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[
1
1]
pr
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ppr
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ba
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h.
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hi
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udy pr
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nt
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h t
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l
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h
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t f
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o
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t
h
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s
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ch
al
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f
r
eq
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en
t
i
t
em
s
et
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er
at
ed
m
et
h
o
d
,
but
i
n
c
ont
r
a
s
t
t
o
[1
1
],
w
e
m
o
d
i
f
i
ed
t
h
e
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ex
t
l
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pr
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o t
ha
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[
1
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]
bui
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n
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a
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mb
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nod
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w
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ow
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us
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b
as
ed
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at
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t
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ct
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[
10]
,
[
11]
s
t
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us
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l
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ge
m
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m
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r
y by
s
c
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cr
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l
gor
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hm
f
or
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node
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i
nde
x of
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he
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r
e
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ha
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hi
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a
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c
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n
am
el
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as
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node
c
a
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ul
a
t
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on a
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i
ni
m
i
z
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t
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os
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of
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/
O
pr
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by us
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r
om
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r
pe
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s
pe
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t
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s
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on t
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us
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put
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r
w
i
t
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u
l
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c
or
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ar
ch
i
t
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r
e
[
12]
i
n s
uppor
t
i
ng
da
t
a
pr
oc
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s
s
i
ng.
T
hi
s
r
a
i
s
e
s
t
he
s
us
pi
c
i
on t
ha
t
mu
lti
-
t
h
r
ead
i
n
[
13]
a
nd
[
14]
c
a
n pr
oduc
e
be
t
t
e
r
pe
r
f
or
m
a
nc
e
a
l
s
o i
n ge
t
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t
hi
s
f
r
e
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nt
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m
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,
a
s
w
e
l
l
a
s
a
c
ha
l
l
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nge
on how
t
o
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et
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m
i
n
e t
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b
es
t
p
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f
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m
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p
r
o
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s
ar
ch
i
t
ect
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r
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t
ha
t
i
s
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ppl
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d t
o w
hi
c
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ubpr
oc
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a
s
t
hr
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a
d
s
a
nd how
bi
g i
s
t
he
i
nc
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e
a
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e
f
or
t
he
be
s
t
mu
lti
-
t
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hi
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c
t
ur
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s
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ngl
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r
onm
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e
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n e
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pe
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i
m
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-
node
s
e
r
ve
r
e
nvi
r
onm
e
nt
w
a
s
pr
opos
e
d by
[
15]
,
[
16]
.
T
he
p
r
oc
e
s
s
of
c
a
l
c
ul
a
t
i
ng
t
he
va
l
ue
o
f
s
uppor
t
i
n
t
he
c
a
ndi
da
t
e
s
e
t
s
g
en
er
at
i
o
n
in
th
is
p
r
o
b
le
m
is
a
bot
t
l
e
ne
c
k pr
oc
e
s
s
,
be
c
a
us
e
t
hi
s
pr
oc
e
s
s
w
i
l
l
c
a
us
e
de
l
a
ys
a
nd que
ue
s
t
o be
f
or
w
a
r
de
d
t
o t
he
ne
x
t
p
r
o
c
e
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I
f
you onl
y us
e
a
s
ta
n
d
a
r
d
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p
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io
r
i a
lg
o
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ith
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t
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a
ta
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tr
u
c
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w
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till
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o
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ead
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n
t
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m
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z
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t
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m
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e
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r
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d
f
or
pr
oc
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s
s
i
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s
uppor
t
can
d
i
d
at
e s
et
s
.
F
or
t
h
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t
hr
e
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d m
ode
l
,
t
hi
s
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s
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a
r
c
h a
ppl
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hr
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n e
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c
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um
of
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r
a
ns
a
c
t
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on da
t
a
a
nd not
i
n
e
a
c
h
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ms
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t c
o
mb
in
a
tio
n
lik
e
[
17]
a
n
d
imp
le
me
n
ts
mu
lti
-
t
h
r
ead
not
l
i
ke
[
1
8]
,
w
h
i
ch
ev
al
u
at
es
i
n
s
i
ngl
e
-
t
h
r
ead
ed
p
er
f
o
r
m
an
ce.
2.
R
ES
EA
R
C
H
M
ETH
O
D
T
h
e r
es
ear
ch
co
n
d
u
ct
ed
i
s
a
q
u
an
t
i
t
at
i
v
e
r
es
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ch
u
s
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n
g
ex
p
er
i
m
en
t
al
r
es
ear
ch
t
ech
n
i
q
u
es
.
T
h
e
e
xpe
r
i
m
e
nt
i
s
di
vi
de
d i
nt
o t
w
o t
ype
s
,
na
m
e
l
y
s
in
g
le
-
t
hr
e
a
d a
nd
mu
lti
-
t
h
r
ead
p
r
o
ces
s
es
.
T
h
e p
r
o
ces
s
i
n
g
t
i
m
e
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un by e
a
c
h m
e
t
hod i
s
c
om
pa
r
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d
t
o be
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yz
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d
i
n t
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r
m
s
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pe
e
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f
i
c
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e
nc
y f
o
r
a
ddi
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va
l
u
e
of
t
he
s
uppor
t
c
ount
c
a
ndi
da
t
e
s
e
t
.
T
he
p
r
oc
e
s
s
i
ng t
i
m
e
de
t
e
r
m
i
ne
s
t
he
qua
l
i
t
y of
t
he
m
e
t
hod de
s
i
gne
d a
s
w
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l
l
a
s
t
he
qua
l
i
t
y of
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e
f
f
i
c
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e
nc
y of
t
he
t
h
r
e
a
d us
e
d w
i
t
h a
da
t
a
s
t
r
uc
t
ur
e
t
ha
t
ha
s
be
e
n s
pe
c
i
a
l
l
y de
s
i
gne
d by
a
ppl
yi
ng
t
h
e
tr
ie
co
n
cep
t.
T
he
num
be
r
of
t
r
a
ns
a
c
t
i
ons
t
ha
t
c
o
n
si
st
d
a
t
a
se
t
fo
r t
h
e
e
xpe
r
i
m
e
nt
i
s
100,
000 t
r
a
ns
a
c
t
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ons
a
nd 5 t
o
150 i
t
e
m
va
r
i
a
nt
s
.
T
h
e d
at
as
et
u
s
ed
i
s
d
i
f
f
er
en
t
f
o
r
each
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p
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i
m
en
t
,
b
ecau
s
e t
h
e d
at
a i
s
g
en
er
at
ed
r
an
d
o
m
l
y
us
i
ng a
m
e
t
hod.
T
he
m
e
t
hod w
a
s
s
pe
c
i
f
i
c
a
l
l
y m
a
de
i
n t
hi
s
s
t
udy
t
o ge
ne
r
a
t
e
da
t
a
a
c
c
or
di
ng t
o
t
he
ne
e
ds
of
t
h
i
s
r
es
ear
ch
s
o
f
t
w
ar
e.
T
ab
l
e
1
c
ont
a
i
ns
e
xa
m
pl
e
s
of
da
t
a
ge
ne
r
a
t
e
d f
or
e
xpe
r
i
m
e
nt
a
l
ne
e
ds
w
i
t
h t
he
num
be
r
of
15
i
te
m v
a
r
ia
n
ts
.
T
o c
a
l
c
ul
a
t
e
t
he
va
l
ue
of
s
uppor
t
c
ount
,
t
r
an
s
act
i
o
n
d
at
a i
s
vi
e
w
e
d one
by one
.
I
f
a
s
ubs
e
t
of
t
r
a
ns
a
c
t
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s
f
ound,
t
he
s
uppor
t
c
ount
v
al
u
e i
n
cr
eas
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d
by 1.
T
r
i
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not
onl
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s
t
or
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s
c
a
ndi
da
t
e
s
but
a
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et
f
r
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m
t
h
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an
s
act
i
o
n
d
at
a.
A
f
t
er
t
h
e f
i
r
s
t
d
at
ab
as
e,
t
h
e f
r
eq
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en
cy
f
o
r
each
i
t
em
i
s
o
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t
ai
n
ed
.
S
to
r
in
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he
s
uppor
t
c
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d
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t
em
s
et
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al
u
es
w
ill i
n
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r
e
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s
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me
mo
r
y
r
e
q
u
ir
e
me
n
t a
little
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in
e
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c
h
a
n
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e
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th
is
i
n
cr
eas
es
t
h
e s
p
eed
o
f
r
et
r
i
ev
i
n
g
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t
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ap
p
ear
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ces
o
r
t
h
e s
u
p
p
o
r
t
c
ount
v
al
u
es
o
f
th
e
ite
ms
e
t
[
19]
.
T
he
obj
e
c
t
i
ve
s
of
c
onduc
t
i
ng
t
hi
s
e
xpe
r
i
m
e
nt
a
r
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
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s
or
s
ba
s
e
d on t
i
m
e
,
a
l
s
o know
i
ng t
he
num
be
r
of
t
hr
e
a
ds
a
nd t
he
e
f
f
i
c
i
e
nt
mu
lti
-
t
h
r
ead
m
ode
l
i
n t
he
a
ppl
i
c
a
t
i
on o
f
t
he
can
d
i
d
at
e s
et
cal
cu
l
at
i
o
n
p
r
o
ces
s
.
A
th
r
e
a
d
is
lik
e
a
s
ma
ll,
lig
h
tw
e
ig
h
t p
r
o
c
e
s
s
i
n
p
r
o
ces
s
.
A
co
l
l
ect
i
o
n
o
f
t
h
r
ead
s
i
s
cal
l
ed
a
p
r
o
ces
s
[
20]
.
M
u
lti
-
t
h
r
ead
c
a
n
be
m
a
na
ge
d i
nde
pe
nde
nt
l
y,
a
l
s
o de
pe
nde
nt
l
y da
t
a
-
dr
i
ve
n.
D
i
s
t
r
i
b
ut
i
on of
t
hr
e
a
ds
on
mu
lti
-
t
h
r
ead
t
h
at
ar
e m
an
ag
ed
d
at
a
-
dr
i
ve
n de
pe
nde
nt
l
y onl
y on t
he
a
m
ount
of
da
t
a
.
E
a
c
h d
a
t
a
goe
s
t
hr
ough a
l
l
pr
oc
e
s
s
e
s
,
t
he
n t
he
pr
oc
e
s
s
f
or
n da
t
a
i
s
a
ppl
i
e
d t
o a
t
hr
e
a
d.
M
e
a
nw
hi
l
e
,
t
he
di
s
t
r
i
but
i
on o
f
t
hr
e
a
ds
i
n
mu
lti
-
t
h
r
ead
i
s
m
a
na
ge
d i
nde
pe
nde
nt
l
y,
na
m
e
l
y i
n e
a
c
h pr
oc
e
s
s
onl
y
[
21]
.
F
i
gur
e
1 s
how
s
t
hi
s
r
e
s
e
a
r
c
h
m
e
t
hod.
T
ab
l
e 1
.
D
a
t
a
t
o be
us
e
d f
or
e
xpe
r
i
m
e
nt
s
T
ID
I
te
ms
T1
{
1, 4, 7, 8, 9, 10, 14}
T2
{
2, 3, 4, 5, 6, 7, 8, 10, 13, 14}
T3
{
4, 6}
…
…
T
100000
{
1, 4, 7, 9, 12, 13}
Problem domain
analysis and
experimental design
:
-
index search
method of candidate
set
;
-
support count
process
;
-
multi
-
threaded model
design
;
-
preparation of
experimental data and
scenario using random
data
;
Results of the
problem
domain
analysis
Experiment
al data
Experiment
al scenario
Software
development
Software
Conducting
experiments
Multi
-
thread
experimental
results
Single
-
thread
experimental
results
Calculates the
average single
-
thread
processing time
Calculates the
average multi
-
thread
processing time
Single
-
thread
processing
average
Multi
-
thread
processing
average
Discussion of
experimental
results
Quality of the
thread model in
the calculation
of support
F
i
gur
e
1.
R
es
ear
ch
m
et
h
o
d
3.
R
ES
U
LTS
A
ND
ANAL
YS
I
S
I
n
t
h
i
s
r
es
ear
ch
,
t
h
e
A
pr
i
or
i
a
l
gor
i
t
hm
i
s
de
ve
l
o
pe
d ba
s
e
d on a
t
r
e
e
us
i
ng t
he
t
r
i
e
da
t
a
s
t
r
uc
t
u
r
e
a
ppr
oa
c
h,
a
s
s
e
e
n i
n
F
i
gur
e
2
.
T
he
m
odi
f
i
c
a
t
i
on of
t
he
A
pr
i
or
i
a
l
gor
i
t
h
m
i
s
c
a
r
r
i
e
d ou
t
ba
s
e
d
on
t
he
r
e
l
a
t
i
ons
hi
p be
t
w
e
e
n t
he
pa
r
e
nt
va
l
ue
a
nd
t
he
n
u
mb
e
r
o
f
c
h
ild
r
e
n
to
o
b
ta
in
a
f
o
r
mu
la
to
c
a
lc
u
l
at
e t
h
e
H
a
sh
-
n
o
d
e cal
cu
l
at
i
o
n
.
T
ab
l
e
2
e
xpl
a
i
ns
how
t
he
t
r
i
e
da
t
a
s
t
r
uc
t
ur
e
i
s
us
e
d t
o
de
t
e
r
m
i
ne
t
he
va
l
ue
of
a
n i
nde
x.
F
i
gur
e
2
.
I
l
lu
s
tr
a
tio
n
o
f
tr
ie
f
o
r
4
-
ite
ms
e
t g
e
n
e
r
a
tio
n
1
0
2
3
4
5
1
2
3
4
2
6
3
7
4
11
3
4
15
4
13
4
8
3
9
4
14
4
10
4
12
Sum
_
Child
n
-
itemset
Parent
n
-
itemset
Node
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
,
Vo
l
.
19
, N
o
.
5
,
O
c
t
obe
r
2021:
1553
-
1563
1556
T
ab
l
e
2
.
I
llu
s
tr
a
tio
n
o
f
n
-
i
t
em
s
et
can
d
i
d
at
e
g
en
er
at
i
o
n
N
ode
P
ar
en
t
S
u
m_
C
h
ild
(n
-
I
te
ms
e
t)
0
-
4
0
1
0
3
1
2
0
2
2
3
0
1
3
4
0
0
4
5
1
2
1,2
6
1
1
1,3
7
1
0
1,4
8
2
1
2,3
9
2
0
2,4
10
3
0
3,4
11
5
1
1,2,3
12
5
0
1,2,4
13
6
0
1,3,4
14
8
0
2,3,4
15
11
0
1,2,3,4
3.
1.
A
n
al
ays
i
s
T
he
i
nde
x i
n
t
hi
s
r
e
s
e
a
r
c
h i
s
not
l
i
ke
a
c
or
r
e
l
a
t
i
on
be
t
w
e
e
n s
om
e
t
hi
ngs
[
22]
,
but
i
t
m
e
a
ns
a
n a
ddr
e
s
s
of
t
he
c
a
ndi
da
t
e
s
e
t
(
c
ol
um
n
N
ode
s
)
of
e
a
c
h s
ubs
e
t
(
c
ol
um
n
n
-
I
t
em
s
et
)
g
en
er
at
ed
i
n
4
ite
m v
a
r
ia
n
t
,
a
s se
e
n
i
n
F
i
gur
e
2
.
T
h
e
b
as
i
c m
ech
an
i
s
m
o
f
t
h
e
A
p
ri
o
ri
a
l
gor
i
t
hm
[
5]
i
s
u
s
ed
i
n
t
h
e
r
ev
er
s
e d
i
r
ect
i
o
n
,
w
h
er
e
t
h
e
d
at
ab
as
e acces
s
i
s
d
o
n
e
f
i
r
s
t
.
T
h
e s
u
p
p
o
r
t
co
u
n
t
f
o
r
each
s
u
p
er
s
et
o
f
t
h
e
i
t
em
s
et
can
d
i
d
at
e
i
s
cal
cu
l
at
ed
.
S
o
i
t
t
ak
es
t
h
e g
en
er
at
i
o
n
o
f
a s
u
p
er
s
et
o
f
i
t
em
s
et
can
d
i
d
at
e as
m
u
ch
as
(
2
n
-
1)
.
F
or
e
xa
m
pl
e
,
i
n
t
he
r
i
ght
c
ol
um
n,
na
m
e
l
y,
t
he
n
-
it
e
ms
e
t c
o
lu
mn
s
h
o
w
s
a
s
u
b
s
e
t o
f
a
p
a
r
tic
u
la
r
ite
ms
e
t th
a
t
u
s
e
s
th
e
f
o
r
mu
la
.
F
o
r
e
x
a
mp
le
,
n
-
ite
ms
e
t {
1
,
3} i
s
i
n
N
ode
6
,
a
nd i
t
ha
s
P
a
r
e
nt
w
hi
c
h node
i
s
1,
a
nd i
t
ha
s
S
um
_C
hi
l
d i
s
1
t
ha
t
i
s
N
ode
13
w
hi
c
h ha
s
n
-
ite
m
s
e
t {
1
,
3,
4},
a
s
s
e
e
n i
n F
i
gur
e
3
.
T
he
num
b
e
r
of
s
e
t
s
pr
oduc
e
d by e
a
c
h va
r
i
a
nt
i
t
e
m
4 t
o 6
c
a
n be
s
e
e
n i
n t
he
f
o
l
l
ow
i
ng
f
i
gur
e
.
(
a)
(
c
)
(
b)
F
i
gur
e
3
.
C
an
d
i
d
at
e s
et
f
o
r
:
(
a
)
4
-
ite
ms
e
t; (
b
)
5
-
ite
ms
e
t; a
n
d
(
c
)
6
-
ite
ms
e
t
T
he
pa
t
t
e
r
n
t
ha
t
r
e
s
ul
t
s
f
r
om
t
he
c
a
l
c
ul
a
t
i
on of
t
he
num
be
r
of
c
a
ndi
da
t
e
s
e
t
s
i
n
F
i
gur
e
1
i
s
t
he
P
a
s
c
a
l
tr
ia
n
g
le
p
a
tte
r
n
[
23]
on n
-
i
t
e
m
s
e
t
,
w
he
r
e
(
a
)
n=
4 i
s
4,
6
,
4,
1;
(
b)
n=
5 i
s
5,
10,
10,
5,
1;
a
nd
(
c
)
n=
6 i
s
6
,
1
5,
2
0,
15,
6,
1.
T
he
f
o
r
m
ul
a
f
o
r
ge
t
t
i
ng t
he
va
l
ue
of
t
he
P
a
s
c
a
l
t
r
i
a
ngl
e
i
n t
he
k
-
c
ol
um
n of
e
a
c
h n
-
ite
ms
e
t is
u
s
e
d
b
y
t
he
f
ol
l
ow
i
ng f
or
m
ul
a
:
(
,
)
=
!
!
(
−
)
!
(
1)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
A
nal
y
s
i
s
of
f
r
e
que
nt
i
t
e
m
s
e
t
ge
ne
r
at
i
on bas
e
d on t
r
i
e
dat
a s
t
r
uc
t
ur
e
i
n A
pr
i
or
i
al
gor
i
t
hm
(
A
de
H
odi
j
a
h
)
1557
T
he
c
om
bi
na
t
i
on va
l
ue
s
obt
a
i
ne
d f
r
om
e
a
c
h of
t
h
e
s
e
c
ol
um
ns
a
r
e
t
he
n a
dde
d up unt
i
l
k
r
e
a
c
he
s
l
e
n
-
1.
T
he
n
t
he
num
be
r
o
f
s
ubs
e
t
s
c
a
n be
c
a
l
c
ul
a
t
e
d us
i
ng t
he
f
ol
l
ow
i
ng f
or
m
ul
a
:
1
=
!
!
(
−
)
!
−
1
=
1
(
2
)
N
e
xt
i
s
t
o t
r
a
c
e
t
he
br
a
nc
h poi
nt
s
(
BP
)
f
or
he
i
ght
/
l
e
ve
l
s
t
a
r
t
i
ng f
r
om
t
he
2
-
ite
ms
e
t (
l
ev
el
=2
)
a
nd i
t
s
va
l
ue
i
s
obt
a
i
ne
d f
r
o
m
l
en
-
2
{…
,
l
en
-
2
,
i,
j
}
,
b
es
i
d
e t
h
at
t
h
e v
al
u
e o
f
B
P
i
s
0
(
zer
o
)
.
T
h
e b
r
a
nc
h poi
n
t
s
its
e
lf
co
n
t
ai
n
node
s
t
ha
t
pr
oduc
e
a
c
e
r
t
a
i
n
num
be
r
o
f
s
ubs
e
t
s
ba
s
e
d on t
he
num
be
r
of
i
t
e
m
s
e
t
c
om
bi
na
t
i
ons
.
T
he
n
um
be
r
of
br
a
nc
h poi
nt
c
a
n
be
c
a
l
c
ul
a
t
e
d
us
i
ng t
he
2
f
or
m
ul
a
,
w
hi
c
h c
ons
i
s
t
s
of
t
w
o
f
or
m
ul
a
s
of
(
3
an
d
4
)
,
as
i
t
can
b
e s
een
i
n
f
o
llo
w
in
g
f
o
r
mu
la
:
2
=
∑
3
(
3)
2
i
s
cal
cu
l
at
ed
b
y
t
r
aci
n
g
t
h
e
tr
i
e
t
o t
he
va
l
ue
of
br
a
n
c
h poi
nt
t
h
at
b
ei
n
g
s
ear
ch
ed
f
r
o
m
each
o
f
t
h
es
e co
l
u
m
n
s
a
nd t
he
n a
dde
d unt
i
l
k
r
e
a
c
he
s
l
en
o
r
l
ev
el
.
T
h
e ca
l
cu
l
at
i
o
n
f
o
r
each
v
al
u
e
o
f
t
h
e b
r
an
ch
es
t
h
at
i
s
a
s
u
b
s
et
can
be
c
a
l
c
ul
a
t
e
d us
i
ng t
he
f
ol
l
ow
i
ng
f
o
r
m
ul
a
:
3
=
(
−
(
+
1
)
)
(
−
)
2
(
4)
y
3
i
s
t
he
t
ot
a
l
of
node
s
f
r
om
t
he
f
i
r
s
t
node
of
a
l
l
t
he
s
i
bl
i
ng c
hi
l
dr
e
n node
s
t
o t
he
l
a
s
t
node
a
t
t
he
br
a
nc
h i
n t
he
s
am
e p
ar
en
t
n
o
d
e.
A
f
t
er
t
h
at
,
t
h
e v
al
u
e o
f
y
3
m
us
t
be
r
e
duc
e
d by t
he
va
l
ue
of
t
he
ol
de
r
br
ot
he
r
node
s
i
n t
he
s
am
e p
ar
en
t
n
o
d
e t
h
at
can
b
e
cal
c
ul
a
t
e
d us
i
ng t
he
f
ol
l
ow
i
ng f
or
m
ul
a
:
4
=
(
−
−
1
)
(
−
−
1
+
1
)
2
(
5)
T
he
l
a
s
t
i
s
t
o t
r
a
c
e
t
he
s
e
que
nc
e
of
c
hi
l
dr
e
n i
n a
s
ubs
e
t
of
t
he
br
a
nc
h poi
nt
s
obt
a
i
ne
d.
T
hi
s
va
l
ue
i
s
obt
a
i
ne
d
f
r
om
t
he
l
a
s
t
2
di
gi
t
s
of
t
he
s
ubs
e
t
.
F
or
e
xa
m
pl
e
,
t
he
s
ubs
e
t
va
l
ue
{1
,
3,
4}
i
s
obt
a
i
ne
d
f
r
om
t
he
c
a
l
c
ul
a
t
i
on of
4
-
3,
w
hi
c
h i
s
1,
w
he
r
e
t
he
s
ubs
e
t
f
or
m
i
s
c
ha
nge
d i
n f
or
m
{…,
i
,
j
}
.
H
e
r
e
i
s
t
he
f
o
r
m
ul
a
f
o
r
c
a
l
c
ul
a
t
i
ng t
he
va
l
ue
of
t
he
s
e
que
nc
e
of
c
hi
l
dr
e
n:
5
=
−
(
6)
A
l
l
t
he
e
qua
t
i
ons
t
ha
t
ha
ve
be
e
n obt
a
i
ne
d
a
r
e
t
he
n a
dde
d up t
o
f
i
nd t
he
f
i
na
l
i
nde
x of
t
he
s
ubs
e
t
.
T
o ge
t
t
he
f
i
n
al
i
n
d
ex
o
f
an
i
t
em
s
et
,
t
h
e cal
cu
l
at
i
o
n
s
t
h
at
m
u
s
t
b
e d
o
n
e ar
e:
=
1
+
2
−
4
+
5
(
7)
3.
2.
D
e
si
g
n
T
r
i
e
o
f
t
h
e
can
d
i
d
at
e s
et
i
s
a
tr
i
e
tr
e
e
w
h
ic
h
i
s
a
ll s
u
p
e
r
s
e
ts
o
f
th
e
ite
ms
e
t th
a
t r
e
p
r
e
s
e
n
t a
ll
c
om
bi
na
t
i
ons
of
i
t
e
m
s
s
ol
d.
T
he
tr
ie
he
r
e
i
s
us
e
d
t
o c
a
l
c
ul
a
t
e
t
he
s
uppor
t
c
ount
of
a
l
l
i
t
e
m
s
e
t
c
om
bi
na
t
i
ons
.
S
u
p
p
o
s
e t
h
er
e ar
e 4
i
t
em
s
et
s
,
t
h
e
s
u
p
er
s
et
i
s
al
l
p
o
s
s
i
b
l
e s
u
b
s
et
s
,
f
o
r
ex
am
p
l
e:
−
1
-
i
t
e
m
s
e
t
:
{1},
{2},
{3}
,
{4};
−
2
-
i
t
e
m
s
e
t
:
{1,
2},
{1
,
3}
,
{1
,
4}
,
{2
,
3}
,
{2
,
4}
,
{3
,
4};
−
3
-
i
t
e
m
s
e
t
:
{1,
2,
3}
,
{1
,
2
,
4}
,
{1
,
3
,
4}
,
{2
,
3
,
4};
−
4
-
ite
ms
e
t:{
1
,
2
,
3
,
4
}
,
T
ot
a
l
i
ng 15
or
2
n
-
1 w
i
t
h n=
4.
T
hi
s
i
s
a
c
om
p
l
e
t
e
c
om
bi
na
t
i
on pa
t
t
e
r
ne
d,
s
o t
ha
t
t
o
ach
i
ev
e t
h
e
ad
d
r
es
s
o
f
a
cer
t
ai
n
s
u
b
s
et
a f
o
r
m
u
l
a
can
b
e f
o
r
m
ed
.
F
ol
l
ow
i
ng i
s
a
n i
l
l
us
t
r
a
t
i
on of
c
a
l
c
ul
a
t
i
ng node
va
l
ue
s
f
or
3
-
ite
ms
e
t c
o
mb
in
a
tio
n
s
,
f
o
r
e
x
a
mp
le
,
{
2
,
3
,
4
}
w
ith
to
ta
l ite
ms
e
t c
o
mb
in
a
tio
n
s
is
4
,
a
s
s
how
n i
n F
i
gur
e
4
.
A
n e
xa
m
pl
e
of
us
i
ng H
a
s
h
-
node
c
a
l
c
ul
a
t
i
on t
o ge
t
t
he
i
nde
x va
l
ue
f
o
r
3
-
ite
ms
e
t {
2
,
3,
4}
a
s
il
lu
s
tr
a
te
d
in
F
ig
u
r
e
4
,
w
h
er
e
B
P
=
1 a
nd 2,
i
=3
,
j
=4
,
l
en
o
r
l
ev
el
=3
i
s a
s
ex
p
l
ai
n
ed
i
n
d
et
ai
l
at
T
ab
l
e 3
an
d
T
ab
l
e
4
.
T
h
e o
t
h
er
ex
am
p
l
e
o
f
H
as
h
-
node
cal
cu
l
at
i
o
n
fo
r
4
-
ite
ms
e
t {
1,
2,
3,
4}
a
s
illu
s
tr
a
te
d
in
F
ig
u
r
e
4
,
w
h
er
e
BP
=
1
,
i
=3
,
j
=4
,
l
en
or
l
e
ve
l
=
4,
s
o t
he
i
nde
x va
l
ue
i
s
15,
a
nd f
o
r
2
-
ite
ms
e
t {
3
,
4} i
s
10
w
i
t
h B
P
=
0.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
,
Vo
l
.
19
, N
o
.
5
,
O
c
t
obe
r
2021:
1553
-
1563
1558
F
i
gur
e
4
.
H
a
sh
-
n
o
d
e cal
cu
l
at
i
o
n
T
ab
l
e
3
.
A
n
ex
am
p
l
e o
f
cal
cu
l
at
i
n
g
t
h
e
1
a
nd
2
v
a
l
ue
f
or
t
he
s
ubs
e
t
{
2
,
3,
4
}
us
i
ng H
a
s
h
-
n
o
d
e cal
cu
l
at
i
o
n
1
=
!
!
(
−
)
!
−
1
=
1
2
=
3
1
=
4
!
1
!
(
4
−
1
)
!
2
=
1
+
4
!
2
!
(
4
−
2
)
!
2
=
2
3
=
(
−
(
+
1
)
)
(
−
)
2
1
=
4
!
1
!
(
3
)
!
2
=
1
+
4
!
2
!
(
2
)
!
2
=
2
3
=
(
4
−
(
1
+
1
)
)
(
4
−
1
)
2
+
3
=
(
4
−
(
2
+
1
)
)
(
4
−
2
)
2
1
=
4
∗
3
∗
2
∗
1
1
(
3
∗
2
∗
1
)
2
=
1
+
4
∗
3
∗
2
∗
1
2
∗
1
(
2
∗
1
)
2
=
2
3
=
(
4
−
(
2
)
)
(
3
)
2
+
3
=
(
4
−
(
3
)
)
(
2
)
2
1
=
24
6
2
=
1
+
24
4
2
=
2
3
=
2
∗
3
2
+
3
=
1
∗
2
2
1
=
4
+
6
3
=
3
+
3
=
1
1
=
10
3
=
4
2
=
4
T
ab
l
e
4
.
A
n
ex
am
p
l
e o
f
cal
cu
l
at
i
n
g
t
h
e
4
,
5
,
an
d
i
nde
x va
l
ue
f
or
t
he
s
ubs
e
t
{
2
,
3,
4} us
i
ng H
a
s
h
-
node
cal
cu
l
at
i
o
n
4
5
I
nde
x
4
=
(
−
−
1
)
(
−
−
1
+
1
)
2
5
=
−
=
1
+
2
−
4
+
5
4
=
(
4
−
3
)
(
4
−
3
+
1
)
2
5
=
4
−
3
=
10
+
4
−
1
+
1
4
=
1
∗
2
2
5
=
1
=
14
4
=
1
D
at
a s
t
r
u
ct
u
r
es
,
a
s
s
e
e
n i
n F
i
gur
e
5,
ar
e ar
r
ay
s
w
i
t
h
at
t
r
i
b
u
t
es
c
ons
i
s
t
of
:
−
N
ode
a
s
a
n i
nde
x va
l
ue
of
H
a
s
h
-
node
c
a
l
c
ul
a
t
i
on r
e
s
ul
t
.
−
D
at
a
as
an
ar
r
ay
o
f
n
-
ite
ms
e
t c
o
mb
in
a
tio
n
s
,
su
c
h
a
s 3
-
ite
ms
e
t
{
2
,
3,
4}
.
T
he
t
ot
a
l
c
om
bi
na
t
i
ons
f
or
4 i
s
(2
n
-
1)
,
t
h
at
i
s
1
5
,
as
s
een
i
n
F
i
gur
e
4.
−
S
uppor
t
is
th
e
va
l
ue
of
s
uppor
t
c
ount
.
T
he
de
f
a
ul
t
f
o
r
e
a
c
h da
t
a
i
s
0 (
z
e
r
o
)
a
nd i
t
w
i
l
l
be
c
ount
e
d p
l
us
one
i
f
i
t
e
xi
s
t
e
d i
n da
t
a
,
a
nd s
o on
.
F
ig
u
r
e 5
.
D
at
a s
t
r
u
ct
u
r
e
f
o
r
n
-
I
te
ms
e
ttr
ie
of
c
a
ndi
da
t
e
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
A
nal
y
s
i
s
of
f
r
e
que
nt
i
t
e
m
s
e
t
ge
ne
r
at
i
on bas
e
d on t
r
i
e
dat
a s
t
r
uc
t
ur
e
i
n A
pr
i
or
i
al
gor
i
t
hm
(
A
de
H
odi
j
a
h
)
1559
A
f
t
e
r
t
he
i
nde
x va
l
ue
i
s
obt
a
i
ne
d,
ne
xt
i
s
how
t
o c
a
l
c
ul
a
t
e
t
he
s
uppor
t
va
l
ue
f
o
r
e
a
c
h s
ubs
e
t
by
a
dopt
i
ng pr
uni
ng
f
r
om
A
p
r
i
or
i
.
T
he
ge
ne
r
a
t
i
on
of
t
he
i
t
e
m
s
e
t
c
a
ndi
da
t
e
i
s
done
pe
r
-
le
v
e
l.
O
n
ly
ite
ms
e
t
c
a
ndi
da
t
e
s
w
ho m
e
e
t
t
he
m
i
ni
m
um
s
uppor
t
(
f
r
e
que
nt
)
a
r
e
f
or
m
e
d.
T
he
n f
i
nd t
he
c
a
ndi
da
t
e
i
t
e
m
s
e
t
's
pos
i
t
i
on
i
n t
he
tr
ie
of
t
he
c
a
ndi
da
t
e
s
e
t
t
o
i
nc
r
e
a
s
e
t
he
s
uppor
t
c
ount
.
T
he
s
t
e
ps
f
or
t
he
A
l
t
e
r
na
t
i
ve
_1 a
l
go
r
i
t
h
m
ar
e
:
−
E
s
t
a
bl
i
s
hi
ng a
tr
ie
o
f
t
h
e
can
d
i
d
at
e s
et
as
m
u
ch
(
2n
-
1)
,
w
he
r
e
k
i
s
t
he
num
be
r
of
ite
ms
e
ts
s
o
ld
.
−
F
o
r
m
i
n
g
a l
i
n
ear
l
i
s
t
o
f
d
at
ab
as
es
an
d
s
u
p
er
s
et
o
f
i
t
em
s
et
f
o
r
each
t
r
an
s
act
i
o
n
b
y
co
m
b
i
n
i
n
g
al
l
i
t
e
m
s
et
pur
c
ha
s
e
d (
t
r
a
ns
a
c
t
i
on)
,
w
hi
c
h i
s
a
s
m
uc
h a
s
(
2n
-
1)
w
he
r
e
ni
i
s
t
he
num
be
r
of
i
t
e
m
s
e
t
s
pur
c
ha
s
e
d i
n t
he
t
r
a
ns
a
c
t
i
on of
i
.
−
F
o
r
each
t
r
an
s
a
c
t
i
on,
a
l
l
s
ubs
e
t
s
of
t
he
s
upe
r
s
e
t
a
r
e
s
e
a
r
c
he
d f
or
a
pos
i
t
i
on
i
n t
he
c
a
ndi
da
t
e
s
e
t
's
tr
ie
t
o
i
nc
r
e
a
s
e
t
he
s
uppor
t
c
ount
.
T
he
pr
oc
e
s
s
m
ode
l
of
t
he
A
l
t
e
r
na
t
i
ve
_1
a
l
gor
i
t
hm
i
s
s
how
n i
n F
i
gur
e
6
.
T
h
e d
i
f
f
er
en
ce b
et
w
een
A
l
t
er
n
at
i
v
e_
1
an
d
A
l
t
e
r
n
at
i
v
e_
2
al
g
o
r
i
t
hm
s
i
s
t
he
ge
ne
r
a
t
i
on
of
n
-
ite
ms
e
t.
S
uppos
e
t
he
c
ons
t
r
uc
t
i
on o
f
n
-
ite
ms
e
t in
A
lte
r
n
a
tiv
e
_
1
is
to
c
o
mb
in
e
a
ll
ite
ms
e
t a
n
d
p
r
o
d
u
c
e
ite
ms
e
t o
f
(2
n
-
1
)
,
w
h
e
r
e
n
i is
th
e
n
u
mb
e
r
o
f
ite
ms
e
ts
in
tr
a
n
s
a
c
tio
n
i.
H
o
w
e
v
e
r
,
th
is
is
n
o
t
th
e
c
a
s
e
w
ith
A
lte
r
n
a
tiv
e
_
2
.
Pr
u
ni
ng i
s
done
by
e
l
i
m
i
na
t
i
ng
[
24]
,
[
25]
t
he
p
r
e
vi
ous
l
ong i
t
e
m
s
e
t
w
hos
e
f
r
e
que
nc
y i
s
be
l
ow
t
he
m
i
ni
m
um
s
uppor
t
t
hr
e
s
hol
ds
(
i
nf
r
e
que
nt
)
,
a
s
s
e
e
n i
n F
i
gur
e
7
.
1
.
Read itembought
from data
transaction
.
2
.
Generate combination
of i
-
itembought from
1
-
itembought up to
n
-
itembought
,
consists of
:
data
,
frequent
.
3
.
Calculate
{
node
}
of i
-
itembought combination
,
formula
:
∑
(
children
from
1
-
itembought to
(
i
-
1
)
-
itembought
) +
(
sequence of children at
i
-
itembought
).
EOF
Yes
No
6
.
Get frequent
itemset from
1
-
itembought to
n
-
itembought
,
if
{
support
}
≥
minimum support
Start
End
4
.
node
(
i
-
itembought
) =
node
(
from
1
-
itembought to
(
i
-
1
)
-
itembought
)
5
.
Update
{
support
}
(
i
-
itembought
).
Yes
No
F
ig
u
r
e 6
.
T
he
pr
oc
e
s
s
m
ode
l
of
A
l
t
e
r
na
t
i
ve
_1 a
l
go
r
i
t
hm
F
ig
u
r
e 7
.
T
he
pr
oc
e
s
s
m
ode
l
of
A
l
t
e
r
na
t
i
ve
_
2
a
lg
o
r
ith
m
1
.
Read itembought from data
transaction
.
2
.
Generate level
-
i
-
itembought
combination
{
node
,
data
,
support
}
.
4
.
Calculate
{
node
}
of level
-
i
-
itembought combination
,
formula
:
∑
(
children from
1
-
itembought to
(
i
-
1
)
-
itembought
) + (
sequence of
children at i
-
itembought
).
12
.
There are still
frequent level
-
itembought
?
15
.
level
=
level
+
1
7
.
EOF
Yes
Yes
No
13
.
Get frequent from
1
-
itembought combination
to
n
-
itembought
combination
Start
End
5
.
node
(
i
-
itembought
) =
node
(
from
1
-
itembought to
(
i
-
1
)
-
itembought
)
6
.
Update
{
support
}
(
i
-
itembought
).
Yes
8
.
support
(
from
1
-
itembought to
n
-
itembought
)
<
minimum
support
11
.
PRUNING
:
delete
node
(
i
-
itembought
)
as
frequent level
-
itembought
No
No
14
.
item
(
data
) =
item
(
non
_
frequent
_
1
_
Itemset
)
9
.
Level
=
1
?
10
.
Set data
(
i
-
itembought
)
as
non
_
frequent
_
1
_
itemset
No
No
3
.
item
(
data
) =
item
(
non
_
frequent
_
1
_
Items
et
)
No
Yes
Yes
Yes
Yes
No
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
:
1693
-
6930
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
,
Vo
l
.
19
, N
o
.
5
,
O
c
t
obe
r
2021:
1553
-
1563
1560
A
l
t
e
r
na
t
i
ve
_3 t
r
e
a
t
s
s
ubpr
oc
e
s
s
e
s
-
2 a
nd
s
ubpr
oc
e
s
s
e
s
-
3 of
A
l
t
e
r
na
t
i
ve
_2 a
s
t
hr
e
a
ds
by i
ns
t
a
l
l
i
ng
c
onc
ur
r
e
nt
a
c
c
e
s
s
c
ont
r
ol
t
o
a
voi
d
r
a
c
e
c
ondi
t
i
o
ns
f
i
ght
i
ng
ove
r
t
he
va
l
ue
of
s
uppor
t
c
ount
a
t
t
he
s
a
m
e
pos
itio
n
in
th
e
tr
ie
.
M
u
lti
-
t
hr
e
a
d a
ppl
i
e
d i
n t
hi
s
r
e
s
e
a
r
c
h us
e
d de
pe
nde
n
c
y da
t
a
-
dr
i
ve
n
[
21]
.
T
r
an
s
act
i
o
n
d
at
a
i
s
di
vi
de
d i
nt
o 4 t
hr
e
a
ds
a
nd 8 t
hr
e
a
ds
.
A
di
f
f
e
r
e
n
t
t
hr
e
a
d pr
oc
e
s
s
e
s
i
n t
hi
s
r
e
s
e
a
r
c
h ba
s
e
d on t
he
s
u
m
of
t
he
t
r
an
s
act
i
o
n
d
at
a
t
h
at
can
b
e s
een
i
n
F
i
gur
e
8 (
a
)
,
s
o t
ha
t
r
a
c
e
c
ondi
t
i
ons
m
a
y
oc
c
ur
w
h
ic
h
is
illu
s
tr
a
te
d
in
F
i
gur
e
8
(
b)
,
c
ons
i
s
t
i
ng of
4 t
h
r
e
a
ds
.
T
o ove
r
c
om
e
r
a
c
e
c
ondi
t
i
on
w
he
n
upda
t
e
va
l
ue
of
S
uppo
r
t
C
ount
,
m
ut
ua
l
e
xc
l
us
i
on i
s
ne
e
de
d t
o
acces
s
t
h
e s
am
e ad
d
r
es
s
o
f
i
t
em
s
et
{
2
,
3
}
as
o
n
e o
f
i
t
e
m
s
e
t
c
om
bi
na
t
i
on
i
n node
8 {2
,
3}
,
node
11 {
1,
2
,
3}
,
node
14 {2,
3,
4},
a
nd node
15
{1,
2,
3,
4} a
s
s
e
e
n i
n
T
a
bl
e
1.
D
i
f
f
e
r
e
nt
t
hr
e
a
ds
pr
oc
e
s
s
i
t
w
i
t
hou
t
di
s
c
a
r
di
ng
one
of
t
he
t
hr
e
a
ds
a
s
c
ol
l
i
s
i
on ha
ndl
i
ng
[
26]
w
h
e
n
tw
o
th
r
e
a
d
s
a
tte
mp
t to
in
s
e
r
t tw
o
d
if
f
e
r
e
n
t s
u
b
tr
e
e
s
a
t th
e
s
am
e l
o
cat
i
o
n
.
I
n
t
h
i
s
r
es
ear
ch
,
t
h
e m
u
t
u
al
ex
cl
u
s
i
o
n
m
ec
ha
ni
s
m
us
e
s
a
m
oni
t
or
us
i
ng
s
ync
hr
oni
z
e
d
c
ons
t
r
uc
t
s
w
he
n upda
t
i
ng s
uppor
t
va
l
ue
s
,
a
s
s
e
e
n i
n F
i
gur
e
9
.
T
hr
e
a
ds
i
n
t
hi
s
r
e
s
e
a
r
c
h do
not
pl
a
c
e
on
e
a
c
h i
t
e
m
s
e
t
c
om
bi
na
t
i
on a
s
i
t
i
s
uni
que
.
F
or
e
xa
m
pl
e
,
ite
ms
e
t {
1
,
3,
4}
pr
oduc
e
s
7 c
om
bi
na
t
i
ons
a
r
e
{1}
,
{3}
,
{4}
,
{1
,
3
},
{
1,
4
},
{
3,
4
},
{
1,
3,
4}
,
s
o t
ha
t
t
hr
e
a
ds
i
s
pl
a
c
e
d on s
um
o
f
t
r
a
ns
a
c
t
i
on da
t
a
ba
s
e
w
hi
c
h ha
s
be
e
n di
vi
de
d by
4 a
nd
8 t
h
r
e
a
ds
.
T
he
e
xpe
r
i
m
e
n
t
s
how
s
t
ha
t
t
he
i
t
e
m
s
e
t
c
om
bi
na
t
i
on
t
hr
e
a
ds
m
e
t
hod ha
s
a
l
onge
r
r
un
t
i
m
e
t
ha
n
t
he
t
r
a
ns
a
c
t
i
on da
t
a
t
hr
e
a
ds
m
e
t
hod.
(
a)
(
b)
F
ig
u
r
e 8
.
P
r
o
c
e
ss
m
ode
l
o
f
A
lte
r
n
a
tiv
e
_
3
a
lg
o
r
ith
m w
ith
th
e
e
x
a
mp
le
o
f
th
e
d
is
tr
ib
u
tio
n
o
f
tr
a
n
s
a
c
tio
n
d
a
ta
(
a
)
i
nt
o
4 t
h
r
e
a
ds
(
b)
1
a
.
Read itembought from data
transaction
.
2
.
Generate level
-
i
-
itembought
combination
{
node
,
data
,
support
}
.
Start
1
b
.
Divide the transaction data
record into
4
or
8
parts
(
threads
).
T
1
{
1
,
4
}
T
2
{
4
}
T
3
{
1
,
2
,
3
}
…
Tn
{
…
}
...
...
T
2
{
2
,
3
}
…
Tn
{
…
}
C
1
{
1
},{
4
},{
1
,
4
}
C
2
{
4
}
C
3
{
1
},{
2
},{
3
},{
1
,
2
},{
1
,
3
},
{
2
,
3
}
,{
1
,
2
,
3
}
…
Cn
{
…
}
...
...
C
2
{
2
},{
3
},
{
2
,
3
}
…
Cn
{
…
}
Thread
1
Thread
2
Thread
3
Thread
4
Node
Support
Data
1
6
{
1
}
2
6
{
2
}
3
6
{
3
}
4
3
{
4
}
1
2
3
4
...
...
{
…
,
...
}
8
2
{
2
,
3
}
3
...
...
{
…
,
...
}
...
{
2
,
3
}
{
2
,
3
}
...
Transaction
database
Itemset combination
Trie frequent
n
-
itemset with minimum support
>
=
2
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
el
eco
m
m
u
n
C
om
put
E
l
C
ont
r
ol
A
nal
y
s
i
s
of
f
r
e
que
nt
i
t
e
m
s
e
t
ge
ne
r
at
i
on bas
e
d on t
r
i
e
dat
a s
t
r
uc
t
ur
e
i
n A
pr
i
or
i
al
gor
i
t
hm
(
A
de
H
odi
j
a
h
)
1561
F
ig
u
r
e 9
.
U
pda
t
i
ng s
uppor
t
va
l
ue
a
l
gor
i
t
hm
(
s
i
m
pl
i
f
i
e
d)
3.
2.
E
x
p
eri
m
en
t
s
T
he
r
un t
i
m
e
of
ge
ne
r
a
t
i
ng
f
r
e
que
nt
i
t
e
m
s
e
t
of
e
a
c
h pr
opos
e
d a
l
gor
i
t
hm
i
n
t
hi
s
r
e
s
e
a
r
c
h,
a
t
e
s
t
i
n a
s
i
ngl
e
s
e
r
ve
r
e
nvi
r
onm
e
nt
us
i
ng a
P
C
w
i
t
h I
nt
e
l
(
R
)
C
or
e
(
T
M
)
s
pe
c
i
f
i
c
a
t
i
ons
i
5
-
8250U
C
P
U
@
1.
60G
H
z
1.
80 G
H
z
us
e
s
12.
0 G
B
R
A
M
a
nd u
s
e
s
t
he
ope
r
a
t
i
ng s
ys
t
e
m
M
i
c
r
o
s
of
t
W
i
ndow
s
10.
T
e
s
t
da
t
a
obt
a
i
ne
d f
r
om
ge
ne
r
a
t
i
ng r
a
ndom
i
t
e
m
s
e
t
c
om
bi
na
t
i
ons
by a
s
i
m
pl
e
a
ppl
i
c
a
t
i
on r
e
pr
e
s
e
nt
i
ng t
he
s
a
l
e
s
t
r
a
ns
a
c
t
i
on da
t
a
s
e
t
.
I
n
g
e
ttin
g
th
e
a
c
c
u
r
a
te
r
u
n
time
r
e
s
u
lts
,
te
s
tin
g
is
c
a
r
r
ie
d
o
u
t
5
time
s
f
o
r
e
a
c
h
m
i
ni
m
um
s
uppor
t
va
l
ue
.
T
he
r
e
a
r
e
t
w
o t
ype
s
of
t
he
pr
opos
e
d a
l
gor
i
t
hm
,
na
m
e
l
y S
i
ngl
e
-
t
hr
e
a
d pr
oc
e
s
s
i
ng a
ve
r
a
ge
c
on
s
i
s
t
s
of
A
l
t
e
r
na
t
i
ve
_1 a
nd
A
l
t
e
r
na
t
i
ve
_2;
mu
lti
-
t
h
r
ead
p
r
o
ces
s
i
n
g
av
er
ag
e co
n
s
i
s
t
s
o
f
A
lte
r
n
a
tiv
e
_
3
w
ith
4
,
8
,
a
nd
20
t
h
r
ead
s
.
T
h
e ex
p
er
i
m
en
t
w
as
car
r
i
ed
o
u
t
w
i
t
h
5
ex
p
er
i
m
en
t
al
s
c
e
na
r
i
os
f
or
e
a
c
h t
ype
of
t
he
p
r
opos
e
d
a
l
gor
i
t
hm
m
a
de
ba
s
e
d on
t
he
3 a
l
t
e
r
na
t
i
ve
s
m
e
nt
i
o
ne
d pr
e
vi
ous
l
y,
e
a
c
h of
w
hi
c
h i
s
de
s
c
r
i
be
d a
s
f
ol
l
o
w
s
:
−
S
1 (
A
l
t
e
r
na
t
i
ve
_1)
:
P
r
oc
e
s
s
i
ng t
he
tr
i
e
s
can
d
i
d
at
e s
et
w
i
t
h
o
n
e m
ai
n
p
r
o
ces
s
.
S
cen
ar
i
o
-
1 i
s
i
nt
e
nde
d t
o
unde
r
s
t
a
nd t
he
w
or
ki
ngs
a
nd pe
r
f
or
m
a
nc
e
of
tr
ie
s
.
−
S
2(
A
l
t
e
r
na
t
i
ve
_2)
:
P
r
oc
e
s
s
i
ng w
i
t
h one
m
a
i
n
pr
oc
e
s
s
l
i
ke
s
c
e
na
r
i
o S
1 but
a
dde
d pr
uni
ng
t
ha
t
w
or
ks
p
er
-
l
e
ve
l
t
r
e
e
he
i
ght
,
na
m
e
l
y L
e
ve
l
P
r
uni
ng.
T
h
i
s
s
cen
ar
i
o
i
n
t
en
d
s
t
o
m
eas
u
r
e w
h
et
h
er
t
h
er
e i
s
an
i
n
cr
eas
e
i
n pe
r
f
or
m
a
nc
e
w
i
t
h pr
un
i
ng.
−
S
3 (
A
l
t
e
r
na
t
i
ve
_3 w
i
t
h
4
t
hr
e
a
ds
)
:
P
r
oc
e
s
s
i
ng A
l
t
e
r
na
t
i
ve
_2 w
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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g
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a)
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(
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ig
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m
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