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i
ng
,
hi
g
hl
i
g
ht
s
o
n
pa
t
t
e
r
n
s
th
a
t r
a
r
e
l
y
o
cc
u
r
r
ed
.
U
s
u
ally
,
t
h
e
i
te
ms
e
t
m
i
n
i
n
g
alg
o
r
it
h
ms
ta
r
g
e
t
t
h
e ex
t
r
a
ct
i
o
n
o
f
f
r
e
q
u
en
t
ite
ms
e
ts
t
h
a
t
h
a
v
e
a
h
i
g
h
f
r
eq
u
e
n
cy
i
n
t
h
e
t
r
an
s
a
ct
i
o
n
a
l
d
at
a
b
a
s
e.
H
o
w
e
v
er
,
t
h
e
i
n
f
r
e
q
u
e
n
t
ite
ms
e
ts
w
ith
lo
w
s
u
p
p
o
r
t a
ls
o
c
an
p
r
o
d
u
c
e
p
o
te
n
ti
al
v
ita
l as
s
o
c
iatio
n
r
u
le
s
a
mo
n
g
ite
ms
e
t
s.
I
t
may
co
n
t
r
ib
u
te
a
s
ig
n
if
ic
a
n
t
ly
r
e
liab
le
d
e
c
is
io
n
s
u
p
p
o
r
t s
y
s
te
m.
I
n t
he
i
nf
re
q
u
e
nt
i
t
e
m
s
e
t
min
in
g
,
th
e f
i
r
s
t
s
t
a
g
e
i
s
t
o
f
i
n
d
o
u
t
t
h
e
i
n
f
r
eq
u
en
t
i
t
em
s
et
s
f
r
o
m
t
h
e
t
r
a
n
s
a
c
t
i
o
n
d
a
t
a
b
a
s
e.
F
o
l
l
o
w
e
d
b
y
t
h
e
s
eco
n
d
s
t
a
g
e
i
s
t
o
s
e
a
r
c
h
o
u
t
t
h
e a
s
s
o
c
i
a
t
i
o
n
r
u
l
es
a
c
co
r
d
i
n
g
t
o
i
n
f
r
eq
u
en
t
i
t
em
s
et
s
.
A
n
y
alg
o
r
i
t
h
m s
h
all
f
in
d
t
h
e
s
ame
s
e
t o
f
r
u
le
s
,
al
t
h
o
u
g
h
t
h
e
i
r
c
o
mp
u
ta
tio
n
al
e
f
f
ic
ie
n
c
ie
s
a
n
d
m
em
o
r
y
r
eq
u
i
r
e
m
e
n
t
s
m
a
y
b
e d
i
f
f
er
en
t
.
T
h
e
t
w
o
b
a
s
i
c
a
l
go
r
i
t
hm
s
o
f
i
n
f
r
e
que
nt
m
i
ni
n
g
a
r
e
A
pr
i
or
i
a
n
d
FP
-
G
ro
w
t
h.
Tw
o
t
y
p
e
s
o
f
d
ata lay
o
u
ts
w
h
ic
h
a
r
e
u
s
u
al
ly
e
mp
lo
y
e
d
in
ite
ms
e
t m
i
n
i
n
g
to
r
e
p
r
e
s
e
n
t d
a
tab
as
e
s
.
T
he
y
a
re
t
he
h
o
r
i
z
o
n
t
a
l
an
d
v
er
t
i
c
al
l
a
y
o
u
t
.
I
n
t
h
e
h
o
r
i
z
o
n
t
a
l
d
a
t
a
b
a
s
e
l
a
y
o
u
t
,
ea
ch
t
r
a
n
s
a
c
t
i
o
n
co
n
si
st
s o
f
a
s
e
t
o
f
i
t
em
s
w
h
e
r
eb
y
t
h
e
d
a
t
a
b
a
s
e
i
s
a
s
et
o
f
tr
a
n
s
ac
tio
n
s
.
Mo
st
Ap
r
i
o
r
i
-
b
as
e
d
a
lg
o
r
it
h
ms
e
mp
lo
y
th
is
ty
p
e
o
f
l
a
you
t
w
h
ile
F
P
-
Gr
o
wt
h
u
s
e
s
bot
h
d
a
t
a
l
a
you
t
for
t
h
e
m
i
n
i
n
g p
ur
p
os
e
.
I
n
t
h
i
s
ar
t
i
cl
e,
an
a
l
y
s
i
s
p
e
r
f
o
r
m
an
ce o
n
t
h
e
i
n
f
r
eq
u
en
t
m
i
n
i
n
g
u
s
in
g
th
e
R
-
Ec
la
t al
g
o
r
i
t
h
m w
ill b
e
di
s
c
us
s
e
d.
E
a
c
h
v
a
ri
a
nt
o
f
R
-
Ec
lat al
g
o
r
i
t
h
m
h
as
a d
if
f
e
r
e
n
t w
o
r
k
-
f
l
ow
.
T
h
us
,
t
hr
o
ug
h
e
xpe
r
i
m
e
nt
a
t
i
o
n,
t
h
e d
i
f
f
er
en
ce
o
f
a
ch
i
ev
e
m
en
t
i
n
r
u
n
n
i
n
g
t
i
m
e a
l
l
o
w
s
t
h
e
d
et
er
m
i
n
at
i
o
n
o
f
t
h
e
f
a
s
t
es
t
R
-
Ec
lat
v
a
r
i
a
n
t i
n
m
in
in
g
in
f
r
e
que
n
t
i
t
e
m
s
e
t
.
A
c
c
o
r
di
ng t
o
t
h
e
e
xpe
r
i
m
e
n
t
a
t
i
o
n,
IF
-
D
i
f
f
s
et
d
em
o
n
s
t
r
at
es
t
h
e f
a
s
t
es
t
p
e
r
f
o
r
m
an
ce
w
i
t
h
t
h
e
l
ow
e
s
t
r
un
n
i
n
g t
i
m
e
d
ur
i
n
g
t
h
e
m
i
n
i
n
g pr
oc
e
s
s
i
n
g
i
n bot
h
s
pa
r
s
e
a
n
d d
e
n
s
e
d
a
t
a
.
2.
RE
SE
ARCH
M
E
T
H
O
D
In
th
e
p
a
s
t
f
e
w
y
e
a
r
s
,
in
f
r
e
q
u
e
n
t min
in
g
h
a
s
ma
d
e
a
l
ea
p
i
n
da
t
a
m
i
n
i
ng.
I
n
f
r
e
que
n
t
pa
t
t
e
rn
s
us
ua
l
l
y
a
ppl
i
e
d i
n
di
v
e
r
s
e
ar
ea
s
c
o
m
pri
s
i
n
g
b
io
lo
g
y
,
me
d
ic
in
e
,
a
n
d
s
e
c
u
r
ity
.
I
n
t
h
e
me
d
ic
al
d
om
a
i
n
,
b
y a
n
a
l
ys
i
n
g
cl
i
n
i
ca
l
d
at
a
b
a
s
es
o
f
p
a
t
i
e
n
t
s
'
d
i
s
ea
s
es
,
t
h
e d
i
s
co
v
e
r
e
d i
n
f
r
e
que
n
t
pa
t
t
e
rn
s
o
r t
r
e
n
ds
w
i
l
l
a
s
s
i
s
t
t
h
e m
ed
i
cal
o
f
f
i
ce
r
t
o
m
a
k
e d
ec
i
s
i
o
n
s
a
b
o
u
t
t
h
e
m
ed
i
ci
n
e p
r
es
c
r
i
b
e
o
r
c
l
i
n
i
c
a
l
car
e.
Th
i
s
p
ap
e
r
ad
d
r
e
s
s
e
s
th
e
p
r
o
b
le
m
o
f
min
i
n
g
i
n
f
r
e
q
u
e
n
t
ite
ms
e
ts
f
r
o
m tr
a
n
s
ac
tio
n
a
l d
at
as
e
ts
.
L
e
t ite
ms
e
t
I
=
{
i
1
,
i
2
, …
,
i
m
}
b
e
a s
e
t o
f
d
ata i
te
ms
.
M
o
r
e
s
p
e
c
if
ic
ally
,
k
-
ite
ms
e
t
d
en
o
t
e
s
a
s
a
s
e
t
of
k
it
e
m
s
in
I
.
A
t
r
an
s
a
ct
i
o
n
al
d
a
t
a
s
et
T
=
{
t
1
,
t
2
, …
,
t
n
}
i
s
a
s
et
o
f
t
r
a
n
s
ac
t
i
o
n
s
,
w
h
e
r
e ea
c
h
t
r
an
s
a
ct
i
o
n
t
q
(
q
∈
[1,
n
])
i
s
a
s
e
t
o
f
ite
ms
i
n
I
an
d
i
s
c
h
ar
a
ct
e
r
i
z
ed
b
y
a
t
r
a
n
s
a
c
t
i
o
n
ID
(
t
i
d).
T
h
e
s
uppo
r
t
(f
r
e
que
n
c
y
of
o
c
c
urr
e
n
c
e
o
f
a
n
ite
ms
e
t)
o
f
a
n
i
te
ms
e
t is
t
h
e
n
u
mb
e
r
o
f
tr
a
n
s
ac
t
io
n
s
c
o
n
t
ai
n
i
n
g
I
in
T
.
A
n
ite
ms
e
t
I
i
s
i
n
f
r
e
que
n
t
i
f
i
t
s
s
uppo
rt
i
s
l
e
s
s
t
h
a
n o
r e
qua
l
t
o
a
m
i
ni
m
um
s
uppo
rt
t
hr
e
s
h
o
l
d
.
O
t
h
er
w
i
s
e
,
i
t
i
s
c
al
l
ed
t
o
b
e
f
r
e
q
u
en
t
.
G
i
v
e
n
a
t
r
a
n
s
ac
tio
n
al
d
a
tas
e
t
T
a
n
d
a
mi
n
im
u
m s
u
p
p
o
r
t
t
h
r
e
s
h
o
ld
,
t
h
e
in
f
r
e
q
u
e
n
t
i
te
ms
e
t
mi
n
i
n
g
p
r
o
b
le
m
in
v
o
lv
e
s
d
e
t
e
r
min
in
g
a
ll
in
f
r
e
q
u
e
n
t
i
t
e
m
s
e
t
s
f
r
o
m
T
.
A
pri
o
r
i
[
6,
7
]
alg
o
r
it
h
m
is
t
h
e
mo
s
t c
o
mmo
n
ly
ite
ms
e
t m
i
n
i
n
g
alg
o
r
i
t
h
ms
t
h
at
u
s
e
s
a b
r
e
ad
t
h
-
f
i
r
s
t
s
e
a
rc
h a
nd
t
he
d
o
w
nw
a
rd
c
l
o
s
u
re
p
ro
p
e
rt
y
.
I
t
i
s
u
s
u
a
l
l
y
a
d
op
t
e
d
ho
r
i
z
o
nt
a
l
l
a
y
o
u
t
t
o
re
p
re
s
e
nt
t
he
t
r
a
ns
a
c
t
i
o
n
da
t
a
b
a
s
e
a
nd t
h
e
f
r
e
que
n
c
y
of
a
n
i
t
e
m
s
e
t
i
s
c
o
m
put
e
d b
y
c
ount
i
ng i
t
s
o
c
c
ur
r
e
n
c
e
i
n
e
a
c
h t
ra
n
s
a
c
t
i
o
n
.
A
p
r
i
o
r
i
d
i
s
c
o
v
er
ed
r
ul
e
s
by
e
xpl
o
i
t
i
n
g
s
uppo
rt
a
n
d c
o
n
f
i
de
n
c
e
re
qui
r
e
m
e
nt
s
a
n
d us
i
n
g
t
h
e
t
hr
e
s
h
o
l
d t
o
pr
u
n
e
t
h
e
s
e
ar
c
h
s
p
ac
e
.
B
u
t,
it
is
n
o
t
e
f
f
ic
ie
n
t
to
f
in
d
a lo
w
-
s
upport
r
ul
e
s
.
U
s
i
n
g
A
p
r
i
o
r
i
,
i
t
n
e
e
ds
t
o
w
a
de
t
hr
o
ugh
t
h
o
us
a
nds
o
f
i
t
e
m
s
e
t
s
(o
f
t
e
n
ha
v
i
ng hi
g
h
s
uppo
rt
) t
o
f
i
nd t
h
e
i
n
f
r
e
que
nt
i
te
ms
e
ts
.
A
no
t
he
r
a
lg
o
r
ith
m
i
s
t
o
u
s
e a
t
r
ee
-
ba
s
e
d
a
p
p
r
oa
c
h
.
M
os
t
t
r
e
e
-
b
a
s
e
d i
n
f
r
e
que
nt
pa
t
t
e
rn
m
i
ni
n
g
ap
p
r
o
ac
h
e
s
f
o
llo
w
th
e
tr
ad
i
tio
n
al F
P
-
Gr
o
wt
h
a
l
go
r
i
t
hm
[8
]
.
F
P
-
G
r
o
wt
h
[
4
] e
m
pl
o
y
s
a
di
v
i
de
a
n
d c
o
n
que
r
s
t
ra
t
e
gy
a
n
d a
F
P
-
t
r
e
e d
a
t
a
s
t
r
u
c
t
u
r
e
t
o
a
ch
i
e
v
e a
c
o
n
d
en
s
ed
r
ep
r
es
e
n
t
a
t
i
o
n
o
f
t
h
e t
r
an
s
a
ct
i
o
n
d
at
a
b
a
s
e
.
I
t
is
a
tw
o
-
p
as
s
ap
p
r
o
ac
h
a
n
d
is
o
n
ly
af
f
o
r
d
ab
le
w
h
e
n
mi
n
i
n
g
a
s
ta
tic
d
at
as
e
t.
Li
u
e
t
a
l.
[
9
]
pr
op
os
e
d
M
ul
t
i
pl
e
S
uppo
rt
A
p
ri
o
r
i
(
MSAp
r
i
o
r
i
)
t
o d
ea
l
w
i
t
h
t
h
e
i
n
f
r
eq
u
e
n
t
i
t
em
s
et
by
us
i
n
g m
ul
t
i
pl
e
min
im
u
m
s
u
p
p
o
r
t
i
n
a
t
r
a
n
s
a
c
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n
t
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re
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a
rc
h p
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he
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h
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t
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a
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t
a
s
et
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h
e
y
c
a
nn
o
t
c
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ri
b
ut
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t
o
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s
ge
n
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r
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pr
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ha
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g
h c
o
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d
e
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h
e
y
o
v
e
r
co
me
th
is
p
r
o
b
le
m
w
ith
a te
c
h
n
iq
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w
h
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by
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a
c
h
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t
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m
i
n
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h
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d
a
t
a
b
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s
e
c
a
n
ha
v
e
i
t
s
o
w
n
m
i
n
i
m
um
i
t
e
m
s
up
po
r
t
(M
IS
).
By
pr
o
v
i
di
n
g
a
d
i
f
f
e
r
e
n
t
M
IS
fo
r
di
ff
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r
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n
t
i
t
e
m
s
,
a
h
i
g
h
e
r
m
i
n
s
up c
a
n
b
e
s
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t
fo
r
r
ul
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s
a
ppl
y
o
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f
r
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que
n
t
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t
e
m
s
a
nd l
o
w
e
r
m
i
n
s
up i
s
r
ul
e
s
th
a
t in
cl
u
d
e
in
f
r
e
q
u
e
n
t it
e
m
s
.
Ra
h
m
a
n
[
10
]
h
a
s
d
e
s
i
g
ne
d
t
he
O
nl
i
ne
A
p
ri
o
ri
-
I
n
f
r
e
que
nt
a
l
go
r
i
t
hm
.
T
h
is
alg
o
r
it
h
m
c
o
n
s
i
d
e
r
s
th
e
s
uppo
r
t
v
a
l
ue
b
ut
do
e
s
n
o
t
us
e
t
h
e
co
n
f
i
d
en
ce
va
l
u
e
.
I
t
e
f
f
ic
ie
n
tly
u
s
es
s
u
p
p
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r
t
t
o c
om
p
u
t
e
a
n
a
n
om
a
l
y s
c
or
e
for
t
h
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r
e
c
or
d
.
It
d
et
er
m
i
n
e
s
w
he
t
he
r t
h
i
s
re
c
o
rd
i
s
a
no
m
a
l
o
u
s
o
r no
t
o
n t
he
f
l
y
.
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n
a
no
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l
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s
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o
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i
s
a
s
s
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g
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d
t
o
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a
c
h p
a
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t
(
re
c
o
rd
)
b
a
s
e
d
o
n w
he
t
he
r t
he
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c
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rd
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a
s
m
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f
re
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u
e
nt
o
r
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f
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q
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n
t p
at
te
r
n
s
.
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h
is
a
lg
o
r
it
h
m
im
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v
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th
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o
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A
p
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i alg
o
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it
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m
w
it
h
a c
o
n
s
t
r
a
i
n
t
.
T
h
e
c
o
n
s
t
r
ai
n
t av
o
id
s
j
o
in
i
n
g
i
te
ms
e
ts
n
o
t lik
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ly
t
o
p
r
o
d
u
c
e
f
r
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q
u
e
n
t
ite
ms
e
ts
as
t
h
e
i
r
r
e
s
u
lts
,
t
h
e
r
e
b
y
imp
r
o
v
in
g
e
f
f
ic
ie
n
cy
an
d
r
u
n
ti
me
s
s
ig
n
if
ic
an
tly
.
H
a
gl
i
n
a
n
d M
a
nni
n
g [
5
]
i
n
t
r
o
duc
e
d a
n
a
l
go
ri
t
hm
k
n
o
w
n
a
s
M
IN
IT
(
M
i
n
i
m
a
l
l
y
In
f
r
e
que
nt
I
te
m s
e
t)
f
o
r
min
in
g
m
in
i
ma
l
in
f
r
e
q
u
e
n
t
it
e
m
s
b
y
s
o
r
t
in
g
a
n
d
r
a
n
k
in
g
i
t
em
s
b
a
s
e
d
o
n
th
e s
u
p
p
o
r
t.
Th
e it
e
m
s
th
a
t
h
o
l
d
s
u
p
p
o
r
t
l
es
s
t
h
a
n
m
i
n
s
u
p
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r
e
s
el
ec
t
e
d
.
T
h
en
,
o
n
l
y
t
h
e
t
r
an
s
act
i
o
n
s
w
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c
h
c
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t
a
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t
h
o
s
e
i
t
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m
s
a
r
e
ch
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s
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n
f
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
2088
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8708
Int
J
E
l
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&
Co
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p
E
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g
,
V
ol
.
9
,
N
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6
,
D
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b
er
201
9
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5
446
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5
453
5448
f
u
rt
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r p
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r
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k
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ep
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b
y
ca
l
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l
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e s
u
p
p
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ch
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t
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c
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di
ng o
r
de
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s
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o
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t
.
M
I
N
I
T is
s
u
i
tab
le
f
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a s
ma
ll
s
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z
e
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t
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et
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E
xt
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n
s
i
o
n t
o
M
IN
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,
G
up
t
a
[1
1
] h
a
s
pr
op
os
e
d
a
t
e
c
h
n
i
q
u
e
c
alle
d
m
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ally
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n
f
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t
h
at
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als
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m
e
nt
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a
s
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II.
M
II
T
h
i
s
t
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c
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n
i
q
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e i
s
d
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s
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g
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b
a
s
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d
o
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I
n
v
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s
e F
P
-
T
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e
e
(IF
P
).
T
h
e
IF
P
-
T
r
ee r
ecu
r
s
i
v
el
y
m
i
n
e
s
mi
n
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ly
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ar
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p
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al
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n
im
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f
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te
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t mi
n
e
d
f
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t
h
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p
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e
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te
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tr
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e
mu
s
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t s
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au
s
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e
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ms
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ts
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lf
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s
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r
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d
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a
l
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r
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t
em
i
s
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t
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p
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en
t
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t
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o
f
t
h
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d
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a
l
d
at
a
b
a
s
e
co
r
r
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p
o
n
d
i
n
g
t
o
t
h
e
i
t
e
m
.
T
h
e
u
s
e
o
f
r
es
i
d
u
a
l
t
r
ees
r
ed
u
c
es
t
h
e
co
m
p
u
t
a
t
i
o
n
t
i
m
e
a
n
d
s
u
i
t
a
b
l
e
f
o
r
l
ar
g
e
d
en
s
e d
a
t
a
s
et
s
.
T
h
e
RP
-
T
r
e
e al
g
o
r
i
t
h
m
w
a
s
d
e
v
el
o
pe
d
by
T
s
a
n
g
e
t
a
l
.
[12
]
t
o
a
voi
d
t
h
e ex
p
e
n
s
i
v
e i
t
em
s
et
ge
n
e
ra
t
i
o
n
a
n
d
p
r
u
ni
n
g s
t
e
ps
by
us
i
n
g
a
t
r
e
e
da
t
a
s
t
r
uc
t
u
re
.
It
i
s
de
s
i
g
n
e
d b
a
s
e
d o
n
F
P
-
T
r
ee an
d
u
til
ize
d
a
t
wo
-
pa
s
s
a
ppr
o
a
c
h
t
o
f
i
n
d
th
e
i
nf
re
q
u
e
nt
p
a
t
t
e
r
ns
.
RP
-
T
r
ee
ex
e
cu
t
e
s
a
d
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b
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t t
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ite
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p
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u
r
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c
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nd
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a
n
,
o
nl
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a
c
t
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w
hi
c
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nc
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w
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i
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a
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p
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s
t
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o
t
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rs
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T
he
p
ro
p
o
s
e
d
R
P
-
T
r
ee a
l
g
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t
h
m
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s
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m
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en
t
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s
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g
a
l
g
o
r
ith
m
s
in
t
h
r
e
e
w
a
y
s a
s f
o
l
l
o
ws:
−
RP
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T
r
ee a
v
o
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d
s
t
h
e ex
p
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n
s
i
v
e i
t
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et
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ep
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s
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t
r
ee
d
at
a s
t
r
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ct
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r
e
,
b
a
s
ed
on
F
P
-
T
r
ee,
t
o
f
i
n
d
r
ar
e
p
a
t
t
er
n
s
.
−
RP
-
T
r
ee f
o
cu
s
e
s
o
n
r
ar
e
-
i
te
m ite
ms
e
ts
w
h
ic
h
g
e
n
e
r
ate
s
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n
t
e
r
e
s
ti
n
g
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u
le
s
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d
d
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s
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o
t c
o
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s
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me
m
uc
h
t
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m
e
l
ook
i
n
g for
un
i
n
t
e
r
e
s
t
i
n
g
n
on
-
ra
re
-
i
te
m ite
ms
e
ts
.
−
RP
-
T
r
ee i
s
b
a
s
ed
o
n
F
P
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G
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o
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th
,
w
h
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f
f
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n
t at
f
in
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g
lo
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s
.
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.
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e
ne
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A
p
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o
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d
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t
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can
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nni
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s
A
p
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o
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.
H
o
w
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l
d
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g
t
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e t
r
ee f
o
r
r
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e p
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t
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m
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m
o
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e co
m
p
l
i
cat
ed
.
R
ece
n
t
l
y
,
J
us
o
h
e
t
.
a
l
[13
, 1
4
]
pr
op
os
e
s
a
v
er
t
i
ca
l
d
a
t
a
r
ep
r
es
e
n
t
at
i
o
n
,
c
a
l
l
ed
R
-
Ec
lat
a
l
g
o
r
ith
m
,
an
E
c
l
at
-
ba
s
e
d
a
p
p
r
o
a
ch
e
s
u
s
i
n
g
i
n
t
e
r
s
ect
i
n
g
t
r
a
n
s
a
ct
i
o
n
I
D
.
E
c
l
at
-
ba
s
e
d
[
15
]
t
a
k
es
a d
ep
t
h
-
f
i
r
s
t
s
ea
r
c
h
an
d
ad
o
p
t
s
a v
er
t
i
c
al
l
a
y
o
u
t
t
o
r
e
p
r
e
s
en
t
d
a
t
a
b
a
s
es
,
i
n
w
h
i
c
h
ea
ch
i
t
e
m
i
s
r
e
p
r
e
s
en
t
ed
b
y
a
s
e
t
o
f
t
r
a
n
s
a
ct
i
o
n
I
D
s
(
als
o
c
alle
d
a
s t
i
d
se
t
s)
.
T
h
e
r
e
ma
i
n
d
e
r
o
f
th
is
p
ap
e
r
is
o
r
g
a
n
ize
d
as
f
o
llo
w
s
: S
e
c
tio
n
3
d
is
c
u
s
s
e
s
th
e
R
-
Ec
la
t a
lg
o
r
it
h
m i
n
d
e
tails
.
T
h
e
r
es
u
l
t
s
o
f
t
h
e
p
er
f
o
r
m
an
c
e
a
n
a
l
y
s
i
s
w
i
l
l
b
e
p
r
e
s
en
t
ed
i
n
S
e
ct
i
o
n
4
.
S
e
c
t
i
o
n
5
s
um
s
up
t
h
e
p
a
pe
r
w
ith
c
on
c
l
u
s
i
on
s
.
3.
R
-
E
CL
AT
AL
G
O
RIT
H
M
In
[15]
,
Z
ak
i p
r
o
p
o
s
e
s
Eq
u
iv
ale
n
c
e
C
las
s
T
r
a
n
s
f
o
r
mat
io
n
(
EC
L
A
T)
a
lg
o
r
i
t
h
m,
w
h
ic
h
t
r
a
n
s
f
o
r
ms
t
h
e
o
r
ig
i
n
a
l d
at
as
e
t i
n
to
a
v
e
r
tic
a
l d
at
ab
as
e
f
o
r
ma
t
.
E
ac
h
s
i
n
g
le
i
te
m is
s
to
r
e
d
i
n
t
h
e
d
a
tas
e
t
to
g
e
th
e
r
w
it
h
a
l
is
t
o
f
tr
a
n
s
ac
t
io
n
-
i
d
s
(
t
i
d
s
et
)
w
h
e
r
e
t
h
e
i
t
e
m
c
an
b
e
f
o
u
n
d.
E
CL
A
T
c
o
n
s
i
de
r
s
t
h
e
f
r
e
que
n
c
y
of
a
pa
t
t
e
rn
P
as
th
e
le
n
g
t
h
o
f
th
e
tr
a
n
s
ac
tio
n
-
id
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l
is
t.
T
h
is
a
lg
o
r
i
t
h
m d
e
te
r
mi
n
e
s
t
h
a
t a
n
y
ite
ms
e
t is
f
r
e
q
u
e
n
t if
it lis
ts
at le
as
t
f
mi
n
t
r
a
n
s
a
ct
i
o
n
-
i
d
s
, i
.e
. |
t
(
P
)
|
≥
f
mi
n
.
A
n
i
mp
o
r
ta
n
t f
e
atu
r
e
o
f
EC
L
A
T is
th
e
f
as
t in
te
r
s
e
c
tin
g
tid
s
lis
t
,
t
h
u
s
t
h
e
s
ize
o
f
tid
s
lis
t is
o
n
e
o
f
th
e
ma
i
n
f
ac
to
r
s
af
f
e
c
tin
g
t
h
e
e
x
ec
u
tio
n
ti
me
a
n
d
me
mo
r
y
u
s
ag
e
o
f
EC
L
A
T.
N
e
v
e
r
t
h
e
le
s
s
,
i
ts
e
x
e
c
u
tio
n
t
ime
is
le
s
s
t
h
a
n
A
p
r
io
r
i
alg
o
r
it
h
m.
EC
L
A
T
is
t
h
e
f
ir
s
t a
lg
o
r
ith
m
th
a
t u
s
e
s
a
v
e
r
tic
al d
a
ta
l
ay
o
u
t
an
d
v
e
r
y
ef
f
ic
ie
n
t
f
o
r
la
r
g
e
ite
ms
e
ts
b
u
t
le
s
s
ef
f
ic
ie
n
t f
o
r
s
mal
l
ite
ms
e
ts
.
T
h
e
f
r
e
q
u
e
n
t
ite
ms
e
ts
a
r
e
d
e
te
r
m
i
n
e
d
u
s
i
n
g
s
i
mp
le
tid
s
lis
t
i
n
te
r
s
e
c
tio
n
s
in
a d
e
p
t
h
-
f
i
rs
t
s
e
a
rc
h g
ra
p
h
.
A
va
r
i
a
t
i
on
of
t
h
e E
c
l
a
t al
g
o
r
i
t
h
m t
h
at
is
imp
le
me
n
te
d
u
s
i
n
g
d
if
f
e
r
e
n
t s
t
r
u
c
tu
r
e
a
r
e
c
al
le
d
tid
s
e
t (
Ec
la
t)
[
1
5
]
,
d
if
f
s
e
t [
1
6
]
,
s
o
r
t
di
f
f
s
e
t
[17] a
n
d
i
E
c
l
a
t
[
13,
18]
.
M
o
tiv
at
i
n
g
f
r
o
m t
h
e
f
as
t i
n
te
r
s
e
c
tio
n
s
o
f
tid
s
lis
t
i
n
EC
L
A
T
as
w
e
ll as
h
o
w
d
o
e
s
i
t
a
f
f
ec
t
s
t
h
e
r
u
n
n
i
n
g
t
i
m
e an
d
m
e
m
o
ry
u
s
a
g
e
,
i
t
b
ri
ng
s
t
he
a
u
t
ho
r t
o
e
x
p
l
o
re
a
nd
d
i
s
c
o
v
e
r a
f
u
rt
he
r
r
es
e
ar
c
h
in
th
i
s
a
lg
o
r
ith
m e
s
p
e
ci
a
l
l
y
f
o
r
m
in
in
g
in
f
r
e
q
u
e
n
t p
a
t
t
er
n
s
.
Th
e
R
-
EC
L
A
T
alg
o
r
it
h
m
is
a
n
o
v
e
l te
c
h
n
iq
u
e
t
h
at s
p
e
c
ially
ge
n
e
ra
t
e
d
f
o
r
i
n
f
r
e
que
n
t
pa
t
t
e
n
m
i
ni
n
g [14
,
19].
It
i
s
de
s
i
g
n
e
d
b
a
s
e
d
o
n
t
h
e
t
ra
di
t
i
o
n
a
l
E
CL
A
T
a
l
go
ri
t
hm
.
T
h
i
s
a
l
go
ri
t
hm
us
e
s
a
de
pt
h
-
f
i
r
s
t
s
e
a
r
c
h
t
o
a
c
h
i
ev
e a
co
n
d
e
n
s
ed
r
ep
r
es
e
n
t
at
i
o
n
o
f
t
h
e t
r
a
n
s
a
c
t
i
o
n
d
a
t
a
b
a
s
e.
I
t
u
t
i
l
i
z
es
co
l
u
m
n
-
b
a
s
e
d
(
v
e
r
t
i
ca
l
)
r
a
t
he
r t
ha
n
ro
w
-
b
a
s
ed
(
h
o
r
i
z
o
n
t
a
l
)
t
o
r
ep
r
es
en
t
t
h
e
d
at
a
s
et
.
R
-
E
CL
A
T
c
o
unt
s
t
h
e
s
u
ppo
r
t
t
hr
o
ug
h de
t
e
rm
i
ni
n
g
s
u
p
p
or
t
of a
n
y k
-
ite
ms
e
ts
o
n
t
h
e
i
n
te
r
s
e
c
ti
n
g
tid
-
lis
ts
o
f
its
k
-
1 s
ub
s
e
t
s
.
I
n
t
h
e
R
-
E
C
LA
T
a
l
g
o
r
ith
m,
t
h
e
t
r
ad
it
io
n
a
l
t
id
s
e
t,
d
if
f
s
e
t
a
n
d
s
o
r
t
-
d
i
f
f
s
et
v
a
r
i
a
n
t
s
ar
e
en
h
an
c
ed
t
o
e
n
s
u
r
e
t
h
a
t
i
t
i
s
a
p
p
r
o
p
r
i
a
t
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f
o
r
m
i
n
i
n
g
an
i
n
f
r
eq
u
en
t
p
a
t
t
e
r
n
.
T
h
e F
i
g
u
r
e
1
i
l
l
u
s
t
r
at
es
t
h
e m
o
d
el
o
f
R
-
Ec
lat d
iv
is
io
n
f
o
r
m
ats
w
h
ic
h
a
r
e
n
ame
d
a
s I
F
-
Tid
s
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t,
I
F
-
D
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f
fs
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t
a
n
d
I
F
-
S
o
rt
d
i
f
f
s
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t
w
he
re
I
F
i
s
re
p
re
s
e
nt
e
d
a
s
i
nf
re
q
u
e
nt
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
E
l
e
c
&
Co
m
p
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n
g
I
SSN:
2088
-
8708
A
nal
y
s
i
s
s
t
udy
on
R
-
E
c
l
at
al
gor
i
t
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i
n
i
n
f
r
e
qu
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t
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t
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m
s
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t
s
m
i
ni
ng
(
Mus
t
af
a M
an)
5449
F
i
g
ur
e
1.
R
-
E
c
l
a
t
a
lg
o
r
ith
m
m
o
d
e
l
[16]
Th
e
ma
in
s
t
e
p
s
in
R
-
E
cl
a
t
o
v
e
r
t
h
e d
a
t
a
s
et
a
r
e
l
i
s
t
e
d
a
s
f
o
l
l
o
w
s
:
St
e
p
1 (
G
e
ne
r
a
t
i
on)
:
s
can
s
t
h
e d
at
a
b
a
s
e t
o
g
e
n
e
r
a
t
e
k
-
it
e
ms
e
t
ca
n
d
i
d
a
t
e
s
f
r
o
m
t
w
o
f
r
e
q
u
en
t
(
k
-
1)
-
i
te
ms
e
ts
an
d
i
t
s
s
uppo
rt
i
s
c
o
unt
e
d.
St
e
p 2
(
P
r
une
)
:
if
its
s
u
p
p
o
r
t is
g
r
e
a
te
r
t
h
a
n
t
h
e
m
i
n
i
mu
m s
u
p
p
o
r
t t
h
r
e
s
h
o
ld
,
t
h
e
n
it w
ill
b
e
d
is
c
ar
d
e
d
,
o
t
h
e
r
w
i
s
e
i
t
i
s
de
n
o
t
e
d a
s
i
n
f
r
e
que
n
t
i
t
e
m
s
e
t
s
a
nd us
e
d
t
o
ge
ne
r
a
t
e
(k+
1)
-
i
te
ms
e
ts
.
S
t
ep
1
i
s
r
e
p
ea
t
ed
u
n
t
i
l
n
o
c
an
d
i
d
a
t
e
i
t
em
s
e
t
ca
n
b
e g
e
n
e
r
at
ed
.
S
u
b
s
e
q
u
en
t
l
y
,
t
h
e
m
i
ni
m
um
s
up
po
r
t
t
hr
e
s
h
o
l
d v
a
l
ue
(M
S
T
V
) i
s
c
o
n
s
i
de
r
e
d a
s
a
b
e
n
c
hm
a
rk t
o
di
s
c
o
ve
r
a
l
o
w
oc
c
ur
r
e
n
c
e
i
n
e
a
c
h
d
a
t
a
s
e
t
.
I
n
[18]
,
M
S
T
V
i
s
d
et
e
r
m
i
n
ed
i
n
t
e
r
m
s
o
f
t
h
e p
er
ce
n
t
a
g
e,
δ
1
0
0
∗
α
w
he
re
δ
=
U
s
e
r
s
pe
c
i
f
i
e
d m
i
ni
m
um
s
uppo
rt
v
a
l
ue
α
=
T
ot
a
l
of r
e
c
or
d
s
i
n
d
at
a
s
et
s
.
In e
a
c
h
l
o
o
p,
s
t
a
rt
s
w
i
t
h
t
h
e
f
i
r
s
t
l
o
o
p,
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f
t
h
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s
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i
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s
s
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qu
a
l
(<
=
)
t
o
m
i
n
_s
upp
,
t
h
e
n
,
−
In IF
-
T
id
s
e
t,
o
b
tain
t
h
e
r
e
s
u
l
t o
f
in
te
r
s
e
c
tio
n
b
e
tw
e
e
n
i
th
co
l
u
m
n
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d
i
th
+
1 c
ol
u
m
n
a
n
d
s
a
ve
t
o
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h
e d
at
a
b
a
s
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−
In
IF
-
D
if
f
s
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t,
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n
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e
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s
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lt o
f
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t (
d
if
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e
r
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e
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1
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[3
]
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.
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.
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[4
]
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. H
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al
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1.
[5
]
D.
J
.
Ha
g
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.
M
.
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.
[6
]
R
.
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g
r
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w
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al
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GM
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3.
[7
]
R
.
Ag
r
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.
[8
]
J
.
Ha
n
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e
t
a
l
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4.
[9
]
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,
pp
.
337
-
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,
199
9.
[
10]
A
.
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l
.
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.
58
40,
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p.
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1
0.
[
11]
A
.
G
upt
a
,
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t a
l.
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“
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m
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l
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r
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es
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RR
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/
1207
.
4
958
,
2012
.
[
12]
S
.T
s
a
n
g
,
e
t
a
l
.
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“
RP
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r
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R
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s
.
)
,
S
p
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r
,
B
e
r
l
i
n,
vol
.
6
86
2,
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.
277
-
288
,
201
1.
[
13]
J.
A
.
Ju
so
h
a
nd
M.
Ma
n
,
“
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o
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n
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E
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g
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d
v
a
n
c
ed
S
ci
en
c
e
L
et
t
er
s
,
vol
.
2
4
,
20
1
8.
[
14]
J.
A
.
Ju
so
h
,
e
t a
l.
,
“
M
i
n
i
ng
I
nf
r
e
que
nt
P
a
t
t
e
r
ns
U
s
i
ng
R
-
E
c
l
a
t
A
l
g
o
r
i
t
h
m
s
,”
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o
ur
n
al
o
f
F
undam
e
nt
a
l
and
A
pp
l
i
e
d
S
c
i
en
c
es
,
vol
.
2
4,
2
0
1
8.
[
15]
M
. J
. Z
a
k
i
,
et
a
l
.
, “
N
e
w
A
l
gor
i
t
hm
s
f
or
F
as
t
D
i
s
c
o
v
e
r
y
of
A
s
s
oc
i
a
t
i
on R
u
l
e
s
,
”
A
C
M
S
I
GKD
D
I
n
t
e
r
n
a
t
i
o
n
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l
C
on
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e
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e
n
c
e
on
K
n
ow
l
e
d
ge
D
i
s
c
ove
r
y
a
nd D
a
t
a
M
i
n
i
ng
,
p
p.
28
3
-
2
86
,
199
7.
[
16]
M
.
J
.
Z
a
ki
a
nd
K
.
G
o
uda
,
“
F
a
s
t
V
e
r
t
i
c
a
l
M
i
n
i
n
g
U
s
i
n
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D
i
f
f
s
e
t
s
,
”
A
C
M
S
I
G
K
D
D
I
nt
e
r
na
t
i
o
na
l
C
o
nf
e
r
e
nc
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o
n
K
n
ow
l
e
d
ge
D
i
s
c
ove
r
y
a
n
d
D
a
t
a
M
i
ni
n
g
,
200
3.
[
17]
T
. A
. T
r
i
e
u
a
nd
Y
.
K
un
i
e
da
,
“
A
n
I
m
p
r
o
v
e
m
e
n
t
f
o
r
D
e
c
l
a
t
A
l
g
o
r
i
t
h
m
,”
T
he
6t
h
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
U
bi
qu
i
t
o
us
I
nf
o
r
m
a
t
i
o
n M
a
na
g
e
m
e
n
t
a
nd
C
o
m
m
uni
c
a
t
i
o
n,
v
o
l
.
54
,
2012
.
[
18]
W.
A.
B.
W.
A
.
B
a
k
a
r
,
e
t
al
.
,
“
I
n
c
r
em
en
t
a
l
-
E
c
l
a
t
M
ode
l
:
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n I
m
pl
e
m
e
nt
at
i
on v
i
a B
e
nc
hm
ar
k
C
a
s
e
St
ud
y
,
”
S
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