<s>
MINimum	B-Algorithm
Relevant	I-Algorithm
Variables	I-Algorithm
in	I-Algorithm
Linear	I-Algorithm
System	I-Algorithm
(	O
Min-RVLS	O
)	O
is	O
a	O
problem	O
in	O
mathematical	O
optimization	O
.	O
</s>
<s>
Given	O
a	O
linear	B-Algorithm
program	I-Algorithm
,	O
it	O
is	O
required	O
to	O
find	O
a	O
feasible	O
solution	O
in	O
which	O
the	O
number	O
of	O
non-zero	O
variables	O
is	O
as	O
small	O
as	O
possible	O
.	O
</s>
<s>
The	O
problem	O
Min-RVLS[=]	O
was	O
presented	O
by	O
Garey	O
and	O
Johnson	O
,	O
who	O
called	O
it	O
"	O
minimum	B-Algorithm
weight	I-Algorithm
solution	I-Algorithm
to	I-Algorithm
linear	I-Algorithm
equations	I-Algorithm
"	O
.	O
</s>
<s>
The	O
Min-RVLS	O
problem	O
is	O
important	O
in	O
machine	O
learning	O
and	O
linear	B-General_Concept
discriminant	I-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
The	O
shortest	O
codeword	O
problem	O
in	O
coding	B-Error_Name
theory	I-Error_Name
is	O
the	O
same	O
problem	O
as	O
Min-RVLS[=]	O
when	O
the	O
coefficients	O
are	O
in	O
GF(2 )	O
.	O
</s>
<s>
In	O
MINimum	B-Algorithm
Unsatisfied	I-Algorithm
Linear	I-Algorithm
Relations	I-Algorithm
(	O
Min-ULR	O
)	O
,	O
we	O
are	O
given	O
a	O
binary	O
relation	O
R	O
and	O
a	O
linear	O
system	O
A	O
x	O
R	O
b	O
,	O
which	O
is	O
now	O
assumed	O
to	O
be	O
infeasible	O
.	O
</s>
<s>
In	O
the	O
complementary	O
problem	O
MAXimum	B-Algorithm
Feasible	I-Algorithm
Linear	I-Algorithm
Subsystem	I-Algorithm
(	O
Max-FLS	O
)	O
,	O
the	O
goal	O
is	O
to	O
find	O
a	O
maximum	O
subset	O
of	O
the	O
constraints	O
that	O
can	O
be	O
satisfied	O
simultaneously	O
.	O
</s>
