<s>
MUMmer	B-Application
is	O
a	O
bioinformatics	O
software	O
system	O
for	O
sequence	B-Algorithm
alignment	I-Algorithm
.	O
</s>
<s>
It	O
is	O
based	O
on	O
the	O
suffix	B-Architecture
tree	I-Architecture
data	O
structure	O
and	O
is	O
one	O
of	O
the	O
fastest	O
and	O
most	O
efficient	O
systems	O
available	O
for	O
this	O
task	O
,	O
enabling	O
it	O
to	O
be	O
applied	O
to	O
very	O
long	O
sequences	O
.	O
</s>
<s>
The	O
acronym	O
"	O
MUMmer	B-Application
"	O
comes	O
from	O
"	O
Maximal	B-Algorithm
Unique	I-Algorithm
Matches	I-Algorithm
"	O
,	O
or	O
MUMs	B-Algorithm
.	O
</s>
<s>
The	O
original	O
algorithms	O
in	O
the	O
MUMMER	B-Application
software	O
package	O
were	O
designed	O
by	O
Art	O
Delcher	O
,	O
Simon	O
Kasif	O
and	O
Steven	O
Salzberg	O
.	O
</s>
<s>
Mummer	B-Application
was	O
the	O
first	O
whole	O
genome	O
comparison	O
system	O
developed	O
in	O
Bioinformatics	O
.	O
</s>
<s>
The	O
MUMmer	B-Application
software	O
is	O
open	O
source	O
and	O
can	O
be	O
found	O
at	O
the	O
MUMmer	B-Application
home	O
page	O
.	O
</s>
<s>
MUMmer	B-Application
is	O
a	O
highly	O
cited	O
bioinformatics	O
system	O
in	O
the	O
scientific	O
literature	O
.	O
</s>
<s>
According	O
to	O
Google	O
Scholar	O
,	O
as	O
of	O
early	O
2013	O
the	O
original	O
MUMmer	B-Application
paper	O
(	O
Delcher	O
et	O
al.	O
,	O
1999	O
)	O
has	O
been	O
cited	O
691	O
times	O
;	O
the	O
MUMmer	B-Application
2	O
paper	O
(	O
Delcher	O
et	O
al.	O
,	O
2002	O
)	O
has	O
been	O
cited	O
455	O
times	O
;	O
and	O
the	O
MUMmer	B-Application
3.0	O
article	O
(	O
Kurtz	O
et	O
al.	O
,	O
2004	O
)	O
has	O
been	O
cited	O
903	O
times	O
.	O
</s>
<s>
Mummer	B-Application
is	O
a	O
fast	O
algorithm	O
mostly	O
used	O
for	O
the	O
rapid	O
alignment	O
of	O
entire	O
genomes	O
.	O
</s>
<s>
MUMmer	B-Application
,	O
as	O
mentioned	O
before	O
,	O
is	O
the	O
system/process	O
for	O
efficient	O
alignment	O
of	O
big-size	O
sequences	O
,	O
this	O
algorithm	O
has	O
been	O
used	O
to	O
make	O
discoveries	O
about	O
genome	O
structure	O
.	O
</s>
<s>
MUMmer1	O
or	O
just	O
MUMmer	B-Application
consists	O
of	O
three	O
parts	O
,	O
the	O
first	O
part	O
consists	O
of	O
the	O
creation	O
of	O
suffix	B-Architecture
trees	I-Architecture
(	O
to	O
get	O
MUMs	B-Algorithm
)	O
,	O
the	O
second	O
part	O
in	O
the	O
longest	O
increasing	O
subsequence	O
or	O
longest	O
common	O
subsequences	O
(	O
to	O
order	O
MUMs	B-Algorithm
)	O
,	O
lastly	O
any	O
alignment	O
to	O
close	O
gaps	O
.	O
</s>
<s>
Once	O
we	O
receive	O
them	O
,	O
we	O
are	O
going	O
to	O
search	O
for	O
the	O
maximal	B-Algorithm
unique	I-Algorithm
matches	I-Algorithm
(	O
MUMs	B-Algorithm
)	O
.	O
</s>
<s>
MUMs’	O
algorithm	O
has	O
its	O
own	O
logic	O
since	O
it	O
can	O
be	O
done	O
in	O
several	O
ways	O
.	O
</s>
<s>
However	O
,	O
since	O
MUMmer	B-Application
has	O
to	O
be	O
fast	O
,	O
it	O
uses	O
the	O
data	O
structure	O
called	O
suffix	B-Architecture
tree	I-Architecture
(	O
Suffix	B-Architecture
tree	I-Architecture
)	O
which	O
takes	O
O( m+m2	O
)	O
.	O
</s>
<s>
From	O
this	O
tree	O
,	O
we	O
extract	O
the	O
MUMs	B-Algorithm
(	O
which	O
are	O
the	O
subsequences	O
that	O
are	O
represented	O
by	O
one	O
internal	O
node	O
by	O
both	O
sequences	O
)	O
.	O
</s>
<s>
Once	O
we	O
identify	O
the	O
MUMs	B-Algorithm
,	O
we	O
need	O
to	O
choose	O
a	O
genome	O
and	O
sort	O
(	O
and	O
possibly	O
remove	O
)	O
the	O
MUMs	B-Algorithm
based	O
on	O
the	O
position	O
of	O
the	O
other	O
genome	O
.	O
</s>
<s>
This	O
step	O
can	O
be	O
done	O
easily	O
by	O
choosing	O
a	O
genome	O
and	O
enumerate	O
the	O
nodes	O
(	O
MUMs	B-Algorithm
)	O
in	O
ascending	O
order	O
,	O
and	O
the	O
other	O
one	O
we	O
enumerate	O
each	O
node	O
according	O
to	O
the	O
node	O
from	O
the	O
first	O
sequence	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
we	O
enumerate	O
a	O
pair	O
of	O
MUMs	B-Algorithm
(	O
with	O
the	O
exact	O
match	O
from	O
both	O
genomes	O
)	O
with	O
the	O
same	O
value	O
regardless	O
of	O
the	O
position	O
.	O
</s>
<s>
At	O
the	O
end	O
of	O
this	O
process	O
,	O
the	O
MUMs	B-Algorithm
on	O
both	O
sequences	O
are	O
aligned/ordered	O
equally	O
(	O
some	O
MUMs	B-Algorithm
are	O
ignored	O
for	O
now	O
,	O
since	O
we	O
cannot	O
have	O
a	O
value	O
enumerated	O
with	O
a	O
big	O
number	O
before	O
one	O
enumerated	O
with	O
a	O
small	O
number	O
)	O
.	O
</s>
<s>
Finally	O
,	O
we	O
have	O
to	O
deal	O
with	O
the	O
interruption	O
between	O
MUMs-alignment	O
,	O
which	O
may	O
be	O
known	O
as	O
gaps	O
.	O
</s>
<s>
Since	O
MUMs	B-Algorithm
can	O
only	O
take	O
unique	O
sequences	O
,	O
that	O
gap	O
can	O
be	O
one	O
repetition	O
of	O
one	O
of	O
the	O
MUMs	B-Algorithm
.	O
</s>
<s>
The	O
improvement	O
was	O
the	O
amount	O
stored	O
in	O
the	O
suffix	B-Architecture
trees	I-Architecture
by	O
employing	O
the	O
one	O
created	O
by	O
Kurtz	O
.	O
</s>
<s>
Finally	O
,	O
the	O
first	O
MUMmer	B-Application
algorithm	O
only	O
aligned	O
the	O
two	O
sequences	O
and	O
jumped	O
to	O
another	O
step	O
.	O
</s>
<s>
However	O
,	O
to	O
achieve	O
better	O
coverage	O
,	O
the	O
MUMs	B-Algorithm
sequences	O
are	O
becoming	O
clusters	O
(	O
meaning	O
that	O
is	O
a	O
group	O
of	O
MUMs	B-Algorithm
that	O
are	O
separated	O
with	O
a	O
smaller	O
number	O
of	O
gaps	O
)	O
.	O
</s>
<s>
the	O
tree	O
described	O
in	O
the	O
article	O
“	O
Reducing	O
the	O
space	O
requirement	O
of	O
suffix	B-Architecture
trees	I-Architecture
”	O
.	O
</s>
<s>
Another	O
improvement	O
was	O
the	O
relaxation	O
of	O
the	O
MUMs	B-Algorithm
.	O
</s>
<s>
This	O
means	O
that	O
now	O
the	O
user	O
has	O
the	O
option	O
of	O
finding	O
all	O
non-unique	O
maximal	O
matches	O
,	O
all	O
the	O
matches	O
that	O
are	O
unique	O
only	O
in	O
a	O
chosen	O
sequence	O
,	O
or	O
original	O
MUMs	B-Algorithm
(	O
which	O
are	O
unique	O
for	O
both	O
sequences	O
)	O
.	O
</s>
<s>
This	O
was	O
added	O
to	O
avoid	O
some	O
kind	O
of	O
missing	O
subsequences	O
that	O
were	O
copies	O
of	O
MUMs	B-Algorithm
.	O
</s>
<s>
Thanks	O
to	O
this	O
,	O
the	O
suffix	B-Architecture
tree	I-Architecture
can	O
be	O
built	O
once	O
and	O
constructed	O
again	O
after	O
running	O
it	O
from	O
the	O
saved	O
suffix	B-Architecture
tree	I-Architecture
.	O
</s>
<s>
MUMmer	B-Application
has	O
open-source	O
software	O
.	O
</s>
<s>
There	O
are	O
other	O
types	O
of	O
sequence	B-Algorithm
alignments	I-Algorithm
,	O
some	O
of	O
the	O
related	O
topics	O
are	O
shown	O
below	O
:	O
</s>
