrue	O
and	O
more	O
specifically	O
Teval	O
≠	O
Ttrue	O
.	O
</s>
<s>
This	O
way	O
,	O
an	O
admissible	B-General_Concept
heuristic	I-General_Concept
can	O
ensure	O
optimality	O
.	O
</s>
<s>
However	O
,	O
note	O
that	O
although	O
an	O
admissible	B-General_Concept
heuristic	I-General_Concept
can	O
guarantee	O
final	O
optimality	O
,	O
it	O
is	O
not	O
necessarily	O
efficient	O
.	O
</s>
