<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
search	B-Application
algorithm	I-Application
is	O
an	O
algorithm	O
designed	O
to	O
solve	O
a	O
search	O
problem	O
.	O
</s>
<s>
Search	B-Application
algorithms	I-Application
work	O
to	O
retrieve	O
information	O
stored	O
within	O
particular	O
data	B-General_Concept
structure	I-General_Concept
,	O
or	O
calculated	O
in	O
the	O
search	O
space	O
of	O
a	O
problem	O
domain	O
,	O
with	O
either	O
discrete	O
or	O
continuous	O
values	O
.	O
</s>
<s>
Although	O
search	O
engines	O
use	O
search	B-Application
algorithms	I-Application
,	O
they	O
belong	O
to	O
the	O
study	O
of	O
information	B-Library
retrieval	I-Library
,	O
not	O
algorithmics	O
.	O
</s>
<s>
The	O
appropriate	O
search	B-Application
algorithm	I-Application
often	O
depends	O
on	O
the	O
data	B-General_Concept
structure	I-General_Concept
being	O
searched	O
,	O
and	O
may	O
also	O
include	O
prior	O
knowledge	O
about	O
the	O
data	O
.	O
</s>
<s>
Search	B-Application
algorithms	I-Application
can	O
be	O
made	O
faster	O
or	O
more	O
efficient	O
by	O
specially	O
constructed	O
database	O
structures	O
,	O
such	O
as	O
search	B-Data_Structure
trees	I-Data_Structure
,	O
hash	B-Algorithm
maps	I-Algorithm
,	O
and	O
database	B-Data_Structure
indexes	I-Data_Structure
.	O
</s>
<s>
Search	B-Application
algorithms	I-Application
can	O
be	O
classified	O
based	O
on	O
their	O
mechanism	O
of	O
searching	O
into	O
three	O
types	O
of	O
algorithms	O
:	O
linear	O
,	O
binary	O
,	O
and	O
hashing	B-Algorithm
.	O
</s>
<s>
Linear	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
check	O
every	O
record	O
for	O
the	O
one	O
associated	O
with	O
a	O
target	O
key	O
in	O
a	O
linear	O
fashion	O
.	O
</s>
<s>
Comparison	O
search	B-Application
algorithms	I-Application
improve	O
on	O
linear	O
searching	O
by	O
successively	O
eliminating	O
records	O
based	O
on	O
comparisons	O
of	O
the	O
keys	O
until	O
the	O
target	O
record	O
is	O
found	O
,	O
and	O
can	O
be	O
applied	O
on	O
data	B-General_Concept
structures	I-General_Concept
with	O
a	O
defined	O
order	O
.	O
</s>
<s>
Digital	O
search	B-Application
algorithms	I-Application
work	O
based	O
on	O
the	O
properties	O
of	O
digits	O
in	O
data	B-General_Concept
structures	I-General_Concept
by	O
using	O
numerical	O
keys	O
.	O
</s>
<s>
Finally	O
,	O
hashing	B-Algorithm
directly	O
maps	O
keys	O
to	O
records	O
based	O
on	O
a	O
hash	B-Error_Name
function	I-Error_Name
.	O
</s>
<s>
Specific	O
applications	O
of	O
search	B-Application
algorithms	I-Application
include	O
:	O
</s>
<s>
The	O
knapsack	B-Algorithm
problem	I-Algorithm
:	O
Given	O
a	O
set	O
of	O
items	O
,	O
each	O
with	O
a	O
weight	O
and	O
a	O
value	O
,	O
determine	O
the	O
number	O
of	O
each	O
item	O
to	O
include	O
in	O
a	O
collection	O
so	O
that	O
the	O
total	O
weight	O
is	O
less	O
than	O
or	O
equal	O
to	O
a	O
given	O
limit	O
and	O
the	O
total	O
value	O
is	O
as	O
large	O
as	O
possible	O
.	O
</s>
<s>
Problems	O
in	O
constraint	B-Application
satisfaction	I-Application
,	O
such	O
as	O
:	O
</s>
<s>
Algorithms	O
for	O
searching	O
virtual	O
spaces	O
are	O
used	O
in	O
the	O
constraint	B-Application
satisfaction	I-Application
problem	I-Application
,	O
where	O
the	O
goal	O
is	O
to	O
find	O
a	O
set	O
of	O
value	O
assignments	O
to	O
certain	O
variables	O
that	O
will	O
satisfy	O
specific	O
mathematical	O
equations	O
and	O
inequations	O
/	O
equalities	O
.	O
</s>
<s>
Algorithms	O
for	O
these	O
problems	O
include	O
the	O
basic	O
brute-force	B-Algorithm
search	I-Algorithm
(	O
also	O
called	O
"	O
naïve	O
"	O
or	O
"	O
uninformed	O
"	O
search	O
)	O
,	O
and	O
a	O
variety	O
of	O
heuristics	B-Algorithm
that	O
try	O
to	O
exploit	O
partial	O
knowledge	O
about	O
the	O
structure	O
of	O
this	O
space	O
,	O
such	O
as	O
linear	O
relaxation	O
,	O
constraint	O
generation	O
,	O
and	O
constraint	B-Application
propagation	I-Application
.	O
</s>
<s>
An	O
important	O
subclass	O
are	O
the	O
local	B-Algorithm
search	I-Algorithm
methods	O
,	O
that	O
view	O
the	O
elements	O
of	O
the	O
search	O
space	O
as	O
the	O
vertices	O
of	O
a	O
graph	O
,	O
with	O
edges	O
defined	O
by	O
a	O
set	O
of	O
heuristics	B-Algorithm
applicable	O
to	O
the	O
case	O
;	O
and	O
scan	O
the	O
space	O
by	O
moving	O
from	O
item	O
to	O
item	O
along	O
the	O
edges	O
,	O
for	O
example	O
according	O
to	O
the	O
steepest	B-Algorithm
descent	I-Algorithm
or	O
best-first	B-Algorithm
criterion	O
,	O
or	O
in	O
a	O
stochastic	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
This	O
category	O
includes	O
a	O
great	O
variety	O
of	O
general	O
metaheuristic	B-Algorithm
methods	O
,	O
such	O
as	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
tabu	B-Algorithm
search	I-Algorithm
,	O
A-teams	O
,	O
and	O
genetic	B-Algorithm
programming	I-Algorithm
,	O
that	O
combine	O
arbitrary	O
heuristics	B-Algorithm
in	O
specific	O
ways	O
.	O
</s>
<s>
The	O
opposite	O
of	O
local	B-Algorithm
search	I-Algorithm
would	O
be	O
global	O
search	O
methods	O
.	O
</s>
<s>
This	O
method	O
is	O
applicable	O
when	O
the	O
search	O
space	O
is	O
not	O
limited	O
and	O
all	O
aspects	O
of	O
the	O
given	O
network	O
are	O
available	O
to	O
the	O
entity	O
running	O
the	O
search	B-Application
algorithm	I-Application
.	O
</s>
<s>
This	O
class	O
also	O
includes	O
various	O
tree	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
,	O
that	O
view	O
the	O
elements	O
as	O
vertices	O
of	O
a	O
tree	O
,	O
and	O
traverse	O
that	O
tree	O
in	O
some	O
special	O
order	O
.	O
</s>
<s>
Examples	O
of	O
the	O
latter	O
include	O
the	O
exhaustive	O
methods	O
such	O
as	O
depth-first	B-Algorithm
search	I-Algorithm
and	O
breadth-first	B-Algorithm
search	I-Algorithm
,	O
as	O
well	O
as	O
various	O
heuristic-based	O
search	B-Algorithm
tree	I-Algorithm
pruning	I-Algorithm
methods	O
such	O
as	O
backtracking	B-Algorithm
and	O
branch	B-Algorithm
and	I-Algorithm
bound	I-Algorithm
.	O
</s>
<s>
Unlike	O
general	O
metaheuristics	B-Algorithm
,	O
which	O
at	O
best	O
work	O
only	O
in	O
a	O
probabilistic	O
sense	O
,	O
many	O
of	O
these	O
tree-search	O
methods	O
are	O
guaranteed	O
to	O
find	O
the	O
exact	O
or	O
optimal	O
solution	O
,	O
if	O
given	O
enough	O
time	O
.	O
</s>
<s>
Another	O
important	O
sub-class	O
consists	O
of	O
algorithms	O
for	O
exploring	O
the	O
game	O
tree	O
of	O
multiple-player	O
games	O
,	O
such	O
as	O
chess	B-Application
or	O
backgammon	B-Application
,	O
whose	O
nodes	O
consist	O
of	O
all	O
possible	O
game	O
situations	O
that	O
could	O
result	O
from	O
the	O
current	O
situation	O
.	O
</s>
<s>
Similar	O
problems	O
occur	O
when	O
humans	O
or	O
machines	O
have	O
to	O
make	O
successive	O
decisions	O
whose	O
outcomes	O
are	O
not	O
entirely	O
under	O
one	O
's	O
control	O
,	O
such	O
as	O
in	O
robot	B-Algorithm
guidance	O
or	O
in	O
marketing	O
,	O
financial	O
,	O
or	O
military	O
strategy	O
planning	O
.	O
</s>
<s>
This	O
kind	O
of	O
problem	O
—	O
combinatorial	B-Algorithm
search	I-Algorithm
—	O
has	O
been	O
extensively	O
studied	O
in	O
the	O
context	O
of	O
artificial	B-Application
intelligence	I-Application
.	I-Application
</s>
<s>
Examples	O
of	O
algorithms	O
for	O
this	O
class	O
are	O
the	O
minimax	B-Algorithm
algorithm	I-Algorithm
,	O
alpha	B-Algorithm
–	I-Algorithm
beta	I-Algorithm
pruning	I-Algorithm
,	O
and	O
the	O
A*	B-Protocol
algorithm	I-Protocol
and	O
its	O
variants	O
.	O
</s>
<s>
The	O
name	O
"	O
combinatorial	B-Algorithm
search	I-Algorithm
"	O
is	O
generally	O
used	O
for	O
algorithms	O
that	O
look	O
for	O
a	O
specific	O
sub-structure	O
of	O
a	O
given	O
discrete	O
structure	O
,	O
such	O
as	O
a	O
graph	O
,	O
a	O
string	O
,	O
a	O
finite	O
group	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
(	O
Since	O
the	O
sub-structure	O
is	O
usually	O
represented	O
in	O
the	O
computer	O
by	O
a	O
set	O
of	O
integer	O
variables	O
with	O
constraints	O
,	O
these	O
problems	O
can	O
be	O
viewed	O
as	O
special	O
cases	O
of	O
constraint	B-Application
satisfaction	I-Application
or	O
discrete	O
optimization	O
;	O
but	O
they	O
are	O
usually	O
formulated	O
and	O
solved	O
in	O
a	O
more	O
abstract	O
setting	O
where	O
the	O
internal	O
representation	O
is	O
not	O
explicitly	O
mentioned	O
.	O
)	O
</s>
<s>
An	O
important	O
and	O
extensively	O
studied	O
subclass	O
are	O
the	O
graph	O
algorithms	O
,	O
in	O
particular	O
graph	B-Algorithm
traversal	I-Algorithm
algorithms	O
,	O
for	O
finding	O
specific	O
sub-structures	O
in	O
a	O
given	O
graph	O
—	O
such	O
as	O
subgraphs	O
,	O
paths	O
,	O
circuits	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
Examples	O
include	O
Dijkstra	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
Kruskal	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
the	O
nearest	B-Algorithm
neighbour	I-Algorithm
algorithm	I-Algorithm
,	O
and	O
Prim	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Another	O
important	O
subclass	O
of	O
this	O
category	O
are	O
the	O
string	B-Algorithm
searching	I-Algorithm
algorithms	I-Algorithm
,	O
that	O
search	O
for	O
patterns	O
within	O
strings	O
.	O
</s>
<s>
Two	O
famous	O
examples	O
are	O
the	O
Boyer	B-Algorithm
–	I-Algorithm
Moore	I-Algorithm
and	O
Knuth	O
–	O
Morris	O
–	O
Pratt	O
algorithms	O
,	O
and	O
several	O
algorithms	O
based	O
on	O
the	O
suffix	B-Architecture
tree	I-Architecture
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
In	O
1953	O
,	O
American	O
statistician	O
Jack	O
Kiefer	O
devised	O
Fibonacci	B-Algorithm
search	I-Algorithm
which	O
can	O
be	O
used	O
to	O
find	O
the	O
maximum	O
of	O
a	O
unimodal	O
function	O
and	O
has	O
many	O
other	O
applications	O
in	O
computer	B-General_Concept
science	I-General_Concept
.	O
</s>
<s>
There	O
are	O
also	O
search	O
methods	O
designed	O
for	O
quantum	B-Architecture
computers	I-Architecture
,	O
like	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
that	O
are	O
theoretically	O
faster	O
than	O
linear	O
or	O
brute-force	B-Algorithm
search	I-Algorithm
even	O
without	O
the	O
help	O
of	O
data	B-General_Concept
structures	I-General_Concept
or	O
heuristics	B-Algorithm
.	O
</s>
<s>
While	O
the	O
ideas	O
and	O
applications	O
behind	O
quantum	B-Architecture
computers	I-Architecture
are	O
still	O
entirely	O
theoretical	O
,	O
studies	O
have	O
been	O
conducted	O
with	O
algorithms	O
like	O
Grover	O
's	O
that	O
accurately	O
replicate	O
the	O
hypothetical	O
physical	O
versions	O
of	O
quantum	B-Architecture
computing	I-Architecture
systems	O
.	O
</s>
