<s>
A	O
search	B-Algorithm
game	I-Algorithm
is	O
a	O
two-person	O
zero-sum	O
game	O
which	O
takes	O
place	O
in	O
a	O
set	O
called	O
the	O
search	O
space	O
.	O
</s>
<s>
As	O
mathematical	O
models	O
,	O
search	B-Algorithm
games	I-Algorithm
can	O
be	O
applied	O
to	O
areas	O
such	O
as	O
hide-and-seek	O
games	O
that	O
children	O
play	O
or	O
representations	O
of	O
some	O
tactical	O
military	O
situations	O
.	O
</s>
<s>
The	O
area	O
of	O
search	B-Algorithm
games	I-Algorithm
was	O
introduced	O
in	O
the	O
last	O
chapter	O
of	O
Rufus	O
Isaacs	O
 '	O
classic	O
book	O
"	O
Differential	O
Games	O
"	O
and	O
has	O
been	O
developed	O
further	O
by	O
Shmuel	O
Gal	O
and	O
Steve	O
Alpern	O
.	O
</s>
<s>
In	O
general	O
,	O
the	O
reasonable	O
framework	O
for	O
searching	O
an	O
unbounded	O
domain	O
,	O
as	O
in	O
the	O
case	O
of	O
an	O
online	B-Algorithm
algorithm	I-Algorithm
,	O
is	O
to	O
use	O
a	O
normalized	O
cost	O
function	O
(	O
called	O
the	O
competitive	B-Algorithm
ratio	I-Algorithm
in	O
Computer	O
Science	O
literature	O
)	O
.	O
</s>
<s>
The	O
minimax	B-Algorithm
trajectory	O
for	O
problems	O
of	O
these	O
types	O
is	O
always	O
a	O
geometric	O
sequence	O
(	O
or	O
exponential	O
function	O
for	O
continuous	O
problems	O
)	O
.	O
</s>
<s>
This	O
result	O
yields	O
an	O
easy	O
method	O
to	O
find	O
the	O
minimax	B-Algorithm
trajectory	O
by	O
minimizing	O
over	O
a	O
single	O
parameter	O
(	O
the	O
generator	O
of	O
this	O
sequence	O
)	O
instead	O
of	O
searching	O
over	O
the	O
whole	O
trajectory	O
space	O
.	O
</s>
<s>
This	O
tool	O
has	O
been	O
used	O
for	O
the	O
linear	O
search	O
problem	O
,	O
i.e.	O
,	O
finding	O
a	O
target	O
on	O
the	O
infinite	O
line	O
,	O
which	O
has	O
attracted	O
much	O
attention	O
over	O
several	O
decades	O
and	O
has	O
been	O
analyzed	O
as	O
a	O
search	B-Algorithm
game	I-Algorithm
.	O
</s>
<s>
It	O
has	O
also	O
been	O
used	O
to	O
find	O
a	O
minimax	B-Algorithm
trajectory	O
for	O
searching	O
a	O
set	O
of	O
concurrent	O
rays	O
.	O
</s>
