I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
202
1
, pp.
207
~
214
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
10
.i
1
.pp
207
-
214
207
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
M
ass
i
ve
l
y sc
al
ab
l
e
d
e
n
si
t
y b
ase
d
c
l
u
s
t
e
r
i
n
g (
D
B
S
C
A
N
)
on
t
h
e
H
PC
C
sys
t
e
m
s b
i
g d
at
a p
l
at
f
or
m
Y
at
is
h
H
R
1
, S
h
u
b
h
am
M
il
in
d
P
h
al
2
, T
an
m
ay S
an
j
ay Hu
k
k
e
r
i
3
, L
il
i
X
u
4
, S
h
ob
h
a G
5
,
Jyot
i
S
h
e
t
t
y
6
,
A
r
j
u
n
a C
h
al
a
7
1
,2,3,5,6
RV College
of Engin
eering,
Bangalor
e, Kar
nataka
, India
4,7
HPCC Sys
tems LexisNexis
Risk Sol
utions
, USA
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
A
ug
1, 20
20
R
e
vi
s
e
d
J
a
n
9
, 20
21
A
c
c
e
pt
e
d
F
e
b
7
, 20
21
Dealing
with
large
samples
of
unlabeled
data
is
a
key
challenge
in
t
oday’s
world,
especially
in
applications
such
as
traffic
pattern
analysis
and
disaster
manageme
nt.
DBSCAN,
or
density
based
spatial
clustering
of
appli
cations
with
noise,
is
a
well
-
known
density
-
based
clustering
algori
thm.
I
ts
key
strengths
lie
in
its
capability
to
detect
outliers
and
handle
arbitrarily
shaped
clusters.
However,
the
algorit
hm,
being
fundament
ally
sequenti
al
in
nature,
proves
expensive
and
time
consuming
when
oper
ated
on
extensivel
y
large
data
chunks.
Th
is
paper
thus
presents
a
novel
implementation
of
a
parallel
and
distributed
DBSCAN
algorithm
on
the
HPCC
systems
platfor
m.
The
algorit
hm
seeks
to
fully
paralleli
ze
the
algorit
hm
implem
entation
by
making
use
of
HPCC
systems
optimal
distributed
architecture
and
performing
a
tree
-
based
union
to
merge
local
clusters.
The
proposed
approach*
was
test
ed
both
on
synthetic
as
well
as
standard
datasets
(MFCCs
Data
Set)
and
foun
d
to
be
completel
y
accurate.
Additi
onally,
when
compared
against
a
singl
e
node
setup,
a
sig
nificant
decrease
in
computation
time
was
observed
with
no
impact
to
accuracy.
The
parallelized
algorithm
performed
eight
time
s
better
for
higher
number
of
data
points
and
takes
exponentially
lesser
time
as
the
number of data points increases.
K
e
y
w
o
r
d
s
:
B
ig
da
ta
D
a
ta
m
in
in
g
D
e
ns
it
y ba
s
e
d
c
lu
s
te
r
in
g
D
is
tr
ib
ut
e
d c
om
put
in
g
H
P
C
C
s
ys
t
e
m
s
M
a
c
hi
ne
l
e
a
r
ni
ng
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
Y
a
ti
s
h H
R
D
e
pa
r
tm
e
nt
of
C
om
put
e
r
S
c
ie
nc
e
a
nd E
ngi
ne
e
r
in
g
R
.V
C
ol
le
ge
of
E
ngi
ne
e
r
in
g
M
ys
or
e
R
d, R
V
V
id
ya
ni
ke
ta
n, P
os
t,
B
e
nga
lu
r
u, K
a
r
na
ta
ka
560
059
, I
ndi
a
E
m
a
il
:
ya
ti
s
hhr
.c
s
16@
r
vc
e
.e
du.i
n
1.
I
N
T
R
O
D
U
C
T
I
O
N
C
l
us
te
r
i
n
g,
o
r
t
h
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g
r
o
u
p
i
n
g
o
f
da
t
a
i
n
t
o
c
l
u
s
t
e
r
s
,
is
o
n
e
o
f
t
h
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m
o
s
t
f
u
n
d
a
m
e
n
t
a
l
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c
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ni
q
u
e
s
i
n
d
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a
l
i
n
g
w
it
h
la
r
g
e
c
h
u
n
ks
o
f
u
nl
a
b
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d
d
a
t
a
.
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t
i
n
v
ol
v
e
s
g
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o
u
p
i
n
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t
h
e
da
t
a
i
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t
o
m
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a
n
i
n
gf
u
l
s
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b
c
la
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s
,
s
u
c
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t
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-
c
l
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s
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d
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t
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s
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m
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,
a
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s
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a
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g
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l
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o
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i
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h
m
s
,
na
m
e
l
y
:
hi
e
r
a
r
c
h
y
-
ba
s
e
d
,
p
a
r
ti
t
i
o
ni
n
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-
b
a
s
e
d,
d
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ns
it
y
-
b
a
s
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d
a
n
d
g
r
i
d
-
b
a
s
e
d
[
1
]
D
B
S
C
A
N
,
o
r
d
e
ns
it
y
ba
s
e
d
s
pa
t
ia
l
c
l
u
s
t
e
r
i
n
g
o
f
a
p
p
li
c
a
t
i
o
ns
w
i
t
h
n
o
is
e
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f
a
ll
s
u
n
de
r
t
he
c
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o
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b
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l
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l
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it
h
m
.
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s
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lg
or
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hm
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ba
s
e
d
on
th
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pr
e
m
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a
t
f
or
e
ve
r
y
da
ta
poi
nt
in
th
e
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lu
s
te
r
,
it
s
ne
ig
hbor
hood
w
it
hi
n
a
gi
v
e
n
r
a
di
us
(
e
ps
)
ha
s
to
c
ont
a
in
a
m
in
im
um
num
be
r
of
poi
nt
s
(
m
in
pt
s
)
.
T
hus
,
f
or
a
gi
ve
n
th
r
e
s
hol
d,
th
e
de
ns
it
y
of
th
e
ne
ig
hbor
hood
f
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ve
r
y
poi
nt
s
houl
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e
xc
e
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d
th
is
th
r
e
s
hol
d.
W
h
e
n
de
a
li
ng
w
it
h
la
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s
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m
pl
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s
of
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D
B
S
C
A
N
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
207
–
214
208
a
lg
or
it
hm
, i
n or
de
r
t
o ove
r
c
om
e
t
he
s
e
pe
r
f
or
m
a
nc
e
bot
tl
e
ne
c
ks
w
it
hout
a
ny i
m
pa
c
t
to
a
c
c
ur
a
c
y. T
h
e
pr
opos
e
d
a
lg
or
it
hm
i
s
i
m
pl
e
m
e
nt
e
d on the
H
P
C
C
s
ys
t
e
m
s
[
2]
.
H
P
C
C
s
ys
te
m
s
is
a
n
ope
n
-
s
our
c
e
,
li
ght
w
e
ig
ht
a
nd
pow
e
r
f
ul
bi
g
da
ta
m
a
na
ge
m
e
nt
pl
a
t
-
f
or
m
,
w
hi
c
h
s
e
r
ve
s
a
s
a
n
e
nd
-
to
-
e
nd
D
a
ta
L
a
k
e
m
a
na
g
e
m
e
nt
s
ol
ut
io
n.
I
ts
ke
y
a
dva
nt
a
ge
s
a
r
is
e
f
r
om
it
s
s
c
a
l
a
bi
li
ty
,
pe
r
f
or
m
a
nc
e
a
nd us
a
bi
li
ty
. T
he
pl
a
tf
or
m
s
e
r
ve
s
a
s
a
n a
lt
e
r
na
ti
v
e
t
o e
xi
s
ti
ng big
-
da
ta
pl
a
tf
or
m
s
s
uc
h a
s
a
pa
c
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ha
doop,
a
pa
c
h
e
s
pa
r
k
a
nd
da
ta
to
r
r
e
nt
R
T
S
[
3]
.
T
he
pl
a
tf
or
m
is
s
uppor
te
d
by
it
s
unde
r
ly
in
g
pr
ogr
a
m
m
in
g
la
ngua
ge
E
C
L
,
w
hi
c
h
is
im
pl
ic
it
ly
pa
r
a
ll
e
l
a
nd
de
c
la
r
a
ti
ve
i
n
na
tu
r
e
,
a
nd
pr
ovi
de
s
s
e
v
e
r
a
l
c
ons
tr
uc
ts
to
s
im
pl
if
y pa
r
a
ll
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l
c
om
put
e
ope
r
a
ti
ons
. T
he
ge
n
e
r
a
l
H
P
C
C
s
y
s
te
m
s
a
r
c
hi
te
c
tu
r
e
i
s
s
how
n i
n F
ig
ur
e
1.
F
ig
ur
e
1. H
P
C
C
s
ys
te
m
s
a
r
c
hi
te
c
tu
r
e
H
P
C
C
s
ys
te
m
s
is
f
ur
th
e
r
s
uppor
te
d
by
a
pa
ir
o
f
pow
e
r
f
ul
da
ta
e
ngi
ne
s
:
T
H
O
R
a
nd
R
O
X
I
E
.
T
H
O
R
s
e
r
ve
s
a
s
th
e
da
ta
r
e
f
in
e
r
y
e
ngi
ne
,
a
nd
gi
ve
s
th
e
u
s
e
r
c
ont
r
ol
ove
r
da
ta
tr
a
ns
f
or
m
a
ti
ons
.
I
t
a
l
s
o
f
a
c
il
it
a
te
s
opt
im
a
l
ope
r
a
ti
ona
l
c
a
p
a
c
it
y
on
m
ix
e
d
s
c
he
m
a
da
ta
.
R
O
X
I
E
s
e
r
ve
s
a
s
th
e
s
e
a
r
c
h
e
ngi
ne
th
a
t
f
a
c
il
it
a
te
s
hi
gh
-
s
pe
e
d
r
e
a
l
-
ti
m
e
que
r
ie
s
th
r
ough
in
te
r
f
a
c
e
s
s
uc
h
a
s
R
E
S
T
,
S
O
A
P
a
nd
X
M
L
.
I
t
is
r
e
s
pons
ib
le
in
gr
e
a
tl
y
r
e
duc
in
g
th
e
la
te
nc
y
a
s
s
oc
ia
te
d
w
it
h
que
r
yi
ng.
T
he
r
e
m
a
in
de
r
of
th
e
pa
pe
r
is
o
r
ga
ni
z
e
d
a
s
f
ol
lo
w
s
.
S
e
c
ti
on
2
a
na
ly
s
e
s
th
e
e
xi
s
ti
ng
s
t
a
te
of
th
e
a
r
t
f
or
di
s
tr
ib
ut
e
d
pa
r
a
ll
e
l
c
lu
s
te
r
in
g
a
lg
or
it
hm
s
.
S
e
c
ti
on
3
de
ta
il
s
bot
h
th
e
tr
a
di
ti
ona
l
D
B
S
C
A
N
a
lg
or
it
hm
a
s
w
e
ll
a
s
th
e
nove
l
pa
r
a
ll
e
l
D
B
S
C
A
N
a
lg
or
it
hm
.
S
e
c
ti
on
4
di
s
c
us
s
e
s
th
e
e
xpe
r
im
e
nt
s
c
a
r
r
ie
d
out
a
nd
th
e
r
e
s
ul
ts
obt
a
in
e
d.
F
in
a
ll
y,
s
e
c
ti
on
5
pr
ovi
de
s
a
c
onc
lu
s
io
n
to
th
e
w
or
k
a
s
w
e
ll
a
s
pr
opos
it
io
ns
f
or
f
ut
ur
e
w
or
k.
2.
L
I
T
E
R
A
T
U
R
E
R
E
V
I
E
W
A
s
tu
dy
of
th
e
s
ta
te
-
of
-
th
e
-
a
r
t
te
c
hni
que
s
r
e
ve
a
ls
c
e
r
ta
in
pr
e
-
e
xi
s
ti
ng
m
e
th
ods
th
a
t
s
e
e
k
to
im
pr
ove
th
e
pe
r
f
or
m
a
nc
e
of
t
he
D
B
S
C
A
N
a
lg
or
it
hm
. T
he
a
ut
hor
s
i
n [
4
-
5]
s
how
e
d t
ha
t
th
e
D
B
S
C
A
N
a
lg
or
it
hm
c
a
n be
s
ol
ve
d
in
O
(
nl
ogn)
f
or
E
uc
li
de
a
n
2D
s
pa
c
e
s
.
H
ow
e
ve
r
,
th
is
m
e
th
od
c
a
n
not
b
e
di
r
e
c
tl
y
a
ppl
ie
d
on
m
a
s
s
iv
e
da
ta
s
e
ts
di
s
tr
ib
ut
e
d
a
c
r
os
s
m
ul
ti
pl
e
node
s
f
or
hi
ghe
r
di
m
e
ns
io
ns
.
T
he
r
e
w
e
r
e
e
f
f
or
ts
pr
e
s
e
nt
e
d
by
a
ut
hor
s
i
n
[
6]
w
hi
c
h
pr
e
s
e
nt
e
d
a
n
a
ppr
oxi
m
a
te
D
B
S
C
A
N
in
O
(
nl
og(
n)
)
ti
m
e
.
T
he
a
ut
hor
s
[
7]
a
ls
o
a
c
hi
e
v
e
d
th
e
s
a
m
e
but
in
O
(
n)
ti
m
e
.
H
ow
e
ve
r
,
none
of
th
e
a
ppr
oa
c
he
s
ta
lk
a
bout
pa
r
a
le
ll
iz
a
ti
on
r
e
qui
r
e
d
in
bi
g
da
ta
a
ppl
ic
a
ti
ons
.
S
om
e
of
t
he
o
th
e
r
t
e
c
hni
que
s
m
a
ke
us
e
of
G
P
U
’
s
a
nd
va
r
io
us
c
onc
e
pt
s
of
pa
r
a
ll
e
li
s
m
t
o a
c
hi
e
ve
t
he
r
e
qui
s
it
e
le
ve
l
of
pe
r
f
or
m
a
nc
e
.
O
th
e
r
pr
opos
a
ls
to
im
pr
o
ve
th
e
pe
r
f
or
m
a
nc
e
in
c
lu
de
th
e
us
e
of
R
*
-
T
r
e
e
s
tr
uc
tu
r
e
[
8]
,
K
D
T
R
E
E
a
lg
or
it
hm
[
9]
,
s
pe
c
ia
l
da
ta
pa
r
ti
ti
on
a
l
gor
it
hm
or
di
s
jo
in
t
s
e
t
da
ta
s
tr
uc
tu
r
e
[
10
-
13
]
.
T
he
im
pl
e
m
e
nt
a
ti
on
of
th
e
s
e
te
c
hni
que
s
how
e
v
e
r
,
is
pe
r
f
or
m
e
d
on
a
s
in
gl
e
phys
ic
a
l
s
ys
te
m
.
D
ue
to
li
m
it
a
ti
ons
on t
he
numbe
r
of
c
or
e
s
, a
nd me
m
or
y of
a
s
in
gl
e
s
ys
t
e
m
t
he
a
m
ount
of
s
c
a
la
bi
li
ty
a
nd pe
r
f
or
m
a
nc
e
boos
t
th
a
t
c
a
n be
a
c
hi
e
ve
d us
in
g t
he
m
i
s
l
im
it
e
d.
W
he
n
w
or
ki
ng
w
it
h
la
r
ge
r
e
a
l
-
w
or
ld
da
ta
s
e
ts
th
e
us
e
of
a
di
s
t
r
ib
ut
e
d
s
ys
te
m
f
or
c
lu
s
te
r
in
g
is
m
or
e
a
ppr
opr
ia
te
[
14
-
17]
.
A
popula
r
s
tr
a
te
gy
f
or
im
pl
e
m
e
nt
in
g
th
e
d
is
tr
ib
ut
e
d
D
B
S
C
A
N
a
lg
or
it
hm
is
th
e
us
a
ge
of
th
e
di
s
jo
in
t
s
e
t
da
ta
s
tr
uc
tu
r
e
.
T
hi
s
a
ppr
oa
c
h
w
a
s
pr
opos
e
d
in
t
he
P
D
S
D
B
S
C
A
N
a
lg
or
it
hm
by
P
a
twa
r
y
e
t.
al
.
[
18
-
19]
.
T
he
a
lg
or
it
hm
m
a
ke
s
us
e
of
a
bot
to
m
-
up
s
tr
uc
tu
r
e
to
c
ons
tr
uc
t
th
e
c
lu
s
te
r
s
a
s
a
c
ol
le
c
ti
on
of
hi
e
r
a
r
c
hi
c
a
l
tr
e
e
s
.
I
n
th
is
a
ppr
oa
c
h
th
e
c
lu
s
t
e
r
in
g
is
pe
r
f
or
m
e
d
in
2
pha
s
e
s
.
I
n
th
e
f
ir
s
t
pha
s
e
lo
c
a
l
c
lu
s
te
r
in
g
is
pe
r
f
or
m
e
d
vi
a
th
e
r
e
gul
a
r
D
B
S
C
A
N
a
lg
or
it
hm
a
c
r
os
s
e
a
c
h
node
.
I
n
th
e
s
e
c
ond
pha
s
e
th
e
gl
ob
a
l
uni
on
of
c
lu
s
te
r
s
a
c
r
os
s
node
s
is
pe
r
f
or
m
e
d
us
i
ng
th
e
uni
on
-
f
in
d
ope
r
a
ti
on.
P
D
S
D
B
S
C
A
N
w
a
s
s
how
n
to
s
ig
ni
f
ic
a
nt
ly
out
pe
r
f
or
m
th
e
pr
e
vi
ous
a
ppr
oa
c
he
s
us
e
d
to
pa
r
a
ll
e
li
z
e
D
B
S
C
A
N
.
S
pe
e
dups
up
to
a
f
a
c
to
r
of
25.97
w
a
s
a
c
hi
e
ve
d
w
h
e
n
u
s
in
g
40
c
or
e
s
on
da
ta
s
e
ts
c
ont
a
in
in
g
s
e
ve
r
a
l
hundr
e
d
m
il
li
on
hi
gh
-
di
m
e
ns
io
n
a
l
poi
nt
s
.
P
D
S
D
B
S
C
A
N
i
s
i
m
pl
e
m
e
nt
e
d us
in
g both Ope
n
M
P
a
nd M
P
I
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
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8938
M
as
s
iv
e
ly
s
c
al
abl
e
de
ns
it
y
ba
s
e
d c
lu
s
te
r
in
g (
D
B
SC
A
N
)
on t
he
H
P
C
C
…
(
Y
at
is
h H
R
)
209
A
n
im
pr
ove
m
e
nt
to
th
e
a
bove
a
lg
or
it
hm
w
a
s
pr
opos
e
d
by
H
u
e
t
al
.
[
20]
w
he
r
e
in
th
e
a
ut
hor
s
m
a
de
us
e
of
th
e
di
s
tr
ib
ut
e
d
f
il
e
s
ys
te
m
of
th
e
K
unpe
ng
s
ys
te
m
.
I
n
th
is
a
lg
or
it
hm
da
ta
w
a
s
di
s
tr
ib
ut
e
d
a
c
r
os
s
di
f
f
e
r
e
nt
w
or
ke
r
s
a
nd
m
e
s
s
a
ge
pa
s
s
in
g
in
te
r
f
a
c
e
(
M
P
I
)
c
om
m
u
ni
c
a
ti
on
pa
tt
e
r
n
w
a
s
us
e
d
to
c
om
m
uni
c
a
te
th
e
da
ta
be
twe
e
n
th
e
w
or
ke
r
s
.
F
ur
th
e
r
th
e
la
r
ge
ove
r
he
a
d
a
s
s
o
c
ia
te
d
w
it
h
M
P
I
w
a
s
ove
r
c
om
e
us
in
g
a
nove
l
pa
r
a
m
e
te
r
s
e
r
ve
r
f
r
a
m
e
-
w
or
k. P
S
-
D
B
S
C
A
N
w
a
s
s
how
t
o outpe
r
f
or
m
t
he
M
P
I
-
ba
s
e
d P
D
S
D
B
S
C
A
N
-
D
w
it
h a
2
-
10
ti
m
e
s
s
pe
e
dup
on
c
om
m
uni
c
a
ti
on
e
f
f
ic
ie
nc
y
in
bot
h
r
e
a
l
-
w
or
ld
a
nd
s
ynt
he
ti
c
da
ta
s
e
ts
,
a
nd
th
e
s
pe
e
dup
w
a
s
f
ound
to
in
c
r
e
a
s
e
w
it
h
th
e
in
c
r
e
a
s
e
in
th
e
num
be
r
o
f
p
r
oc
e
s
s
or
c
or
e
s
a
nd
th
e
da
ta
s
e
t
s
c
a
le
.
I
n
R
P
-
D
B
S
C
A
N
[
21]
th
e
a
ut
hor
s
m
a
de
us
e
of
ps
e
udo
r
a
ndom
pa
r
ti
ti
oni
ng
to
ge
th
e
r
w
it
h
a
two
-
le
ve
l
c
e
ll
di
c
ti
ona
r
y.
RP
-
D
B
S
C
A
N
w
a
s
im
pl
e
m
e
nt
e
d
u
s
in
g
48
c
or
e
s
(
12
A
z
ur
e
M
a
-
c
hi
ne
s
)
on
a
n
A
pa
c
he
S
pa
r
k
s
y
s
te
m
.
RP
-
D
B
S
C
A
N
w
a
s
f
ound
to
a
c
hi
e
ve
a
n
a
lm
os
t
pe
r
f
e
c
t
lo
a
d
b
a
la
nc
e
a
m
ong
da
ta
s
pl
it
s
in
lo
c
a
l
c
lu
s
te
r
in
g
a
nd
di
d
not
dupli
c
a
te
poi
nt
s
a
m
ong the
m
. H
e
nc
e
R
P
-
D
B
S
C
A
N
dr
a
m
a
ti
c
a
ll
y outpe
r
f
or
m
e
d t
he
s
ta
te
-
of
-
th
e
-
a
r
t
pa
r
a
ll
e
l
D
B
S
C
A
N
a
lg
or
it
hm
s
by
up
to
180
ti
m
e
s
.
F
ur
t
he
r
m
or
e
,
onl
y
R
P
-
D
B
S
C
A
N
w
a
s
a
bl
e
to
ha
ndl
e
la
r
ge
da
ta
s
e
ts
(
362 G
B
)
w
he
r
e
a
s
t
he
ot
he
r
a
lg
or
it
hm
s
c
oul
d not.
A
lt
hough
th
e
us
a
ge
of
di
s
jo
in
t
s
e
t
da
ta
s
tr
uc
tu
r
e
f
or
D
B
S
C
A
N
is
popul
a
r
in
di
s
tr
ib
ut
e
d
s
ys
te
m
s
s
e
ve
r
a
l
ot
he
r
m
e
th
ods
s
uc
h
a
s
th
e
c
onve
x
-
hul
l
m
e
th
od
a
r
e
us
e
d
a
s
w
e
ll
[
22]
.
I
n
th
e
c
onve
x
-
hul
l
m
e
th
od
a
c
onve
x
hul
l
e
nc
lo
s
in
g
th
e
poi
nt
s
w
it
hi
n
a
c
lu
s
te
r
is
c
r
e
a
te
d
lo
c
a
ll
y
a
c
r
os
s
node
s
.
I
n
th
e
m
e
r
ge
ope
r
a
ti
on,
th
e
c
onve
x
hul
ls
of
th
e
lo
c
a
l
c
lu
s
te
r
s
a
r
e
m
e
r
ge
d
ba
s
e
d
on
th
e
a
m
ou
nt
of
ove
r
la
p.
H
ow
e
ve
r
,
th
is
a
lg
or
it
h
m
is
not
c
a
pa
bl
e
of
ha
ndl
in
g
c
on
c
a
ve
s
ha
pe
s
a
nd
he
n
c
e
do
e
s
not
c
or
r
e
c
tl
y
c
a
pt
ur
e
th
e
e
s
s
e
nc
e
of
th
e
unde
r
ly
in
g
poi
nt
s
.
I
n
th
e
a
lg
o
r
it
hm
[
23]
th
e
a
ut
hor
s
p
r
opos
e
a
gr
id
ba
s
e
d
di
s
jo
in
t
s
e
t
a
lg
or
it
hm
f
or
s
ol
vi
ng
th
e
p
r
obl
e
m
e
f
f
ic
ie
nt
ly
.
H
ow
e
ve
r
due
to
th
e
f
a
c
t
th
a
t
di
s
tr
ib
ut
io
n
of
da
ta
by
T
hor
a
m
ong
node
s
i
s
r
a
ndom,
it
is
not
pos
s
ib
le
t
o a
ppl
y t
he
a
lg
or
it
hm
di
r
e
c
tl
y. T
he
s
e
e
xi
s
ti
ng a
lg
or
it
hm
s
a
r
e
not
a
s
tr
a
ig
ht
f
or
w
a
r
d f
it
i
nt
o t
he
H
P
C
C
B
ig
D
a
ta
P
la
tf
or
m
a
nd
r
e
qui
r
e
m
odi
f
ic
a
ti
ons
.
H
e
nc
e
th
e
r
e
is
a
ne
e
d
f
or
a
be
tt
e
r
a
lg
or
it
hm
w
hi
c
h
c
a
n
e
xpl
oi
t
th
e
c
om
pone
nt
s
of
H
P
C
C
s
u
c
h a
s
T
hor
a
nd R
oxi
e
i
n or
de
r
t
o ga
in
m
a
s
s
iv
e
pe
r
f
or
m
a
nc
e
i
m
pr
ove
m
e
nt
s
dur
in
g
pa
r
a
ll
e
l
e
xe
c
ut
io
n of
t
he
D
B
S
C
A
N
a
lg
or
it
hm
.
3.
M
E
T
H
O
D
O
L
O
G
Y
3.1. DB
S
C
A
N
a
lg
or
it
h
m
T
he
D
B
S
C
A
N
a
lg
or
it
hm
[
24]
is
non
-
pa
r
a
m
e
tr
ic
s
pa
ti
a
l
c
lu
s
te
r
in
g
a
lg
or
it
hm
.
T
he
m
a
in
c
onc
e
pt
of
th
e
c
lu
s
te
r
in
g
a
lg
or
it
hm
is
th
a
t
f
or
e
a
c
h
c
lu
s
te
r
th
e
num
be
r
of
poi
nt
s
w
it
hi
n
e
ps
di
s
ta
n
c
e
is
gr
e
a
t
e
r
th
a
n
c
e
r
ta
in
m
in
im
um
poi
nt
s
i.
e
..,
th
r
e
s
hol
d
de
ns
it
y.
T
he
ps
e
udo
c
ode
f
or
D
B
S
C
A
N
a
lg
or
it
hm
is
e
lu
c
id
a
te
d
in
A
lg
or
it
hm
1.
T
he
a
lg
or
it
hm
s
ta
r
ts
w
it
h
a
poi
nt
p
∈
D
a
nd
r
e
tr
ie
ve
s
th
e
ne
ig
hbor
in
g
poi
nt
s
in
th
e
e
ps
-
ne
ig
hbor
hood
of
it
s
e
lf
.
I
f
th
e
r
e
tr
ie
ve
d
n
e
ig
hbor
hood
c
ont
a
in
s
a
t
le
a
s
t
m
in
pt
s
poi
nt
s
,
th
e
n
a
ne
w
c
lu
s
t
e
r
,
C
i
s
a
dde
d.
T
he
a
lg
or
it
hm
th
e
n
f
in
ds
a
ll
poi
n
ts
in
X
,
th
a
t
a
r
e
r
e
a
c
ha
bl
e
f
r
om
x
(
ne
ig
hbor
in
g
poi
nt
)
a
nd
a
dds
th
e
m
to
th
e
c
lu
s
te
r
C
.
I
f
th
e
e
p
s
-
ne
ig
hbor
hood
of
x
ha
s
le
s
s
th
a
n
m
in
pt
s
,
th
e
n
x
is
m
a
r
ke
d
a
s
noi
s
e
.
T
he
ps
e
udo
c
ode
c
a
n be
s
um
m
a
r
iz
e
d i
n
A
lg
or
it
hm
1.
A
lg
or
it
hm
1
.
D
B
S
C
A
N
a
lg
or
it
hm
T
he
ti
m
e
c
om
pl
e
xi
ty
of
A
lg
or
it
hm
1
is
O
(
n^
2)
,
w
he
r
e
n
is
t
he
num
be
r
of
poi
nt
s
in
X
.
B
ut
i
f
R
*
tr
e
e
s
or
K
-
D
t
r
e
e
s
a
r
e
us
e
d t
o obta
in
t
he
ne
a
r
e
s
t
ne
ig
hbor
s
t
he
t
i
m
e
c
om
pl
e
xi
ty
i
s
r
e
duc
e
d t
o O
(
n*l
og
n)
.
T
he
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
207
–
214
210
D
B
S
C
A
N
a
lg
or
it
hm
is
a
hi
ghl
y
s
e
qu
e
nt
ia
l
a
lg
or
it
hm
.
T
hi
s
m
a
ke
s
it
c
om
put
a
ti
ona
ll
y
in
e
f
f
ic
ie
nt
ta
s
k
w
h
e
n
a
ppl
ie
d
to
la
r
ge
a
m
ount
s
of
da
ta
,
e
s
pe
c
ia
ll
y
on
bi
g
da
ta
pl
a
tf
or
m
s
.
H
e
nc
e
th
e
r
e
is
a
ne
e
d
to
pa
r
a
ll
e
li
z
e
th
e
al
gor
it
hm
f
or
a
c
hi
e
vi
ng
be
tt
e
r
e
f
f
ic
ie
nc
y
in
s
uc
h
bi
g
da
ta
s
ys
te
m
s
.
T
he
f
ol
lo
w
in
g
s
e
c
ti
on
gi
ve
s
th
e
ove
r
a
ll
pr
oc
e
dur
e
f
or
t
he
s
a
m
e
.
3.2.
P
ar
al
le
l
D
B
S
C
A
N
al
gor
it
h
m
T
he
pr
opos
e
d
m
e
th
odol
ogy
pr
ovi
de
s
a
s
c
a
l
a
bl
e
s
ol
ut
io
n
to
th
e
D
B
S
C
A
N
c
lu
s
te
r
in
g
on
H
P
C
C
bi
g
da
ta
pl
a
tf
or
m
. T
hi
s
i
s
a
c
hi
e
ve
d by de
c
om
pos
in
g t
he
c
lu
s
te
r
in
g
a
lg
or
it
hm
i
nt
o
t
hr
e
e
s
ta
ge
s
na
m
e
ly
-
s
pr
a
yi
ng of
da
ta
, l
oc
a
l
c
lu
s
te
r
in
g pha
s
e
a
nd globa
l
m
e
r
gi
ng of
r
e
s
ul
ts
. E
a
c
h
of
t
he
s
e
s
ta
ge
s
a
r
e
e
xpl
a
in
e
d i
n
s
e
c
ti
ons
:
3.2.1
.
S
p
r
ayi
n
g of
d
at
a
I
n t
hi
s
s
ta
ge
th
e
da
ta
poi
nt
s
a
r
e
a
s
s
ig
ne
d gl
oba
l
uni
que
i
ds
a
nd
di
s
tr
ib
ut
e
d a
c
r
os
s
di
f
f
e
r
e
nt
node
s
i
n a
c
lu
s
te
r
by T
hor
e
ngi
ne
. T
he
di
s
tr
ib
ut
io
n by
t
he
T
hor
e
ngi
ne
e
ns
ur
e
s
t
ha
t
th
e
da
ta
poi
nt
s
a
r
e
di
s
tr
ib
u
te
d e
ve
nl
y
a
c
r
os
s
a
ll
th
e
node
s
.
E
a
c
h
of
th
e
lo
c
a
l
node
s
th
e
n s
or
t
th
e
da
ta
poi
nt
s
by
th
e
ir
uni
que
id
s
a
nd
s
e
nd
th
e
da
ta
to
lo
c
a
l
c
lu
s
te
r
in
g s
ta
ge
. T
he
s
e
uni
que
id
s
do
not
c
h
a
nge
ti
ll
th
e
e
nd
of
a
ll
th
e
s
ta
ge
s
a
nd
th
e
y
id
e
nt
if
y
e
a
c
h
da
ta
poi
nt
uni
que
ly
.
O
ne
m
or
e
im
por
ta
nt
poi
nt
to
not
e
is
th
a
t
th
e
a
lg
or
it
hm
doe
s
not
d
e
pe
nd
on
th
e
na
tu
r
e
of
di
s
tr
ib
ut
io
n of
da
ta
a
c
r
os
s
t
he
node
s
.
3.2.2
.
L
oc
al
c
lu
s
t
e
r
in
g
I
n
th
is
pha
s
e
e
a
c
h
node
pe
r
f
or
m
s
D
B
S
C
A
N
c
lu
s
te
r
in
g
ope
r
a
ti
ons
on
th
e
da
ta
poi
nt
s
th
a
t
a
r
e
lo
c
a
l
to
th
e
node
i
n t
he
H
P
C
C
c
lu
s
te
r
. T
he
l
oc
a
l
D
B
S
C
A
N
a
lg
or
it
hm
us
e
s
di
s
jo
in
t
s
e
t
ope
r
a
ti
ons
na
m
e
ly
-
U
N
I
O
N
a
nd
F
I
N
D
f
or
pe
r
f
or
m
in
g
lo
c
a
l
D
B
S
C
A
N
c
lu
s
te
r
in
g.
E
a
c
h
s
e
t
(
f
in
a
l
c
lu
s
te
r
)
is
uni
que
ly
r
e
pr
e
s
e
nt
e
d
by
hi
ghe
s
t
c
or
e
poi
nt
.
T
he
F
I
N
D
ope
r
a
ti
on
is
us
e
d
to
id
e
nt
if
y
th
e
p
a
r
e
nt
i.
e
..,
hi
ghe
s
t
c
or
e
poi
nt
,
f
or
e
a
c
h
poi
nt
(
node
)
in
th
e
tr
e
e
.
T
he
F
I
N
D
ope
r
a
ti
on
is
s
um
m
a
r
iz
e
d
in
A
lg
or
it
hm
2.
T
he
uni
on
ope
r
a
ti
on
m
e
r
ge
s
two
tr
e
e
s
to
f
or
m
a
bi
gge
r
tr
e
e
ba
s
e
d
on
r
e
m
’
s
a
lg
or
it
hm
.
T
h
e
uni
on
ope
r
a
ti
on
i
s
pe
r
f
or
m
e
d
on
a
c
or
e
poi
nt
a
nd
ot
he
r
c
or
e
or
a
non
-
c
or
e
poi
nt
. T
he
uni
on ope
r
a
ti
on i
s
s
um
m
a
r
iz
e
d i
n A
lg
or
it
hm
3.
A
lg
or
it
hm
2
.
F
in
d
o
pe
r
a
ti
on
A
lg
or
it
hm
3
.
U
ni
on ope
r
a
ti
on
I
ni
ti
a
ll
y
e
a
c
h
da
ta
poi
nt
is
r
e
pr
e
s
e
nt
e
d
a
s
a
node
c
ont
a
in
in
g
th
e
f
ie
ld
s
a
nd
pa
r
e
nt
id
.
T
he
pa
r
e
nt
of
e
a
c
h
da
ta
poi
nt
is
m
a
d
e
to
poi
nt
to
it
s
e
lf
i.
e
..,
p(
x)
=
x
a
nd
th
e
poi
nt
s
a
r
e
m
a
r
ke
d
a
s
non
-
c
or
e
poi
nt
.
E
a
c
h
c
lu
s
te
r
is
uni
que
ly
r
e
pr
e
s
e
nt
e
d
by
th
e
pa
r
e
nt
id
(
hi
ghe
s
t
c
or
e
poi
nt
of
th
a
t
c
lu
s
te
r
)
.
T
he
ps
e
udo
c
ode
f
or
lo
c
a
l
D
B
S
C
A
N
c
lu
s
te
r
in
g i
s
gi
ve
n i
n A
lg
or
it
hm
4. L
e
t
X
de
not
e
t
he
s
e
t
of
da
ta
poi
nt
s
t
ha
t
a
r
e
i
n t
he
l
oc
a
l
node
a
nd
Y
de
not
e
s
e
t
of
da
ta
poi
n
ts
th
a
t
a
r
e
p
r
e
s
e
nt
on
a
r
e
m
ot
e
node
.
T
he
poi
nt
s
th
a
t
a
r
e
in
th
e
e
ps
ne
ig
hbor
hood
o
f
e
a
c
h
x
∈
X
in
th
e
s
e
t
X
U
Y
is
f
ound.
T
h
e
ne
ig
hbor
hood
poi
nt
s
c
a
n
be
f
ound
by
us
in
g
num
e
r
ous
di
s
ta
nc
e
m
e
tr
ic
s
li
ke
E
uc
li
de
a
n,
M
a
nha
tt
a
n,
a
nd
C
he
by
s
he
v’
s
di
s
ta
n
c
e
f
unc
ti
ons
.
I
f
th
e
num
be
r
of
poi
nt
s
in
th
e
ne
ig
hbor
hood
is
gr
e
a
te
r
th
a
n
th
e
m
in
im
um
num
be
r
of
poi
nt
s
,
t
he
n
it
is
m
a
r
ke
d
a
s
a
c
or
e
poi
nt
.
E
a
c
h
poi
nt
y
in
t
he
ne
ig
hbor
hood of
x c
a
n e
it
he
r
be
l
oc
a
l
to
t
ha
t
node
or
i
n
a
r
e
m
ot
e
node
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
M
as
s
iv
e
ly
s
c
al
abl
e
de
ns
it
y
ba
s
e
d c
lu
s
te
r
in
g (
D
B
SC
A
N
)
on t
he
H
P
C
C
…
(
Y
at
is
h H
R
)
211
A
lg
or
it
hm
4. L
oc
a
l
D
B
S
C
A
N
I
f
y
is
in
lo
c
a
l
node
th
e
n
th
e
r
e
c
a
n
be
two
c
a
s
e
s
:
(
a
)
y
is
c
or
e
poi
nt
,
(
b)
y
is
non
-
c
or
e
poi
nt
i.
e
..,
a
bor
de
r
poi
nt
.
I
f
c
ondi
ti
on
(
a
)
is
tr
ue
U
ni
on
(
x,
y)
is
pe
r
f
or
m
e
d.
I
f
c
ondi
ti
on
(
b)
is
tr
ue
th
e
n
it
s
m
a
r
ke
d
a
s
vi
s
it
e
d
a
nd
U
ni
on
(
x,
y)
is
pe
r
f
or
m
e
d.
I
f
y
is
a
r
e
m
ot
e
poi
nt
t
he
n
y
c
a
n
b
e
e
it
he
r
a
c
or
e
poi
nt
or
a
non
-
c
or
e
poi
nt
.
I
f
th
e
la
tt
e
r
c
ondi
ti
on
is
tr
ue
th
e
n
th
e
n
e
ig
hbor
hood
of
y
i
s
f
ound.
I
f
th
e
ne
ig
hbor
hood
doe
s
not
c
ont
a
in
m
in
im
um
poi
nt
s
th
e
n
y
is
a
bor
de
r
poi
nt
e
ls
e
it
is
m
a
r
ke
d
a
s
a
c
or
e
poi
nt
a
nd
uni
on
(
x,
y)
is
p
e
r
f
or
m
e
d.
I
f
th
e
poi
nt
y
is
c
or
e
th
e
n
uni
on
(
x,
y)
ope
r
a
ti
on
is
pe
r
f
or
m
e
d
a
n
d
th
e
pr
oc
e
s
s
is
c
ont
in
ue
d
f
or
ot
he
r
poi
nt
s
.
T
he
r
e
f
or
e
,
a
t
th
e
e
nd
of
th
e
a
lg
or
it
hm
it
c
a
n
be
not
e
d
th
a
t
t
he
p
oi
nt
s
w
hi
c
h
a
r
e
noi
s
y
ha
ve
s
in
gl
e
tr
e
e
s
(
s
in
gl
e
to
n
tr
e
e
s
)
w
it
h
it
s
pa
r
e
nt
poi
nt
in
g
to
it
s
e
lf
.
I
f
th
e
poi
n
t
is
a
bor
de
r
poi
nt
th
e
n
it
is
a
s
s
ig
ne
d
to
th
e
hi
ghe
s
t
c
or
e
poi
nt
of
th
e
c
lu
s
te
r
of
it
s
ne
a
r
e
s
t
ne
ig
hbor
.
I
f
th
e
poi
nt
is
a
c
or
e
poi
nt
th
e
n
th
e
U
ni
on
o
pe
r
a
ti
on
a
s
s
ig
ns
it
to
pa
r
e
nt
w
it
h
h
ig
he
s
t
c
or
e
poi
nt
.
T
he
ti
m
e
c
om
pl
e
xi
ty
of
th
e
lo
c
a
l
D
B
S
C
A
N
ope
r
a
ti
on
is
O
(
n
2
)
.
T
he
a
bove
a
lg
or
it
hm
m
e
r
ge
s
poi
nt
s
to
it
s
c
lu
s
te
r
s
(
tr
e
e
s
)
w
it
ho
ut
a
ny
pa
r
ti
c
ul
a
r
o
r
de
r
in
g
o
f
da
ta
-
poi
nt
s
.
T
he
out
put
m
a
ppi
ng of
da
ta
poi
nt
t
o
th
e
pa
r
e
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ds
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s
i
nput
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o t
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xt
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s
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gl
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r
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m
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o t
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a
c
h da
ta
poi
nt
i
s
r
e
tu
r
ne
d one
by one
f
r
om
t
he
T
hor
.
3.2.3. Gl
ob
al
m
e
r
ge
I
n
th
is
pha
s
e
,
th
e
tr
e
e
s
f
or
m
e
d
in
th
e
pr
e
vi
ous
s
ta
ge
a
r
e
m
e
r
ge
d
to
obt
a
in
th
e
gl
oba
l
c
lu
s
te
r
s
.
A
m
e
r
ge
of
tr
e
e
s
a
c
r
os
s
nod
e
s
ha
pp
e
ns
w
he
n
a
poi
nt
be
lo
ngs
to
m
or
e
th
a
n
one
tr
e
e
in
di
f
f
e
r
e
nt
node
s
.
A
f
te
r
th
e
tr
e
e
s
a
r
e
m
e
r
ge
d
th
e
f
in
a
l
c
lu
s
te
r
s
a
r
e
obt
a
in
e
d
w
hi
c
h
a
r
e
r
e
pr
e
s
e
nt
e
d
by
th
e
ir
hi
ghe
s
t
c
or
e
poi
nt
a
c
r
os
s
a
ll
node
s
. T
hi
s
c
a
n
b
e
a
c
hi
e
v
e
d
by
us
in
g
s
im
il
a
r
a
ppr
oa
c
he
s
of
uni
on
a
nd
f
in
d
ope
r
a
ti
on
s
of
di
s
jo
in
t
s
e
t
s
tr
uc
tu
r
e
a
s
de
s
c
r
ib
e
d
be
f
or
e
.
T
he
ps
e
udo
c
ode
is
e
lu
c
id
a
te
d
in
A
lg
or
it
hm
5.
I
ni
ti
a
ll
y
th
e
out
put
m
a
ppi
ng
of
s
ta
ge
2
(
onl
y
c
or
e
poi
nt
s
a
nd
lo
c
a
l
poi
nt
s
th
a
t
node
)
i
s
di
s
tr
ib
ut
e
d
b
a
c
k
a
m
ong
th
e
node
s
a
s
w
e
ll
a
s
non
out
li
e
r
poi
nt
s
in
or
de
r
to
f
in
d
th
e
ul
ti
m
a
te
id
.
E
a
c
h
da
ta
poi
nt
h
a
s
two
a
tt
r
ib
ut
e
s
-
lo
c
a
l
pa
r
e
nt
id
(
lo
c
a
l
to
th
e
nod
e
)
a
nd
gl
oba
l
pa
r
e
nt
id
(
gl
oba
l/
ul
ti
m
a
te
id
)
.
I
n
e
a
c
h
node
,
th
e
r
e
m
ot
e
pa
r
e
nt
s
of
e
a
c
h
d
a
ta
poi
nt
in
r
e
m
ot
e
nod
e
s
a
r
e
f
ound
(
by
ha
vi
ng
a
lo
c
a
l
lo
okup
ta
bl
e
)
.
I
n
c
a
s
e
s
s
uc
h
a
s
a
hi
ghe
s
t
c
or
e
poi
nt
be
in
g
pr
e
s
e
nt
in
a
not
he
r
node
,
th
e
t
r
e
e
s
a
r
e
m
e
r
ge
d
(
c
ha
ngi
ng t
he
i
ds
)
a
nd t
he
un
io
n ope
r
a
ti
on
r
e
s
ul
ts
i
n t
he
hi
ghe
s
t
c
or
e
poi
n
t
to
t
ha
t
c
lu
s
te
r
(
by
c
ha
ngi
ng
th
e
pa
r
e
nt
id
s
)
.
H
e
nc
e
a
t
th
e
e
nd
of
th
e
a
lg
or
it
hm
e
a
c
h
c
lu
s
te
r
is
r
e
pr
e
s
e
nt
e
d
by
hi
ghe
s
t
c
or
e
poi
nt
a
s
c
lu
s
te
r
id
.
S
in
c
e
th
e
e
nt
ir
e
c
om
put
a
ti
on
i
s
done
pa
r
a
ll
e
ll
y,
a
n
in
c
r
e
a
s
e
d
s
pe
e
dup
is
a
c
hi
e
v
e
d.
A
f
te
r
th
is
, c
lu
s
te
r
s
a
r
e
r
e
num
be
r
e
d by a
s
s
ig
ni
ng 0 to t
he
out
li
e
r
s
f
ound in s
ta
ge
t
w
o a
nd 1 ba
s
e
d i
nde
xi
ng t
o t
he
r
e
s
t
of
poi
nt
s
ba
s
e
d
on
th
e
or
de
r
of
th
e
ir
oc
c
ur
r
e
nc
e
s
in
da
ta
s
e
t.
T
h
e
f
in
a
l
r
e
s
ul
t
is
r
e
tu
r
ne
d
to
E
C
L
W
a
tc
h
f
or
th
e
us
e
r
a
s
t
a
bl
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
10
, N
o.
1
,
M
a
r
c
h
20
2
1
:
207
–
214
212
A
lg
or
it
hm
5
.
G
lo
ba
l
m
e
r
ge
4.
E
X
P
E
R
I
M
E
N
T
S
A
N
D
R
E
S
U
L
T
S
T
he
P
a
r
a
ll
e
l
D
B
S
C
A
N
a
lg
or
it
hm
w
a
s
im
pl
e
m
e
nt
e
d
in
E
nt
e
r
pr
is
e
C
ont
r
ol
L
a
ngua
ge
on
H
P
C
C
s
ys
te
m
s
.
E
a
c
h
node
in
th
e
c
lu
s
te
r
ha
d
6G
B
of
R
A
M
a
nd
128G
B
of
H
a
r
d
D
is
k.
T
he
pr
oc
e
s
s
or
u
s
e
d
w
a
s
in
te
l
X
e
on
w
it
h
2.4G
H
z
c
lo
c
k
f
r
e
que
nc
y.
T
a
bl
e
1
e
lu
c
id
a
te
s
th
e
pr
o
c
e
s
s
or
s
pe
c
if
ic
a
ti
ons
.
I
n
or
de
r
to
m
e
a
s
ur
e
th
e
pe
r
f
or
m
a
nc
e
of
th
e
pa
r
a
ll
e
l
D
B
S
C
A
N
a
lg
or
it
hm
a
c
om
pa
r
is
on
be
twe
e
n
s
in
gl
e
node
a
nd
m
ul
ti
nod
e
(
c
ons
is
ti
ng
of
two
node
s
a
nd
th
r
e
e
node
s
)
c
lu
s
te
r
s
w
a
s
m
a
de
.
E
a
c
h
da
ta
s
e
t
w
a
s
r
un
w
it
h
di
f
f
e
r
e
nt
e
ps
a
nd
m
in
pt
s
. A
H
ig
he
r
va
lu
e
o
f
m
in
pt
s
i
nc
r
e
a
s
e
s
t
he
noi
s
e
c
ount
s
.
T
he
r
e
s
ul
ts
a
r
e
t
a
bul
a
te
d
a
s
s
ho
w
n i
n T
a
bl
e
2.
T
he
pa
r
a
ll
e
l
D
B
S
C
A
N
im
pl
e
m
e
nt
a
ti
on
a
nd
s
e
r
ia
l
D
B
S
C
A
N
i
m
pl
e
m
e
nt
a
ti
on
w
e
r
e
te
s
t
e
d
s
e
pa
r
a
te
ly
f
or
c
onve
nt
io
na
l
s
in
gl
e
node
pr
oc
e
s
s
in
g
ve
r
s
u
s
th
e
us
e
of
a
t
w
o
node
H
P
C
C
c
lu
s
te
r
.
T
h
e
r
e
s
ul
ts
obt
a
in
e
d
w
e
r
e
c
om
pa
r
e
d
w
it
h
th
e
out
put
of
s
kl
e
a
r
n
im
pl
e
m
e
nt
a
ti
on
of
D
B
S
C
A
N
to
c
om
pa
r
e
th
e
c
lu
s
te
r
a
c
c
ur
a
c
y.
T
h
e
c
lu
s
te
r
de
ns
it
ie
s
in
bot
h
c
a
s
e
s
w
e
r
e
f
ound
to
be
id
e
nt
ic
a
l.
T
he
t
e
s
t
s
e
t
c
on
s
is
te
d
of
6
te
s
t
c
a
s
e
s
in
c
lu
di
ng
bot
h
s
ynt
he
ti
c
da
ta
s
e
ts
a
nd
r
e
a
l
da
t
a
s
e
t
(
f
r
ogs
’
M
F
C
C
da
ta
s
e
t*
[
25]
)
.
T
he
te
s
t
s
e
ts
ha
d
up
to
20
di
m
e
n
s
io
ns
.
A
ls
o,
one
m
or
e
poi
nt
to
not
e
is
th
a
t
th
e
da
ta
is
di
s
tr
ib
ut
e
d
uni
f
or
m
ly
a
m
ong
th
e
node
s
.
T
he
da
ta
poi
nt
s
in
d
is
jo
in
t
s
e
ts
(
r
e
pr
e
s
e
nt
in
g
e
a
c
h
c
lu
s
te
r
)
m
a
y
or
m
a
y
not
be
in
th
e
s
a
m
e
node
.
H
e
nc
e
th
e
e
xpe
r
im
e
nt
s
c
ondu
c
te
d
doe
s
not
a
s
s
um
e
a
ny
pa
r
ti
c
ul
a
r
di
s
tr
ib
ut
io
n
o
f
da
ta
poi
nt
s
a
m
ong
th
e
w
or
ke
r
node
s
a
nd
no
f
ur
th
e
r
r
e
di
s
tr
ib
ut
io
n
is
r
e
qui
r
e
d
a
t
a
ny
s
ta
ge
of
a
lg
or
it
hm
.
T
he
out
put
s
in
di
c
a
te
th
a
t
s
u
bs
ta
nt
ia
l
im
pr
ove
m
e
nt
s
in
ti
m
e
c
om
pl
e
xi
ty
of
th
e
pa
r
a
ll
e
l
a
lg
or
it
hm
t
ha
n t
he
s
e
r
ia
l
ve
r
s
io
n (
s
in
gl
e
node
)
.
T
he
ta
bul
a
te
d
r
e
s
ul
ts
obt
a
in
e
d
a
r
e
de
pi
c
te
d
gr
a
phi
c
a
ll
y
in
F
ig
u
r
e
2.
W
e
c
a
n
ob
s
e
r
ve
th
a
t
th
e
r
e
is
no
s
ig
ni
f
ic
a
nt
i
m
pr
ove
m
e
nt
i
n
t
he
e
xe
c
ut
io
n t
im
e
f
or
lo
w
e
r
numbe
r
of
poi
nt
s
f
or
hi
ghe
r
nu
m
be
r
of
node
s
. I
t
i
s
i
n
f
a
c
t
s
li
ght
ly
hi
ghe
r
due
to
th
e
f
a
c
t
th
a
t
th
e
ti
m
e
r
e
qui
r
e
d
to
di
s
t
r
ib
ut
e
da
ta
poi
nt
s
is
not
c
om
pe
n
s
a
te
d
w
e
ll
by
th
e
t
im
e
ga
in
e
d due
t
o pa
r
a
ll
e
li
z
a
ti
on.
H
ow
e
ve
r
, i
t
i
s
c
le
a
r
t
ha
t
f
or
l
a
r
ge
r
numbe
r
of
da
ta
poi
nt
s
a
s
t
he
numb
e
r
of
node
s
in
c
r
e
a
s
e
s
,
s
ub
s
ta
nt
ia
l
s
pe
e
dup
is
obt
a
in
e
d.
T
he
r
e
s
u
lt
s
c
le
a
r
ly
in
di
c
a
te
th
a
t
th
e
m
ul
ti
node
s
e
tu
p
out
pe
r
f
or
m
s
th
e
s
in
gl
e
nod
e
s
e
tu
p
in
a
ll
c
a
s
e
s
.
W
he
n
th
e
nu
m
be
r
of
poi
nt
s
is
le
s
s
,
th
e
r
e
is
no
s
ig
ni
f
ic
a
nt
im
pr
ove
m
e
nt
of
pa
r
a
ll
e
l
D
B
S
C
A
N
ove
r
s
e
que
nt
ia
l
D
B
S
C
A
N
.
A
s
th
e
num
be
r
of
da
ta
po
in
ts
in
c
r
e
a
s
e
s
th
e
pa
r
a
ll
e
l
a
lg
or
it
hm
pe
r
f
or
m
s
w
a
y
be
tt
e
r
(
4x
be
tt
e
r
f
or
30000
poi
nt
s
c
om
pa
r
e
d
to
two
node
c
lu
s
te
r
)
th
a
n
it
s
s
e
r
ia
l
c
ount
e
r
pa
r
t.
T
he
c
ode
f
or
th
e
s
a
m
e
w
a
s
m
e
r
ge
d
to
H
P
C
C
s
ys
t
e
m
s
r
e
pos
it
or
y
a
nd
c
a
n
b
e
f
ound
on
G
it
hub.
T
a
bl
e
1. P
r
oc
e
s
s
or
s
pe
c
if
ic
a
ti
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f
or
e
a
c
h node
S
pe
c
i
f
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c
a
t
i
on
V
a
l
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A
r
c
hi
t
e
c
t
ur
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x86_64
C
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a
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ode
l
N
a
m
e
I
nt
e
l
X
e
on
C
P
U
G
H
z
2.4
C
or
e
(
s
)
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
M
as
s
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e
ly
s
c
al
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e
de
ns
it
y
ba
s
e
d c
lu
s
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in
g (
D
B
SC
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)
on t
he
H
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…
(
Y
at
is
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)
213
T
a
bl
e
2. R
e
s
ul
ts
of
r
un t
im
e
of
di
f
f
e
r
e
nt
da
ta
s
e
ts
w
it
h va
r
io
us
v
a
lu
e
s
of
e
ps
a
nd mi
npt
s
f
or
s
e
r
ia
l
a
nd pa
r
a
ll
e
l
a
lg
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R
E
F
E
R
E
N
C
E
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