<s>
A	O
Supnick	B-Algorithm
matrix	I-Algorithm
or	O
Supnick	B-Algorithm
array	I-Algorithm
named	O
after	O
Fred	O
Supnick	O
of	O
the	O
City	O
College	O
of	O
New	O
York	O
,	O
who	O
introduced	O
the	O
notion	O
in	O
1957	O
is	O
a	O
Monge	O
array	O
which	O
is	O
also	O
a	O
symmetric	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
A	O
Supnick	B-Algorithm
matrix	I-Algorithm
is	O
a	O
square	O
Monge	O
array	O
that	O
is	O
symmetric	B-Algorithm
around	O
the	O
main	B-Algorithm
diagonal	I-Algorithm
.	O
</s>
<s>
A	O
matrix	B-Architecture
is	O
a	O
Supnick	B-Algorithm
matrix	I-Algorithm
iff	O
it	O
can	O
be	O
written	O
as	O
the	O
sum	O
of	O
a	O
sum	O
matrix	B-Architecture
S	O
and	O
a	O
non-negative	O
linear	O
combination	O
of	O
LL-UR	O
block	O
matrices	O
.	O
</s>
<s>
The	O
sum	O
matrix	B-Architecture
is	O
defined	O
in	O
terms	O
of	O
a	O
sequence	O
of	O
n	O
real	O
numbers	O
 { αi } 	O
:	O
</s>
<s>
and	O
an	O
LL-UR	O
block	O
matrix	B-Architecture
consists	O
of	O
two	O
symmetrically	O
placed	O
rectangles	O
in	O
the	O
lower-left	O
and	O
upper	O
right	O
corners	O
for	O
which	O
aij	O
=	O
1	O
,	O
with	O
all	O
the	O
rest	O
of	O
the	O
matrix	B-Architecture
elements	O
equal	O
to	O
zero	O
.	O
</s>
<s>
Adding	O
two	O
Supnick	O
matrices	O
together	O
will	O
result	O
in	O
a	O
new	O
Supnick	B-Algorithm
matrix	I-Algorithm
(	O
Deineko	O
and	O
Woeginger	O
2006	O
)	O
.	O
</s>
<s>
Multiplying	O
a	O
Supnick	B-Algorithm
matrix	I-Algorithm
by	O
a	O
non-negative	O
real	O
number	O
produces	O
a	O
new	O
Supnick	B-Algorithm
matrix	I-Algorithm
(	O
Deineko	O
and	O
Woeginger	O
2006	O
)	O
.	O
</s>
<s>
If	O
the	O
distance	O
matrix	B-Architecture
in	O
a	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
can	O
be	O
written	O
as	O
a	O
Supnick	B-Algorithm
matrix	I-Algorithm
,	O
that	O
particular	O
instance	O
of	O
the	O
problem	O
admits	O
an	O
easy	O
solution	O
(	O
even	O
though	O
the	O
problem	O
is	O
,	O
in	O
general	O
,	O
NP	O
hard	O
)	O
.	O
</s>
