<s>
SSS*	B-Algorithm
is	O
a	O
search	B-Application
algorithm	I-Application
,	O
introduced	O
by	O
George	O
Stockman	O
in	O
1979	O
,	O
that	O
conducts	O
a	O
state	B-Algorithm
space	I-Algorithm
search	I-Algorithm
traversing	O
a	O
game	O
tree	O
in	O
a	O
best-first	B-Algorithm
fashion	O
similar	O
to	O
that	O
of	O
the	O
A*	B-Protocol
search	I-Protocol
algorithm	I-Protocol
.	O
</s>
<s>
SSS*	B-Algorithm
is	O
based	O
on	O
the	O
notion	O
of	O
solution	O
trees	O
.	O
</s>
<s>
Informally	O
,	O
a	O
solution	O
tree	O
can	O
be	O
formed	O
from	O
any	O
arbitrary	O
game	O
tree	O
by	O
pruning	O
the	O
number	O
of	O
branches	O
at	O
each	O
MAX	B-Algorithm
node	O
to	O
one	O
.	O
</s>
<s>
Such	O
a	O
tree	O
represents	O
a	O
complete	O
strategy	O
for	O
MAX	B-Algorithm
,	O
since	O
it	O
specifies	O
exactly	O
one	O
MAX	B-Algorithm
action	O
for	O
every	O
possible	O
sequence	O
of	O
moves	O
made	O
by	O
the	O
opponent	O
.	O
</s>
<s>
Given	O
a	O
game	O
tree	O
,	O
SSS*	B-Algorithm
searches	O
through	O
the	O
space	O
of	O
partial	O
solution	O
trees	O
,	O
gradually	O
analyzing	O
larger	O
and	O
larger	O
subtrees	O
,	O
eventually	O
producing	O
a	O
single	O
solution	O
tree	O
with	O
the	O
same	O
root	O
and	O
Minimax	B-Algorithm
value	O
as	O
the	O
original	O
game	O
tree	O
.	O
</s>
<s>
SSS*	B-Algorithm
never	O
examines	O
a	O
node	O
that	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
would	O
prune	O
,	O
and	O
may	O
prune	O
some	O
branches	O
that	O
alpha-beta	B-Algorithm
would	O
not	O
.	O
</s>
<s>
Stockman	O
speculated	O
that	O
SSS*	B-Algorithm
may	O
therefore	O
be	O
a	O
better	O
general	O
algorithm	O
than	O
alpha-beta	B-Algorithm
.	O
</s>
<s>
However	O
,	O
Igor	O
Roizen	O
and	O
Judea	O
Pearl	O
have	O
shown	O
that	O
the	O
savings	O
in	O
the	O
number	O
of	O
positions	O
that	O
SSS*	B-Algorithm
evaluates	O
relative	O
to	O
alpha/beta	O
is	O
limited	O
and	O
generally	O
not	O
enough	O
to	O
compensate	O
for	O
the	O
increase	O
in	O
other	O
resources	O
(	O
e.g.	O
,	O
the	O
storing	O
and	O
sorting	O
of	O
a	O
list	O
of	O
nodes	O
made	O
necessary	O
by	O
the	O
best-first	B-Algorithm
nature	O
of	O
the	O
algorithm	O
)	O
.	O
</s>
<s>
However	O
,	O
Aske	O
Plaat	O
,	O
Jonathan	O
Schaeffer	O
,	O
Wim	O
Pijls	O
and	O
Arie	O
de	O
Bruin	O
have	O
shown	O
that	O
a	O
sequence	O
of	O
null-window	O
alpha-beta	B-Algorithm
calls	O
is	O
equivalent	O
to	O
SSS*	B-Algorithm
(	O
i.e.	O
,	O
it	O
expands	O
the	O
same	O
nodes	O
in	O
the	O
same	O
order	O
)	O
when	O
alpha-beta	B-Algorithm
is	O
used	O
with	O
a	O
transposition	B-General_Concept
table	I-General_Concept
,	O
as	O
is	O
the	O
case	O
in	O
all	O
game-playing	O
programs	O
for	O
chess	O
,	O
checkers	O
,	O
etc	O
.	O
</s>
<s>
This	O
allowed	O
the	O
implementation	O
of	O
(	O
an	O
algorithm	O
equivalent	O
to	O
)	O
SSS*	B-Algorithm
in	O
tournament	O
quality	O
game-playing	O
programs	O
.	O
</s>
<s>
Experiments	O
showed	O
that	O
it	O
did	O
indeed	O
perform	O
better	O
than	O
Alpha-Beta	B-Algorithm
in	O
practice	O
,	O
but	O
that	O
it	O
did	O
not	O
beat	O
NegaScout	B-General_Concept
.	O
</s>
<s>
The	O
reformulation	O
of	O
a	O
best-first	B-Algorithm
algorithm	O
as	O
a	O
sequence	O
of	O
depth-first	O
calls	O
prompted	O
the	O
formulation	O
of	O
a	O
class	O
of	O
null-window	O
alpha-beta	B-Algorithm
algorithms	O
,	O
of	O
which	O
MTD(f )	O
is	O
the	O
best	O
known	O
example	O
.	O
</s>
<s>
There	O
is	O
a	O
priority	B-Application
queue	I-Application
OPEN	O
that	O
stores	O
states	O
or	O
the	O
nodes	O
,	O
where	O
-	O
node	O
identificator	O
(	O
Dot-decimal	B-Protocol
notation	I-Protocol
is	O
used	O
to	O
identify	O
nodes	O
,	O
is	O
a	O
root	O
)	O
,	O
-	O
state	O
of	O
the	O
node	O
(	O
L	O
-	O
the	O
node	O
is	O
live	O
,	O
which	O
means	O
it	O
's	O
not	O
solved	O
yet	O
and	O
S	O
-	O
the	O
node	O
is	O
solved	O
)	O
,	O
-	O
value	O
of	O
the	O
solved	O
node	O
.	O
</s>
