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Gr
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elief
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c
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rticle
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n
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CC B
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se
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r
e
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uth
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r
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UCT
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O
N
I
n
th
e
th
eo
r
y
o
f
B
ay
esian
n
etwo
r
k
s
[
1
]
–
[
3
]
,
th
e
id
ea
s
o
f
M
ar
k
o
v
[
4
]
–
[
6
]
p
lay
a
k
e
y
r
o
le,
esp
ec
ially
in
d
ev
elo
p
in
g
ef
f
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alg
o
r
it
h
m
s
f
o
r
d
ata
p
r
o
ce
s
s
in
g
u
n
d
e
r
u
n
ce
r
tain
ty
.
Ma
r
k
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v
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r
o
ce
s
s
es
ar
e
o
f
p
ar
ticu
lar
in
ter
est
to
r
esear
ch
er
s
f
o
r
s
ev
er
al
r
ea
s
o
n
s
.
First,
th
ey
a
r
e
in
tu
itiv
ely
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n
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er
s
tan
d
ab
le
a
n
d
n
atu
r
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f
o
r
m
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y
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p
lied
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s
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m
ak
in
g
th
em
at
tr
ac
tiv
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f
o
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io
u
s
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ield
s
.
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co
n
d
,
in
co
r
p
o
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ati
n
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Ma
r
k
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v
i
d
ea
s
in
to
B
ay
esian
n
etwo
r
k
s
(
B
Ns)
[
7
]
–
[
9
]
ca
n
s
ig
n
if
ican
tly
s
im
p
lify
c
o
m
p
u
tatio
n
al
alg
o
r
ith
m
s
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e
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y
s
p
ee
d
in
g
u
p
th
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p
r
o
b
a
b
ilit
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ca
lcu
latio
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p
r
o
ce
s
s
an
d
ex
p
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th
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p
o
s
s
ib
ilit
ies
o
f
wo
r
k
in
g
with
lar
g
e
r
n
etwo
r
k
s
.
Fin
ally
,
Ma
r
k
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v
p
r
o
ce
s
s
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ar
e
well
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s
tu
d
ied
with
in
th
e
f
r
am
ewo
r
k
o
f
Ma
r
k
o
v
ch
ain
th
eo
r
y
[
1
0
]
–
[
1
2
]
,
wh
ich
allo
ws
f
o
r
ad
ap
tin
g
ex
is
tin
g
d
ev
elo
p
m
e
n
ts
to
wo
r
k
with
B
ay
esian
n
etwo
r
k
s
.
I
n
tellig
en
t
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
s
[
1
3
]
,
[
1
4
]
,
esp
ec
ially
in
v
ar
io
u
s
ty
p
es
o
f
u
n
ce
r
tain
ties
,
ar
e
o
f
ten
d
escr
ib
ed
u
s
in
g
B
ay
esian
n
etwo
r
k
s
.
On
e
o
f
th
e
m
ain
c
h
allen
g
es
in
wo
r
k
i
n
g
with
B
Ns
is
th
e
n
ee
d
to
p
er
f
o
r
m
ca
lcu
latio
n
s
co
n
s
id
er
i
n
g
th
e
p
r
esen
ce
o
f
ev
id
en
ce
-
in
f
o
r
m
atio
n
th
at
ca
n
alter
th
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
t
io
n
in
th
e
n
etwo
r
k
.
Stan
d
a
r
d
m
eth
o
d
s
,
s
u
ch
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
1
8
1
-
2
1
9
1
2182
alg
o
r
ith
m
s
b
ased
o
n
j
u
n
ctio
n
tr
ee
s
[
1
5
]
,
[
1
6
]
,
r
e
q
u
ir
e
co
m
p
lex
c
o
m
p
u
tatio
n
al
p
r
o
ce
d
u
r
e
s
.
T
h
e
m
o
s
t
well
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k
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eth
o
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f
o
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ex
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e
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s
th
e
p
r
o
b
ab
ilit
y
p
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o
p
ag
atio
n
m
eth
o
d
[
1
7
]
–
[
1
9
]
in
clu
s
ter
tr
ee
s
(
PP
T
C
)
,
p
r
o
p
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y
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itzen
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en
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o
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th
e
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elief
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k
in
to
a
m
o
r
e
co
m
p
u
tatio
n
-
f
r
ien
d
ly
s
tr
u
ctu
r
e;
h
o
we
v
er
,
its
ap
p
licatio
n
ca
n
b
e
tim
e
-
co
n
s
u
m
i
n
g
an
d
s
lo
w.
Sh
ay
ak
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m
eto
v
a
et
a
l.
[
2
1
]
d
i
s
cu
s
s
es
cr
itical
is
s
u
es
r
elate
d
to
u
s
in
g
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ay
esian
n
etwo
r
k
s
f
o
r
s
o
lv
in
g
p
r
ac
tical
p
r
o
b
lem
s
in
wh
ich
g
r
ap
h
ical
m
o
d
els
co
n
tain
d
ir
ec
ted
cy
cles.
T
h
e
s
tr
ict
r
eq
u
ir
em
en
t
f
o
r
th
e
ac
y
clicity
o
f
th
e
d
ir
ec
ted
g
r
ap
h
r
ep
r
esen
tin
g
a
B
ay
esian
n
et
wo
r
k
d
o
es
n
o
t
allo
w
f
o
r
th
e
e
f
f
ec
tiv
e
s
o
lu
tio
n
o
f
m
o
s
t
task
s
th
at
in
v
o
lv
e
d
ir
ec
te
d
cy
cles.
Mo
d
er
n
B
ay
esian
n
etwo
r
k
th
eo
r
y
p
r
o
h
ib
its
th
e
u
s
e
o
f
d
ir
ec
ted
c
y
cles.
T
h
e
r
eq
u
i
r
em
en
t
f
o
r
g
r
ap
h
ac
y
clicity
ca
n
s
ig
n
if
ican
tly
s
im
p
lify
th
e
g
en
e
r
al
th
eo
r
y
o
f
B
ay
esian
n
etwo
r
k
s
an
d
s
im
p
lify
th
e
d
ev
el
o
p
m
e
n
t
o
f
alg
o
r
ith
m
s
an
d
th
eir
im
p
le
m
en
tatio
n
in
c
o
d
e
f
o
r
c
o
m
p
u
tatio
n
s
in
B
ay
esian
n
etwo
r
k
s
.
Ak
h
m
eto
v
a
et
a
l.
[
2
2
]
ex
am
in
es
th
e
u
r
g
en
t
p
r
o
b
lem
o
f
m
ax
im
izin
g
h
u
m
an
s
u
r
v
iv
al
d
u
r
i
n
g
a
f
ir
e
an
d
th
eir
im
m
ed
iate
ev
ac
u
at
io
n
.
Var
io
u
s
m
eth
o
d
s
ar
e
b
ein
g
p
r
o
p
o
s
ed
wo
r
ld
wid
e,
i
n
clu
d
in
g
in
tellig
en
t
d
ev
ices
an
d
wir
eless
s
y
s
tem
s
,
co
n
ce
r
n
in
g
t
h
is
is
s
u
e.
T
h
e
m
ain
g
o
al
is
to
ef
f
icien
tly
u
ti
lize
tim
e,
r
eg
u
lar
l
y
in
f
o
r
m
p
eo
p
le,
an
d
g
u
id
e
t
h
e
m
o
u
t
o
f
d
an
g
er
z
o
n
es,
th
e
r
e
b
y
r
e
d
u
cin
g
th
e
n
u
m
b
er
o
f
c
a
s
u
alties.
T
h
e
ar
ticle
also
d
escr
ib
es
th
e
co
n
ce
p
t
o
f
an
em
er
g
en
cy
an
d
its
ca
u
s
es.
Mo
d
er
n
m
eth
o
d
s
o
f
d
et
ec
tin
g
p
eo
p
le
an
d
n
av
ig
atio
n
d
u
r
in
g
a
f
ir
e,
as
w
ell
as
th
e
u
s
e
o
f
wir
eless
eq
u
i
p
m
en
t
an
d
i
n
tellig
en
t
alg
o
r
ith
m
s
,
ar
e
d
is
cu
s
s
ed
in
d
etail.
T
h
e
s
y
s
tem
’
s
ar
c
h
itectu
r
e,
g
o
als,
o
b
jectiv
es,
an
d
s
o
lu
tio
n
s
ar
e
p
r
esen
ted
.
E
x
am
p
l
es
ar
e
p
r
o
v
id
ed
to
ex
p
lain
th
e
im
p
o
r
tan
ce
an
d
u
s
ef
u
ln
ess
o
f
th
is
r
esear
ch
f
o
r
p
eo
p
le.
T
h
e
ar
ticle
i
n
clu
d
es
in
f
o
r
m
atio
n
o
n
th
e
u
s
e
o
f
s
en
s
o
r
s
,
with
tab
les
illu
s
tr
atin
g
th
eir
ap
p
licatio
n
,
in
ter
c
o
n
n
ec
tio
n
s
,
a
n
d
wir
eless
co
m
m
u
n
icatio
n
with
t
h
e
ce
n
tr
al
s
er
v
er
.
As
a
r
esu
lt,
a
s
y
s
tem
was
d
ev
elo
p
ed
th
at
o
p
e
r
ates
b
ased
o
n
elec
tr
o
n
ic
in
d
i
ca
to
r
s
s
h
o
win
g
th
e
d
ir
ec
tio
n
to
a
s
af
e
p
lace
in
th
e
ev
en
t
o
f
an
em
er
g
en
cy
,
wh
ich
r
ec
eiv
es
s
ig
n
als
f
r
o
m
th
e
ce
n
tr
al
s
er
v
er
.
Alim
h
an
et
a
l.
[
2
3
]
ad
d
r
ess
es
th
e
p
r
o
b
lem
o
f
g
lo
b
al
p
r
a
ctica
l
o
u
tp
u
t
tr
ac
k
in
g
f
o
r
a
class
o
f
h
ig
h
-
o
r
d
er
n
o
n
lin
ea
r
s
y
s
tem
s
with
tim
e
d
elay
s
(
u
s
in
g
s
tate
f
ee
d
b
ac
k
)
.
Un
d
er
m
o
d
er
ate
g
r
o
wth
co
n
d
itio
n
s
o
f
s
y
s
tem
n
o
n
lin
ea
r
ities
,
in
clu
d
i
n
g
tim
e
d
elay
s
,
a
s
tate
f
ee
d
b
ac
k
r
eg
u
lato
r
d
esig
n
with
a
n
ad
ju
s
ta
b
le
s
ca
lin
g
f
ac
to
r
is
p
r
o
p
o
s
ed
.
Usi
n
g
th
e
L
y
ap
u
n
o
v
-
Kr
aso
v
s
k
ii
f
u
n
ctio
n
al,
th
is
s
ca
lin
g
f
ac
to
r
is
ad
ju
s
ted
t
o
d
o
m
in
ate
th
e
tim
e
-
d
elay
n
o
n
lin
ea
r
ities
,
b
o
u
n
d
e
d
b
y
g
r
o
wth
c
o
n
d
itio
n
s
,
an
d
to
m
ak
e
th
e
tr
ac
k
in
g
er
r
o
r
ar
b
itra
r
ily
s
m
all
wh
ile
all
s
tates
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
r
em
ain
b
o
u
n
d
e
d
.
A
s
im
u
latio
n
ex
am
p
le
is
p
r
o
v
id
ed
to
illu
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
t
r
ac
k
in
g
r
eg
u
lato
r
.
Alim
h
an
et
a
l.
[
2
4
]
d
is
cu
s
s
es t
h
e
p
r
o
b
lem
o
f
g
lo
b
al
p
r
ac
tical
o
u
tp
u
t tr
ac
k
in
g
u
s
in
g
s
tate
f
ee
d
b
ac
k
f
o
r
a
class
o
f
u
n
ce
r
tain
n
o
n
lin
ea
r
s
y
s
tem
s
with
tim
e
d
ela
y
s
.
Un
d
er
m
o
d
er
ate
c
o
n
d
iti
o
n
s
o
n
th
e
s
y
s
tem
n
o
n
lin
ea
r
ities
,
in
clu
d
i
n
g
tim
e
d
elay
s
,
a
h
o
m
o
g
e
n
eo
u
s
s
tate
f
ee
d
b
ac
k
r
eg
u
lat
o
r
d
esig
n
with
an
ad
ju
s
tab
le
s
ca
lin
g
f
ac
to
r
is
p
r
o
p
o
s
ed
.
T
h
r
o
u
g
h
th
e
h
o
m
o
g
en
eo
u
s
L
y
ap
u
n
o
v
-
Kr
aso
v
s
k
ii
f
u
n
ctio
n
al
m
eth
o
d
,
th
is
s
ca
lin
g
f
ac
to
r
is
a
d
ju
s
ted
to
d
o
m
in
at
e
th
e
tim
e
-
d
elay
n
o
n
lin
ea
r
ities
,
b
o
u
n
d
ed
b
y
h
o
m
o
g
en
eo
u
s
g
r
o
wth
c
o
n
d
itio
n
s
,
an
d
to
m
a
k
e
th
e
tr
ac
k
in
g
e
r
r
o
r
ar
b
itra
r
ily
s
m
all
wh
ile
all
s
tates
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
r
em
ain
b
o
u
n
d
ed
.
Alim
h
an
et
a
l.
[
2
5
]
ex
p
lo
r
es
th
e
p
r
o
b
lem
o
f
g
l
o
b
al
p
r
ac
tica
l
o
u
tp
u
t
tr
ac
k
in
g
u
s
in
g
s
tate
f
ee
d
b
ac
k
f
o
r
a
class
o
f
u
n
ce
r
tain
h
i
g
h
-
o
r
d
er
n
o
n
lin
ea
r
s
y
s
tem
s
with
tim
e
d
elay
s
.
A
h
o
m
o
g
en
eo
u
s
s
tate
f
ee
d
b
ac
k
r
eg
u
lato
r
with
a
n
ad
ju
s
tab
le
s
ca
lin
g
f
ac
to
r
is
th
en
d
ev
elo
p
ed
u
n
d
er
m
o
d
er
ate
c
o
n
d
itio
n
s
o
n
t
h
e
s
y
s
tem
n
o
n
li
n
ea
r
ities
,
in
clu
d
in
g
tim
e
d
elay
s
.
T
h
r
o
u
g
h
th
e
h
o
m
o
g
e
n
eo
u
s
L
y
ap
u
n
o
v
-
Kr
aso
v
s
k
ii
f
u
n
ctio
n
al
m
eth
o
d
,
th
is
s
ca
l
in
g
f
ac
to
r
is
ad
ju
s
ted
to
d
o
m
in
ate
th
e
tim
e
-
d
elay
n
o
n
lin
ea
r
ities
,
b
o
u
n
d
ed
b
y
h
o
m
o
g
en
e
o
u
s
g
r
o
wth
co
n
d
itio
n
s
,
an
d
to
m
ak
e
th
e
tr
ac
k
in
g
e
r
r
o
r
ar
b
itra
r
il
y
s
m
all
wh
ile
all
s
tates o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
r
em
ain
b
o
u
n
d
ed
.
T
o
ad
d
r
ess
th
is
p
r
o
b
lem
,
Ma
r
k
o
v
p
r
o
ce
s
s
es
n
ee
d
m
o
r
e
ef
f
icien
t
u
s
e,
wh
ich
allo
ws
f
o
r
s
i
m
p
ler
an
d
f
aster
alg
o
r
ith
m
s
.
T
h
e
m
ai
n
id
ea
is
th
at
th
e
p
r
o
b
a
b
ilit
y
in
a
n
o
d
e
d
e
p
en
d
s
o
n
ly
o
n
th
e
s
tate
o
f
n
eig
h
b
o
r
in
g
n
o
d
es
(
p
ar
en
ts
an
d
ch
ild
r
en
)
,
wh
ich
is
a
le
s
s
s
tr
in
g
en
t
r
eq
u
i
r
em
en
t
th
an
th
e
co
n
ce
p
t
o
f
th
e
Ma
r
k
o
v
b
lan
k
et.
T
h
is
s
im
p
lific
atio
n
ca
n
s
ig
n
if
ican
tly
s
p
ee
d
u
p
co
m
p
u
tatio
n
s
,
av
o
id
in
g
th
e
c
o
m
p
lex
ities
o
f
b
u
ild
in
g
ju
n
ctio
n
tr
ee
s
.
T
h
is
wo
r
k
p
r
o
p
o
s
es
a
n
ew
ap
p
r
o
ac
h
th
at
d
iv
id
es
th
e
v
er
tices
o
f
a
B
ay
esian
n
et
wo
r
k
in
t
o
lev
els
to
s
im
p
lify
ca
lcu
latio
n
s
.
T
h
e
v
e
r
tices
th
at
h
av
e
r
ec
eiv
e
d
ev
i
d
en
ce
f
o
r
m
th
e
ze
r
o
lev
el
,
w
h
ile
th
e
r
em
ain
in
g
v
er
tices
ar
e
d
iv
id
ed
in
to
s
u
b
s
eq
u
en
t
le
v
els
b
ased
o
n
th
eir
c
o
n
n
ec
tio
n
s
to
t
h
e
p
r
ev
io
u
s
le
v
els.
T
h
is
ap
p
r
o
ac
h
allo
ws
f
o
r
m
o
r
e
ef
f
icien
t
p
r
o
b
ab
ilit
y
ca
lcu
latio
n
s
in
th
e
n
etwo
r
k
n
o
d
es
u
s
in
g
alr
ea
d
y
k
n
o
wn
v
alu
es
f
r
o
m
p
r
ev
io
u
s
lev
els.
T
h
e
ex
a
m
p
les
p
r
o
v
id
ed
illu
s
tr
ate
th
e
p
r
o
p
o
s
ed
m
eth
o
d
s
u
s
in
g
e
d
u
ca
tio
n
al
d
ata
in
th
e
HUGI
N
E
XPERT
en
v
ir
o
n
m
e
n
t,
wh
i
ch
v
is
u
ally
d
em
o
n
s
tr
ates
th
e
o
p
er
atio
n
o
f
t
h
e
alg
o
r
ith
m
s
.
T
h
e
e
x
am
p
les
co
n
s
id
er
ed
in
th
e
ar
ticle
ar
e
ed
u
ca
tio
n
al
an
d
d
o
n
o
t r
eq
u
ir
e
th
e
s
ea
r
ch
f
o
r
r
ea
l m
ea
n
in
g
s
,
b
u
t th
ey
d
em
o
n
s
tr
ate
th
e
m
ain
p
r
i
n
cip
les an
d
a
d
v
an
t
ag
es o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
2.
M
E
T
H
O
D
C
o
n
s
id
er
in
g
an
ar
b
itra
r
y
B
ay
e
s
ian
n
etwo
r
k
(
B
N)
[
2
6
]
–
[
2
8
]
,
o
n
e
m
ig
h
t
q
u
esti
o
n
th
e
d
ep
e
n
d
en
cy
o
f
a
s
elec
ted
n
o
d
e
o
n
o
th
e
r
n
o
d
es
with
in
th
e
n
etwo
r
k
.
T
h
e
p
r
im
ar
y
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
lies
in
th
e
f
ac
t
th
at
th
e
s
elec
ted
n
o
d
e
g
e
n
er
ally
d
ep
en
d
s
o
n
m
an
y
o
th
er
n
o
d
es,
wh
ich
b
ec
o
m
es
p
ar
ticu
la
r
ly
ch
allen
g
in
g
in
th
e
p
r
esen
ce
o
f
ev
i
d
en
ce
.
Var
io
u
s
ap
p
r
o
ac
h
es
to
s
o
lv
in
g
th
is
p
r
o
b
lem
e
x
is
t
[
2
9
]
–
[
3
1
]
,
wh
ich
ca
n
b
e
ca
teg
o
r
ize
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Ma
r
ko
v
p
r
o
ce
s
s
es in
B
a
ye
s
ia
n
n
etw
o
r
k
co
mp
u
ta
tio
n
(
A
s
s
em
S
h
a
ya
k
h
meto
va
)
2183
in
to
s
ev
er
al
g
r
o
u
p
s
.
First,
o
n
e
m
eth
o
d
in
v
o
lv
es
b
r
ea
k
in
g
d
o
wn
co
m
p
u
tatio
n
s
in
a
B
N
in
to
b
lo
ck
s
u
s
in
g
th
e
co
n
ce
p
t
o
f
d
-
s
ep
ar
atio
n
.
T
h
is
ap
p
r
o
ac
h
allo
ws
th
e
n
etwo
r
k
to
b
e
d
iv
id
e
d
in
to
in
d
ep
en
d
en
t
b
l
o
ck
s
,
wh
e
r
e
co
m
p
u
tatio
n
s
c
an
b
e
p
er
f
o
r
m
e
d
s
ep
ar
ately
,
s
ig
n
if
ican
tly
r
ed
u
cin
g
o
v
er
all
co
m
p
u
tatio
n
al
c
o
m
p
lex
ity
.
Seco
n
d
,
th
e
B
N
ca
n
b
e
tr
an
s
f
o
r
m
ed
in
t
o
an
o
th
e
r
,
m
o
r
e
s
im
p
lifie
d
n
et
wo
r
k
wh
er
e
c
o
m
p
u
tatio
n
s
b
ec
o
m
e
ea
s
ier
an
d
less
r
eso
u
r
ce
-
in
ten
s
iv
e.
Af
ter
p
er
f
o
r
m
in
g
th
e
n
ec
ess
ar
y
ca
lcu
latio
n
s
in
th
is
s
im
p
lifie
d
n
etwo
r
k
,
th
e
r
esu
lts
ca
n
b
e
tr
an
s
f
er
r
ed
b
ac
k
to
th
e
m
ain
B
ay
esian
n
etwo
r
k
.
T
h
e
th
ir
d
a
p
p
r
o
ac
h
is
th
e
elim
in
atio
n
o
f
s
p
ec
if
ic
n
o
d
es
f
r
o
m
th
e
B
N
u
s
in
g
th
e
th
eo
r
y
o
f
p
o
t
en
tials
.
T
h
is
th
eo
r
y
is
well
-
d
e
v
elo
p
ed
b
o
th
in
g
en
e
r
al
ter
m
s
an
d
s
p
ec
if
ically
f
o
r
B
ay
esian
n
etwo
r
k
s
.
Alth
o
u
g
h
th
is
ap
p
r
o
ac
h
ca
n
f
o
r
m
alize
m
an
y
co
m
p
u
tatio
n
s
,
it
o
f
ten
lo
s
es
th
e
in
tu
itiv
e
clar
ity
in
h
e
r
en
t
i
n
th
e
f
r
am
ew
o
r
k
o
f
B
Ns.
T
h
e
f
o
u
r
th
m
eth
o
d
s
u
g
g
ests
s
im
p
lify
in
g
co
m
p
u
tatio
n
s
in
a
B
N
b
y
ass
u
m
in
g
th
at
ca
lcu
latio
n
s
in
th
e
s
elec
ted
n
o
d
e
d
e
p
en
d
o
n
l
y
o
n
its
n
eig
h
b
o
r
in
g
n
o
d
es
an
d
th
at
d
e
p
en
d
e
n
cies
o
n
o
th
er
n
o
d
es
ar
e
m
ed
iated
o
n
ly
th
r
o
u
g
h
th
ese
n
eig
h
b
o
r
i
n
g
n
o
d
es.
W
h
ile
th
is
m
ay
lead
to
a
r
ed
u
ctio
n
i
n
ca
lcu
latio
n
ac
cu
r
ac
y
with
in
t
h
e
co
n
tex
t
o
f
B
ay
esian
id
ea
s
,
th
is
m
eth
o
d
ess
en
tially
r
ep
r
e
s
en
ts
a
s
h
if
t
in
th
e
id
eo
lo
g
y
o
f
B
ay
esian
n
etwo
r
k
s
.
T
h
is
wo
r
k
ex
a
m
in
es
a
ca
s
e
wh
er
e
co
m
p
u
tatio
n
s
in
th
e
c
u
r
r
en
t
n
o
d
e
d
e
p
en
d
o
n
ly
o
n
its
n
eig
h
b
o
r
in
g
n
o
d
e
s
,
p
o
s
s
ib
ly
n
o
t
all
o
f
t
h
em
.
T
h
e
m
ain
co
m
p
u
tatio
n
al
ch
al
len
g
e
ar
is
es
wh
en
ev
id
en
ce
is
p
r
esen
t
in
th
e
n
etwo
r
k
.
I
n
t
h
e
ab
s
en
ce
o
f
p
r
o
o
f
,
th
e
Ma
r
k
o
v
p
r
o
p
er
t
y
is
au
to
m
atica
lly
f
u
lf
illed
,
an
d
ca
lcu
latio
n
s
in
th
e
n
o
d
e
d
ep
en
d
o
n
ly
o
n
a
s
u
b
s
et
o
f
n
eig
h
b
o
r
i
n
g
n
o
d
es,
m
ak
in
g
th
e
m
r
elativ
ely
s
im
p
le.
T
h
e
ar
ticle
ex
p
l
o
r
es
th
e
p
o
s
s
ib
ilit
y
o
f
ex
te
n
d
in
g
th
is
id
eo
l
o
g
y
to
co
m
p
u
tatio
n
s
in
B
ay
e
s
ian
n
etwo
r
k
s
with
ev
id
en
ce
in
s
o
m
e
n
o
d
es,
aim
in
g
to
s
im
p
lify
ca
lcu
latio
n
s
an
d
im
p
r
o
v
e
th
eir
ef
f
icien
cy
.
L
et
a
g
r
ap
h
G
=
<
V
,
E
>
b
e
g
iv
en
,
wh
e
r
e
is
th
e
s
et
o
f
v
er
tices
o
f
th
e
g
r
ap
h
,
an
d
E
is
th
e
s
et
o
f
e
d
g
es.
A
d
ir
ec
ted
ac
y
clic
g
r
a
p
h
is
ca
lled
a
B
ay
esian
n
etwo
r
k
if
ea
ch
v
er
tex
∈
is
a
s
s
o
ciate
d
w
ith
a
r
an
d
o
m
v
ar
ia
b
le
X
v
,
an
d
ea
ch
ed
g
e
=
(
u
,
v
)
∈
E
r
ep
r
esen
ts
a
p
r
o
b
a
b
ilis
tic
d
ep
en
d
en
ce
o
f
th
e
r
a
n
d
o
m
v
ar
i
ab
le
X
v
o
n
th
e
r
a
n
d
o
m
v
ar
iab
le
X
u
u
.
T
h
e
r
an
d
o
m
v
ar
ia
b
le
Xj
co
n
tain
s
s
ev
er
al
in
d
e
p
en
d
e
n
t
s
tates
{
1
,
2
,
3
,
…
,
}
.
A
p
r
o
b
ab
ilit
y
ch
ar
ac
ter
iz
es
ea
ch
s
tate.
T
h
e
n
u
m
b
er
o
f
s
tates f
o
r
ea
ch
r
an
d
o
m
v
ar
ia
b
le
m
ay
v
ar
y
.
I
t is
ass
u
m
ed
th
at
(
1
)
(
2
)
.
(
1
)
+
(
2
)
+
(
3
)
+
⋯
+
(
)
=
1
(
1
)
(
1
+
2
)
=
(
1
)
+
(
2
)
(
2
)
T
h
e
f
o
llo
win
g
b
asic r
u
les ar
e
u
s
ed
wh
en
wo
r
k
in
g
with
B
ay
e
s
ian
n
etwo
r
k
s
:
−
Mu
ltip
licatio
n
:
(
,
|
)
=
(
|
,
)
∗
(
|
)
=
(
|
,
)
∗
(
|
)
−
Su
m
m
atio
n
:
(
X
|
Z
)
=
∑
(
,
=
|
)
=
∑
(
|
=
,
)
∗
(
=
|
)
−
B
ay
es
'
th
eo
r
em
:
(
X
|
Y
,
Z
)
=
P
(
Y
|
X
,
Z
)
∗
P
(
X
|
Z
)
P
(
Y
|
Z
)
=
(
Y
|
X
,
Z
)
∗
P
(
X
|
Z
)
∑
(
Y
|
X
=
x
,
Z
)
∗
P
(
X
=
x
|
Z
)
I
n
d
ep
e
n
d
en
ce
o
f
r
an
d
o
m
v
a
r
ia
b
les:
(
,
)
=
(
)
∗
(
)
.
I
n
itially
,
co
n
d
itio
n
al
p
r
o
b
ab
ilit
ies
an
d
p
r
o
b
a
b
ilit
ies
f
o
r
s
o
m
e
n
o
d
es
a
r
e
s
et
in
th
e
B
ay
esian
n
etwo
r
k
.
B
ased
o
n
t
h
is
d
ata,
an
y
co
m
b
in
atio
n
o
f
ev
e
n
ts
in
th
e
n
etwo
r
k
ca
n
b
e
d
eter
m
i
n
ed
.
A
v
er
tex
is
a
p
ar
en
t
o
f
v
er
tex
v
if
ed
g
e
(
u
,
v
)
∈
E
.
T
h
e
s
et
o
f
all
p
ar
en
t
v
er
tices
o
f
v
is
d
en
o
ted
b
y
pa
r
e
n
ts
(
X
v
)
.
T
o
ca
lcu
late
th
e
p
r
o
b
ab
ilit
y
,
th
er
e
is
a
ch
ain
r
u
le
f
o
r
B
ay
esian
n
etwo
r
k
s
(
3
)
:
(
1
,
2
,
3
,
…
,
)
=
∏
(
|
(
)
)
=
1
(
3
)
T
h
e
ch
ain
r
u
le
allo
ws
f
o
r
d
ec
o
m
p
o
s
in
g
a
jo
i
n
t
d
is
tr
ib
u
tio
n
in
to
a
p
r
o
d
u
ct
o
f
co
n
d
itio
n
al
d
is
tr
ib
u
tio
n
s
.
I
t
is
ev
id
en
t
th
at
d
u
r
in
g
th
e
ca
lc
u
l
atio
n
,
th
e
Ma
r
k
o
v
p
r
in
cip
le
is
o
b
s
er
v
ed
:
a
v
a
r
iab
le
d
ep
e
n
d
s
o
n
ly
o
n
its
p
ar
en
t
v
ar
iab
les,
r
eg
a
r
d
less
o
f
h
o
w
th
e
p
ar
e
n
t
v
a
r
iab
les
o
b
tain
e
d
th
eir
v
alu
es.
I
t
is
also
clea
r
th
at
th
e
n
u
m
b
e
r
o
f
p
ar
en
ts
f
o
r
a
v
er
tex
s
h
o
u
ld
n
o
t
b
e
lar
g
e
d
u
e
to
th
e
lim
itatio
n
s
o
f
co
m
p
u
tatio
n
al
r
es
o
u
r
ce
s
.
Ho
wev
e
r
,
th
eo
r
etica
lly
,
t
h
e
n
u
m
b
e
r
o
f
p
ar
e
n
ts
ca
n
b
e
ar
b
itra
r
y
.
I
t
is
im
p
o
r
tan
t
t
o
em
p
h
asize
th
at
s
p
ec
if
y
in
g
th
e
co
n
d
itio
n
al
p
r
o
b
a
b
ilit
y
f
o
r
p
a
r
en
t
-
ch
ild
p
air
s
is
n
o
t e
n
o
u
g
h
.
T
h
is
in
f
o
r
m
atio
n
d
o
es n
o
t d
e
f
in
e
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
th
e
p
ar
e
n
ts
.
L
et
th
e
v
ar
iab
les
X,
Y,
a
n
d
Z
b
e
r
e
p
r
es
en
ted
as
in
d
ep
en
d
en
t
e
v
en
ts
,
with
X
an
d
Y
b
ein
g
th
e
p
ar
en
ts
o
f
Z
(
4
)
.
=
{
1
,
2
,
3
,
…
,
}
;
=
{
1
,
2
,
3
,
…
,
}
;
=
{
1
,
2
,
3
,
…
,
}
(
4
)
T
o
u
n
i
q
u
ely
d
eter
m
in
e
t
h
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
,
t
h
e
f
o
llo
win
g
s
et
o
f
co
n
d
itio
n
al
p
r
o
b
ab
ilit
ies
m
u
s
t
b
e
s
p
ec
if
ied
:
P
(
z
i
|
x
j
,
y
k
)
.
T
h
e
p
r
im
ar
y
task
o
f
co
m
p
u
tatio
n
s
in
a
B
ay
esi
an
Netwo
r
k
(
B
N)
is
to
ca
lcu
l
ate
th
e
p
r
o
b
a
b
ilit
y
o
f
in
d
e
p
en
d
e
n
t
ev
en
ts
wh
en
co
n
d
itio
n
al
p
r
o
b
a
b
i
liti
es
ar
e
s
p
ec
if
ied
at
ea
ch
v
er
tex
.
T
h
is
p
r
o
ce
s
s
is
ca
lled
in
itial
p
r
o
p
a
g
atio
n
.
I
f
th
e
B
N
is
s
tr
u
ctu
r
ed
as
a
p
o
ly
tr
ee
,
p
r
o
p
ag
atio
n
alg
o
r
ith
m
s
ar
e
s
ig
n
if
ican
tly
s
im
p
lifie
d
an
d
y
ield
a
u
n
iq
u
e
r
esu
lt.
T
h
is
i
s
b
ec
au
s
e,
in
th
is
ca
s
e,
an
y
two
v
er
tices
i
n
th
e
B
N
g
r
ap
h
ar
e
co
n
n
ec
ted
b
y
a
s
in
g
le
p
at
h
.
C
o
n
s
eq
u
en
tly
,
th
e
in
f
lu
e
n
ce
o
f
ev
id
en
ce
ca
n
also
p
r
o
p
ag
ate
al
o
n
g
a
s
in
g
le
p
ath
.
I
f
th
e
B
N
g
r
ap
h
co
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tain
s
u
n
d
ir
e
cted
cy
cles,
it
h
as
b
ee
n
s
h
o
wn
in
[
3
]
th
at
a
m
ar
g
in
al
p
r
o
b
ab
i
lity
d
is
tr
ib
u
tio
n
ca
n
b
e
co
n
s
tr
u
cted
.
T
h
e
m
ain
g
o
a
l
(
eith
er
in
itial
o
r
ev
id
en
ce
p
r
o
p
ag
atio
n
)
is
to
ca
lcu
late
th
e
d
is
tr
ib
u
tio
n
o
v
e
r
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
1
8
1
-
2
1
9
1
2184
s
u
b
s
et
o
f
v
ar
ia
b
les
with
in
th
e
B
ay
esian
n
etwo
r
k
.
I
f
th
e
d
is
tr
ib
u
tio
n
is
f
u
lly
s
p
ec
if
ied
,
it
is
s
im
p
ly
a
m
atter
o
f
s
u
m
m
in
g
th
is
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u
tio
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le
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ig
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m
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h
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ia
b
les
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o
t
in
cl
u
d
ed
in
t
h
e
s
u
b
s
et
f
o
r
wh
ich
we
wan
t
to
o
b
tain
th
e
d
is
tr
ib
u
tio
n
.
Ho
wev
er
,
th
e
s
ize
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f
th
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p
r
o
b
lem
g
r
o
ws
ex
p
o
n
en
tially
with
th
e
n
u
m
b
er
o
f
n
o
d
es
in
th
e
B
N,
an
d
d
u
e
to
th
e
d
ata
v
o
lu
m
e,
th
ese
ca
lcu
latio
n
s
m
ay
b
e
p
r
ac
tically
im
p
o
s
s
ib
le.
T
h
e
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
f
o
r
a
n
ar
b
itra
r
y
n
o
d
e
with
m
u
ltip
le
p
iece
s
o
f
ev
id
en
ce
ca
n
b
e
ca
lcu
lated
u
s
in
g
f
o
r
m
u
la
(
5
)
:
(
1
2
3
…
)
=
∑
(
1
2
3
…
1
=
1
2
=
2
3
=
3
…
=
)
1
,
2
,
3
,
…
,
(
5
)
T
h
e
s
p
ec
if
ied
m
eth
o
d
d
ef
in
es
lo
ca
l
d
is
tr
ib
u
tio
n
s
.
B
ased
o
n
t
h
ese
lo
ca
l
d
is
tr
ib
u
tio
n
s
,
c
o
n
d
i
tio
n
al
p
r
o
b
ab
ilit
ies
ca
n
b
e
ca
lcu
lated
(
6
)
:
(
1
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1
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1
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1
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∑
(
1
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1
=
1
…
=
1
=
1
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=
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1
,
…
,
1
,
…
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(
6
)
wh
er
e
th
e
v
ar
iab
les
Z
k
–
ar
e
th
e
v
ar
iab
les
th
at
h
a
v
e
r
ec
ei
v
ed
ev
id
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ce
.
W
h
en
ev
i
d
en
ce
is
p
r
esen
t,
th
e
a
b
o
v
e
f
o
r
m
u
la
n
o
lo
n
g
er
w
o
r
k
s
.
I
t is
n
ec
ess
ar
y
to
u
s
e
m
o
r
e
g
en
e
r
al
f
o
r
m
u
las (
7
)
-
(
1
0
)
:
(
|
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=
(
)
(
)
(
7
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(
|
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(
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(
)
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)
(
8
)
∑
(
=
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1
(
9
)
(
=
|
=
)
=
(
=
|
=
)
(
=
)
∑
(
=
|
=
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(
=
)
(
1
0
)
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
L
et's
co
n
s
id
er
th
e
ed
u
ca
tio
n
al
ex
am
p
le
ASI
A
in
Fig
u
r
e
1
,
wid
ely
k
n
o
wn
i
n
th
e
lit
er
atu
r
e
o
n
B
ay
esian
n
etwo
r
k
s
,
wh
ich
an
aly
ze
s
v
ar
io
u
s
s
ce
n
ar
io
s
o
f
s
ettin
g
ev
id
en
ce
an
d
c
o
m
p
ar
es
two
ap
p
r
o
ac
h
es
to
alg
o
r
ith
m
co
n
s
tr
u
ctio
n
c
o
n
s
id
er
in
g
Ma
r
k
o
v
p
r
o
p
e
r
ties
.
I
n
th
is
ex
am
p
le,
th
e
v
e
r
tex
r
ep
r
e
s
en
ts
th
e
f
ac
t
o
f
th
e
s
u
b
ject's
v
is
it
to
Asi
a
in
Fig
u
r
e
2
(
a)
,
th
e
v
er
te
x
r
ep
r
esen
ts
th
e
f
ac
t
o
f
s
m
o
k
in
g
in
Fig
u
r
e
2(
b
)
,
th
e
v
e
r
tex
r
ep
r
esen
ts
th
e
p
r
esen
ce
o
f
t
u
b
er
cu
lo
s
is
,
wh
ich
s
ig
n
if
ica
n
tly
d
ep
en
d
s
o
n
th
e
v
is
it
to
Asi
a
in
Fig
u
r
e
2(
c
)
,
a
n
d
th
e
v
er
te
x
in
d
icate
s
th
e
p
r
e
s
en
ce
o
f
lu
n
g
ca
n
ce
r
in
Fig
u
r
e
2
(
d
)
.
T
h
e
v
er
tex
r
ep
r
ese
n
ts
th
e
p
r
esen
ce
o
f
b
r
o
n
c
h
itis
in
Fig
u
r
e
2
(
e)
,
t
h
e
v
er
tex
r
ef
lects
th
e
f
ac
t
o
f
eith
er
lu
n
g
ca
n
ce
r
o
r
t
u
b
er
c
u
lo
s
is
,
th
e
v
er
tex
co
r
r
esp
o
n
d
s
to
th
e
r
esu
lts
o
f
a
n
X
-
r
ay
,
a
n
d
th
e
v
er
tex
in
d
icate
s
th
e
p
r
esen
ce
o
f
d
y
s
p
n
ea
in
th
e
s
u
b
ject.
I
n
th
is
an
al
y
s
is
,
a
co
m
p
a
r
is
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n
o
f
s
o
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tio
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s
a
n
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m
eth
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s
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o
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ith
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c
o
n
s
tr
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n
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,
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in
g
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to
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o
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n
t
th
e
Ma
r
k
o
v
p
r
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p
e
r
ty
,
wh
ich
h
elp
s
id
en
tify
th
e
d
if
f
er
e
n
ce
s
an
d
ad
v
an
tag
es
o
f
ea
ch
ap
p
r
o
ac
h
in
th
e
co
n
tex
t
o
f
t
h
is
ex
am
p
le.
A
v
is
it
to
Asi
a
tr
ig
g
er
s
th
e
r
is
k
o
f
co
n
tr
ac
tin
g
tu
b
er
cu
lo
s
is
.
Sm
o
k
in
g
ca
n
co
n
tr
ib
u
te
to
d
ev
el
o
p
in
g
lu
n
g
ca
n
ce
r
(
L
)
,
b
r
o
n
c
h
itis
(
B
)
,
o
r
b
o
th
s
im
u
ltan
e
o
u
s
ly
.
T
h
e
r
esu
lt
o
f
a
ch
est
X
-
r
ay
(
X)
m
ay
i
n
d
icate
th
e
p
r
esen
ce
o
f
l
u
n
g
ca
n
ce
r
o
r
tu
b
er
cu
lo
s
is
with
a
ce
r
tain
p
r
o
b
a
b
ilit
y
,
b
u
t
it
ca
n
n
o
t
d
is
tin
g
u
is
h
b
etwe
en
th
ese
d
is
ea
s
es.
L
u
n
g
ca
n
ce
r
,
tu
b
er
c
u
lo
s
is
,
an
d
b
r
o
n
ch
itis
ca
n
ca
u
s
e
d
y
s
p
n
ea
with
a
ce
r
tain
p
r
o
b
ab
ilit
y
.
Fig
u
r
e
2
s
h
o
ws
a
B
ay
esian
n
etwo
r
k
d
es
cr
ib
in
g
th
e
r
elatio
n
s
h
ip
s
b
etw
ee
n
f
iv
e
v
a
r
iab
les
in
v
o
lv
ed
in
d
iag
n
o
s
in
g
lu
n
g
d
is
ea
s
es.
Fig
u
r
e
2
(
a)
s
h
o
ws
th
e
p
r
o
b
ab
ilit
y
o
f
a
s
u
b
ject
tr
av
elin
g
to
Asi
a
(
A)
,
wh
er
e
d
is
ea
s
es
s
u
ch
as
tu
b
er
cu
lo
s
is
ca
n
b
e
co
n
tr
ac
ted
.
T
h
e
p
r
o
b
ab
ilit
y
th
at
th
e
s
u
b
ject
h
as
v
is
ited
Asi
a
is
0
.
0
1
f
o
r
“y
es”
an
d
0
.
9
9
f
o
r
“n
o
.
”
Fig
u
r
e
2
(
c
)
s
h
o
ws
th
e
p
r
o
b
a
b
ilit
y
o
f
a
s
u
b
ject
h
av
in
g
tu
b
er
c
u
lo
s
is
(
T
)
,
d
ep
en
d
i
n
g
o
n
wh
eth
e
r
th
e
s
u
b
ject
h
as
v
is
ited
Asi
a.
I
f
th
e
s
u
b
ject
h
as
v
is
ited
Asi
a,
th
e
p
r
o
b
ab
ilit
y
o
f
h
av
in
g
tu
b
er
cu
lo
s
is
is
0
.
0
5
f
o
r
“y
es”
an
d
0
.
9
5
f
o
r
“
n
o
.
”
I
f
th
e
s
u
b
je
ct
h
as
n
o
t
v
is
ited
Asi
a,
t
h
e
p
r
o
b
ab
ilit
y
o
f
h
av
in
g
th
e
d
is
ea
s
e
is
0
.
0
1
f
o
r
“y
es”
an
d
0
.
9
9
f
o
r
“n
o
.
”
Fig
u
r
e
2
(
b
)
s
h
o
ws
th
e
p
r
o
b
ab
ilit
y
th
at
th
e
s
u
b
ject
is
a
s
m
o
k
er
(
S),
wh
ich
is
eq
u
ally
d
iv
id
e
d
:
0
.
5
f
o
r
“y
es”
a
n
d
0
.
5
f
o
r
“
n
o
.
”
Fig
u
r
e
2
(
d
)
illu
s
tr
ates
th
e
p
r
o
b
ab
ilit
y
o
f
a
s
u
b
ject
h
av
in
g
lu
n
g
ca
n
ce
r
(
L
)
,
d
ep
e
n
d
in
g
o
n
wh
eth
er
t
h
e
s
u
b
ject
s
m
o
k
es.
I
f
th
e
s
u
b
ject
s
m
o
k
es,
th
e
p
r
o
b
a
b
ilit
y
o
f
lu
n
g
ca
n
ce
r
is
0
.
1
f
o
r
“
y
es”
an
d
0
.
9
f
o
r
“n
o
.
”
I
f
th
e
s
u
b
ject
d
o
es
n
o
t
s
m
o
k
e,
th
e
p
r
o
b
a
b
ilit
y
o
f
ca
n
ce
r
d
ec
r
ea
s
es
to
0
.
0
1
f
o
r
“
y
es”
an
d
0
.
9
9
f
o
r
“n
o
.
”
Fig
u
r
e
2
(
e)
s
h
o
ws
th
e
p
r
o
b
a
b
ilit
y
th
at
th
e
s
u
b
ject
will
h
av
e
b
r
o
n
ch
itis
(
B
)
,
also
d
e
p
en
d
en
t
o
n
s
m
o
k
in
g
.
Fo
r
s
m
o
k
er
s
,
th
e
p
r
o
b
ab
ilit
y
o
f
b
r
o
n
ch
i
tis
is
0
.
6
f
o
r
“y
es”
an
d
0
.
4
f
o
r
“n
o
,
”
wh
er
ea
s
f
o
r
n
o
n
s
m
o
k
e
r
s
,
th
ese
v
alu
es
ar
e
0
.
3
f
o
r
“y
es”
an
d
0
.
7
f
o
r
“n
o
.
”
T
h
u
s
,
ea
ch
f
ig
u
r
e
in
th
is
m
o
d
el
s
h
o
ws th
e
r
elatio
n
s
h
ip
s
b
etwe
en
th
e
v
a
r
iab
les th
at
af
f
ec
t th
e
s
u
b
ject'
s
h
ea
lth
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Ma
r
ko
v
p
r
o
ce
s
s
es in
B
a
ye
s
ia
n
n
etw
o
r
k
co
mp
u
ta
tio
n
(
A
s
s
em
S
h
a
ya
k
h
meto
va
)
2185
W
e
p
er
f
o
r
m
th
e
tr
ian
g
u
latio
n
o
f
th
e
g
r
ap
h
in
Fig
u
r
e
3
.
Acc
o
r
d
in
g
to
th
e
th
eo
r
y
,
d
u
r
in
g
tr
ia
n
g
u
latio
n
,
we
f
ir
s
t e
lim
in
ate
v
er
tices wit
h
o
n
e
n
ei
g
h
b
o
r
,
a
n
d
.
T
h
e
n
,
we
elim
in
ate
v
er
tices with
two
n
eig
h
b
o
r
s
,
an
d
D.
T
h
ese
v
er
tices a
r
e
p
ar
t o
f
cliq
u
es,
s
o
th
er
e
is
n
o
n
ee
d
to
ad
d
ed
g
es.
T
h
e
r
em
ain
i
n
g
s
u
b
g
r
ap
h
co
n
s
is
ts
o
f
th
e
v
er
tices
,
,
,
,
an
d
th
e
e
d
g
es {
SL,
L
E
,
E
B
,
B
S},
f
o
r
m
in
g
a
cy
cle
o
f
len
g
th
4
.
Fig
u
r
e
1
.
E
d
u
ca
tio
n
al
e
x
am
p
le
ASI
A
(
a)
(
b
)
(
c)
(
d
)
(
e)
Fig
u
r
e
2
.
T
h
e
f
ac
t o
f
th
e
s
u
b
je
cts
'
v
is
its
to
A
s
ia
Fig
u
r
e
3
.
Gr
a
p
h
tr
ian
g
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
1
8
1
-
2
1
9
1
2186
Fo
r
th
e
g
r
ap
h
in
Fig
u
r
e
1
,
we
co
n
s
tr
u
ct
th
e
m
o
r
al
g
r
ap
h
.
Her
e,
th
e
d
ir
ec
tio
n
s
o
f
th
e
ed
g
es
ar
e
r
em
o
v
ed
,
an
d
two
ed
g
es
ar
e
a
d
d
ed
to
co
n
n
ec
t
th
e
n
o
d
es
a
n
d
,
as
well
as
th
e
n
o
d
es
a
n
d
.
An
ed
g
e
L
B
(
o
r
e
d
g
e
)
m
u
s
t
b
e
ad
d
e
d
t
o
co
m
p
lete
th
e
tr
ia
n
g
u
latio
n
.
T
h
e
tr
ian
g
u
lated
g
r
ap
h
is
s
h
o
wn
in
Fig
u
r
e
4
.
T
o
co
n
s
tr
u
ct
th
e
s
ec
o
n
d
ar
y
g
r
ap
h
,
we
s
elec
t
two
m
in
im
al
cliq
u
es
an
d
f
r
o
m
th
e
g
r
ap
h
in
Fig
u
r
e
4
.
T
h
e
n
eig
h
b
o
r
in
g
cliq
u
e
t
o
th
ese
cl
iq
u
es
will
b
e
th
e
cliq
u
e
.
T
h
e
n
eig
h
b
o
r
in
g
cliq
u
e
t
o
will
b
e
th
e
cliq
u
e
.
T
h
e
n
eig
h
b
o
r
in
g
cliq
u
es to
will b
e
an
d
.
Fig
u
r
e
4
.
T
h
e
jo
in
tr
ee
co
r
r
esp
o
n
d
in
g
to
th
e
B
ay
esian
n
etwo
r
k
(
B
N)
T
h
e
an
aly
s
is
o
f
th
e
ASI
A
ed
u
ca
tio
n
al
ex
am
p
le
s
h
o
ws
th
at,
d
esp
ite
s
ig
n
if
ican
t
o
p
p
o
r
t
u
n
ities
f
o
r
s
im
p
lify
in
g
ca
lcu
latio
n
s
,
th
e
c
o
m
p
u
tatio
n
al
lo
a
d
f
o
r
la
r
g
e
B
ay
esian
n
etwo
r
k
s
(
B
Ns)
ca
n
b
e
v
er
y
s
u
b
s
tan
tial,
an
d
tr
an
s
f
o
r
m
atio
n
s
in
to
a
s
ec
o
n
d
ar
y
g
r
ap
h
ca
n
b
e
c
o
m
p
le
x
an
d
n
o
t
alwa
y
s
tr
an
s
p
ar
en
t
to
r
esear
ch
er
s
.
T
h
is
r
aises
th
e
q
u
esti
o
n
:
h
o
w
ca
n
we
r
ed
u
ce
an
d
s
im
p
lify
co
m
p
u
tatio
n
s
,
m
ak
i
n
g
th
em
m
o
r
e
tr
an
s
p
ar
e
n
t?
T
o
ac
h
iev
e
th
ese
g
o
als,
it
is
im
p
o
r
tan
t
to
en
s
u
r
e
th
at
t
h
e
ac
c
u
r
a
cy
o
f
th
e
ca
lcu
latio
n
s
r
em
ain
s
with
in
r
ea
s
o
n
ab
le
lim
its
an
d
th
at
th
e
th
eo
r
etica
l
f
o
u
n
d
atio
n
o
f
th
e
n
ew
a
p
p
r
o
a
ch
is
b
ased
o
n
p
r
ev
io
u
s
ly
d
e
v
elo
p
ed
th
eo
r
ies
a
n
d
m
eth
o
d
s
.
I
t
is
n
ec
ess
ar
y
f
o
r
th
e
alg
o
r
ith
m
s
,
t
h
eir
s
o
f
twar
e
im
p
lem
en
tatio
n
,
an
d
th
e
s
p
ee
d
o
f
ca
lcu
latio
n
s
t
o
b
e
s
ig
n
if
ican
tly
s
im
p
ler
an
d
f
aster
,
allo
win
g
f
o
r
th
e
ef
f
icien
t
p
r
o
ce
s
s
in
g
o
f
an
y
r
ea
s
o
n
ab
le
B
N
to
p
o
lo
g
ies.
A
k
ey
asp
ec
t
is
a
ls
o
th
e
ab
ilit
y
to
id
en
tify
ce
r
tain
s
u
b
g
r
ap
h
s
o
f
th
e
B
N
f
o
r
in
teg
r
ated
co
m
p
u
tatio
n
s
,
wh
ich
will
h
elp
o
p
tim
ize
th
e
p
r
o
ce
s
s
.
At
th
e
s
am
e
tim
e,
p
o
ten
tial
er
r
o
r
s
th
at
m
ay
ar
is
e
d
u
r
in
g
th
e
s
im
p
lific
atio
n
o
f
co
m
p
u
tatio
n
s
s
h
o
u
l
d
b
e
co
n
s
i
d
er
ed
,
an
d
th
eir
im
p
ac
t
o
n
th
e
f
in
al
r
esu
lts
s
h
o
u
ld
b
e
ass
es
s
ed
.
As
p
ar
t
o
f
th
e
d
ev
elo
p
m
e
n
t
o
f
a
n
ew
a
p
p
r
o
ac
h
to
co
m
p
u
tatio
n
s
in
B
ay
esian
n
etwo
r
k
s
,
it
was
d
ec
id
ed
to
r
ef
er
to
a
well
-
k
n
o
wn
p
a
r
ad
ig
m
f
r
o
m
th
e
th
e
o
r
y
o
f
Ma
r
k
o
v
ch
ai
n
s
,
ac
co
r
d
i
n
g
to
wh
ich
in
f
o
r
m
atio
n
in
th
e
n
o
d
e
u
n
d
er
s
tu
d
y
d
ep
en
d
s
o
n
ly
o
n
th
e
in
f
o
r
m
ati
o
n
in
n
eig
h
b
o
r
i
n
g
n
o
d
es,
r
eg
a
r
d
less
o
f
h
o
w
th
at
in
f
o
r
m
atio
n
was
o
b
tain
ed
.
T
h
is
wo
r
k
ass
u
m
es
th
at
th
e
i
n
f
o
r
m
atio
n
in
th
e
n
o
d
e
u
n
d
er
s
tu
d
y
in
a
B
ay
esian
n
etwo
r
k
d
ep
en
d
s
o
n
ly
o
n
s
p
ec
if
ic
n
eig
h
b
o
r
in
g
n
o
d
es,
i
n
clu
d
in
g
p
ar
en
ts
an
d
c
h
ild
r
en
.
Var
io
u
s
im
p
lem
en
tatio
n
s
o
f
t
h
is
ap
p
r
o
ac
h
ar
e
p
o
s
s
ib
le:
in
o
n
e,
th
e
in
f
o
r
m
atio
n
in
th
e
n
o
d
e
d
e
p
en
d
s
o
n
ly
o
n
th
e
p
a
r
en
ts
,
ch
ild
r
en
,
an
d
o
th
e
r
p
a
r
e
n
ts
o
f
th
e
ch
ild
r
e
n
,
wh
ich
co
r
r
esp
o
n
d
s
t
o
th
e
co
n
ce
p
t
o
f
th
e
n
o
d
e'
s
Ma
r
k
o
v
b
la
n
k
et
Fig
u
r
e
5
.
I
n
an
o
t
h
er
v
ar
i
an
t,
th
e
i
n
f
o
r
m
atio
n
in
th
e
n
o
d
e
d
ep
en
d
s
o
n
n
eig
h
b
o
r
in
g
n
o
d
es,
d
esig
n
ated
as
s
et
,
with
th
e
ad
d
itio
n
o
f
all
n
ei
g
h
b
o
r
in
g
n
o
d
es
f
o
r
ea
ch
n
o
d
e
in
s
et
.
W
h
en
co
n
s
id
er
in
g
o
p
tio
n
s
,
we
will
co
n
s
id
er
th
e
d
-
s
ep
ar
atio
n
o
f
n
o
d
es
in
th
e
B
ay
esian
n
etwo
r
k
(
B
N)
.
Nex
t,
we
will
co
n
s
id
er
th
e
ch
o
ice
o
f
t
h
e
B
ay
esian
b
la
n
k
et.
W
ith
o
u
t
e
v
id
en
ce
,
co
m
p
u
tatio
n
s
in
th
e
B
N
d
o
n
o
t
p
r
esen
t
d
if
f
icu
lties
.
L
et's
s
y
s
tem
atize
th
e
o
r
d
er
o
f
co
m
p
u
tatio
n
s
in
th
e
a
b
s
en
ce
o
f
p
r
o
o
f
.
W
e
will
d
iv
id
e
th
e
v
er
tices o
f
th
e
B
N
in
to
s
ev
er
al
lev
els.
W
e
wil
l in
c
lu
d
e
v
er
tices wh
er
e
n
o
co
m
p
u
tatio
n
s
ar
e
r
eq
u
ir
ed
at
th
e
ze
r
o
lev
el.
T
h
ese
a
r
e
n
o
d
es
with
o
u
t
p
ar
en
ts
—
an
d
.
A
an
d
S
ar
e
at
th
e
ze
r
o
lev
el.
T
,
L
,
an
d
B
ar
e
at
th
e
f
ir
s
t
lev
el,
with
p
ar
en
ts
b
e
lo
n
g
in
g
o
n
ly
to
t
h
e
ze
r
o
lev
el.
E
is
at
th
e
s
ec
o
n
d
lev
el,
with
p
ar
en
ts
b
elo
n
g
in
g
o
n
ly
to
th
e
f
ir
s
t
lev
el.
X
an
d
D
ar
e
at
th
e
t
h
ir
d
le
v
el,
wit
h
p
ar
e
n
ts
b
elo
n
g
in
g
o
n
l
y
to
th
e
f
ir
s
t
an
d
s
ec
o
n
d
lev
els.
A
an
d
S
ar
e
at
th
e
ze
r
o
lev
el.
T
,
L
,
an
d
B
ar
e
at
th
e
f
i
r
s
t
lev
el,
with
p
ar
en
ts
b
elo
n
g
in
g
o
n
l
y
to
th
e
ze
r
o
lev
el.
E
is
at
th
e
s
ec
o
n
d
lev
el,
with
p
ar
en
ts
b
elo
n
g
in
g
o
n
ly
to
th
e
f
ir
s
t
lev
el.
X
an
d
D
ar
e
at
th
e
th
ir
d
lev
el,
with
p
ar
en
ts
b
elo
n
g
in
g
o
n
ly
to
th
e
f
ir
s
t
an
d
s
ec
o
n
d
lev
els.
X
is
at
th
e
ze
r
o
lev
el,
an
d
th
e
v
er
tex
with
ev
id
en
ce
d
o
es
n
o
t
n
ee
d
to
b
e
ca
lc
u
lated
.
E
is
at
th
e
f
ir
s
t
lev
el,
with
v
er
tex
X
co
n
n
ec
ted
o
n
ly
to
v
er
tex
E
.
T
,
L
,
a
n
d
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Ma
r
ko
v
p
r
o
ce
s
s
es in
B
a
ye
s
ia
n
n
etw
o
r
k
co
mp
u
ta
tio
n
(
A
s
s
em
S
h
a
ya
k
h
meto
va
)
2187
ar
e
at
th
e
s
ec
o
n
d
lev
el;
th
ese
v
er
tices
ar
e
n
o
t
d
-
s
ep
ar
ated
f
r
o
m
v
e
r
tex
X
th
r
o
u
g
h
v
e
r
tex
E
,
an
d
th
u
s
,
th
ey
ar
e
in
f
lu
en
ce
d
b
y
v
er
tex
X
th
r
o
u
g
h
v
e
r
tex
E
.
A
an
d
S
ar
e
at
t
h
e
th
ir
d
lev
el;
th
ese
v
e
r
tices
ar
e
n
o
t
d
-
s
ep
ar
ated
f
r
o
m
v
er
tex
X
an
d
ar
e
th
er
e
f
o
r
e
in
f
lu
en
ce
d
b
y
v
er
tex
X
th
r
o
u
g
h
v
er
tices
E
,
T
,
an
d
L
.
B
is
at
th
e
f
o
u
r
th
lev
el;
th
is
v
er
tex
is
n
o
t
d
-
s
ep
ar
ated
f
r
o
m
v
er
te
x
X.
Ver
tex
B
is
in
f
lu
en
ce
d
b
y
v
er
tex
S
at
th
e
th
ir
d
lev
el;
h
o
wev
er
,
v
er
tices
E
an
d
B
ar
e
in
d
ep
en
d
en
t
co
n
ce
r
n
i
n
g
th
e
co
n
v
er
g
in
g
co
n
n
ec
tio
n
at
v
e
r
tex
D.
T
h
u
s
,
all
v
er
tices
in
th
e
B
N
en
d
u
p
d
ep
en
d
i
n
g
o
n
v
e
r
t
ex
.
T
h
e
f
o
llo
win
g
o
r
d
e
r
o
f
c
alcu
latin
g
th
e
v
er
tices
in
th
e
B
N
ca
n
b
e
p
r
o
p
o
s
ed
(
1
1
)
:
−
>
−
>
−
>
−
>
−
>
−
>
−
>
(
1
1
)
Fig
u
r
e
5
.
Mo
r
al
g
r
a
p
h
B
ay
es
'
th
eo
r
em
a
n
d
th
e
p
r
io
r
p
r
o
b
a
b
ilit
ies
o
f
s
p
ec
if
ic
v
er
tic
es
m
ay
b
e
u
s
ed
in
th
e
ca
lcu
la
tio
n
s
.
T
h
e
v
er
tices
in
v
o
lv
e
d
in
th
e
ca
lc
u
latio
n
s
ar
e
d
eter
m
in
ed
b
y
t
h
e
Ma
r
k
o
v
B
ay
esian
b
lan
k
et
o
f
th
e
v
er
tex
b
ein
g
ca
lcu
lated
o
r
b
y
n
eig
h
b
o
r
in
g
v
er
tices.
T
h
e
B
ay
esian
b
lan
k
ets
f
o
r
th
e
v
er
tices
will
b
e
as
f
o
llo
ws:
th
e
b
lan
k
et
f
o
r
v
er
tex
E
will
b
e
{T
,
L
,
X,
D,
B
};
th
e
b
lan
k
et
f
o
r
v
er
tex
T
will
b
e
{A,
E
,
L
};
th
e
b
lan
k
et
f
o
r
v
er
tex
L
will
b
e
{S,
E
,
T
};
th
e
b
lan
k
et
f
o
r
v
er
tex
D
will
b
e
{B,
E
};
th
e
b
lan
k
et
f
o
r
v
er
tex
A
will
b
e
{T
};
th
e
b
lan
k
et
f
o
r
v
er
tex
S
will
b
e
{L
,
B
};
an
d
th
e
b
lan
k
et
f
o
r
v
er
tex
B
will
b
e
{S,
D,
E
}.
W
e
co
n
s
id
er
ed
a
r
elativ
ely
s
im
p
le
ex
am
p
le.
E
v
id
en
ce
in
th
e
s
in
g
le
v
er
tex
X
in
f
l
u
en
ce
s
all
th
e
r
em
ain
in
g
v
e
r
tices.
Ver
tex
X
is
n
o
t
s
ep
ar
ated
f
r
o
m
an
y
o
f
th
e
o
th
er
v
er
tices.
L
et's
co
m
p
licate
th
e
task
a
b
it.
Su
p
p
o
s
e
th
e
ev
id
en
ce
is
in
v
er
tex
A.
Ver
tex
E
co
n
tain
s
a
co
n
v
er
g
in
g
co
n
n
ec
tio
n
.
T
h
is
m
ea
n
s
th
at
v
er
tices
A
an
d
T
will
b
e
in
d
ep
en
d
en
t
(
d
-
s
ep
ar
ated
)
f
r
o
m
v
er
tices
L
a
n
d
S.
Similar
ly
,
v
e
r
tices
E
an
d
B
a
r
e
in
d
ep
en
d
en
t
co
n
ce
r
n
in
g
th
e
co
n
v
er
g
i
n
g
c
o
n
n
ec
tio
n
at
v
er
tex
D.
T
h
e
p
ar
titi
o
n
i
n
g
o
f
v
er
tice
s
b
y
lev
els
in
th
is
ca
s
e
will
b
e
as
f
o
llo
ws:
A
an
d
S
ar
e
at
t
h
e
ze
r
o
le
v
el,
with
v
er
tex
A
co
n
tain
in
g
ev
id
e
n
ce
an
d
v
er
tex
S
b
ei
n
g
d
-
s
ep
ar
ate
d
f
r
o
m
v
er
tex
A,
m
ea
n
in
g
th
e
y
ar
e
in
d
ep
e
n
d
en
t.
T
,
L
,
an
d
B
ar
e
at
th
e
f
ir
s
t
lev
el,
with
v
er
tex
T
d
ep
en
d
in
g
o
n
ly
o
n
v
er
tex
A,
an
d
v
er
tices
L
an
d
B
d
ep
en
d
in
g
o
n
ly
o
n
v
er
tex
S.
E
is
at
t
h
e
s
ec
o
n
d
le
v
el,
d
e
p
en
d
i
n
g
o
n
v
er
tices
T
an
d
L
.
X
a
n
d
D
ar
e
at
th
e
th
ir
d
lev
el.
T
h
e
v
er
tices
in
v
o
lv
ed
in
th
e
ca
lcu
l
atio
n
s
ar
e
d
eter
m
in
e
d
eith
er
b
y
th
e
Ma
r
k
o
v
B
ay
esian
b
la
n
k
et
o
f
th
e
ca
lc
u
lated
v
er
tex
o
r
b
y
n
eig
h
b
o
r
in
g
v
er
ti
ce
s
.
T
h
e
B
ay
esian
b
lan
k
ets
f
o
r
th
e
v
er
tices
will
b
e
as
f
o
llo
ws:
th
e
b
lan
k
et
f
o
r
v
er
tex
T
will
b
e
{A,
E
,
L
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
L
will
b
e
{S,
E
,
T
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
B
will
b
e
{S,
D,
E
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
E
will
b
e
{T
,
L
,
X,
D,
B
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
X
will
b
e
{E
};
an
d
th
e
b
lan
k
et
f
o
r
v
er
tex
D
will b
e
{B,
E
}.
I
n
th
e
ca
lc
u
latio
n
s
,
we
will
u
s
e
th
e
p
r
o
b
ab
ilit
ies
o
f
t
h
e
n
o
d
e
s
ca
lcu
lated
in
th
e
p
r
ev
i
o
u
s
s
tep
.
I
n
th
e
in
itial st
ep
,
we
ca
lcu
late
th
e
n
o
d
es with
o
u
t e
v
id
en
ce
.
T
h
e
d
a
ta
o
b
tain
ed
is
th
en
u
s
ed
in
th
e
ca
lcu
latio
n
s
f
o
r
th
e
s
u
b
s
eq
u
en
t
s
tep
s
.
I
n
th
e
f
ir
s
t
s
tep
,
we
esti
m
ate
th
e
p
r
o
b
ab
ilit
ies
o
f
o
n
e
o
f
th
e
n
eig
h
b
o
r
in
g
n
o
d
es
o
f
t
h
e
f
ir
s
t
p
iece
o
f
ev
id
e
n
ce
.
I
f
t
h
er
e
ar
e
m
o
r
e
p
iece
s
o
f
ev
id
en
c
e,
we
esti
m
ate
th
e
p
r
o
b
ab
ili
ties
o
f
o
n
e
o
f
th
e
n
eig
h
b
o
r
in
g
n
o
d
es
o
f
th
e
s
ec
o
n
d
p
iece
o
f
ev
id
e
n
ce
,
an
d
s
o
o
n
.
Af
ter
p
r
o
ce
s
s
in
g
all
th
e
ev
id
en
ce
,
we
r
ep
lace
th
e
p
r
o
o
f
with
th
e
n
o
d
es
th
at
we
h
av
e
ju
s
t
p
r
o
ce
s
s
ed
.
W
e
th
en
co
n
s
tr
u
ct
th
eir
Ma
r
k
o
v
b
la
n
k
ets.
I
n
th
e
s
ec
o
n
d
s
tep
,
we
ca
lcu
late
th
e
p
r
o
b
a
b
ilit
ies
o
f
th
e
n
ew
n
o
d
es.
T
h
is
B
N
ex
am
p
le
is
to
o
s
im
p
le
t
o
p
r
o
v
id
e
e
x
am
p
les
with
m
u
ltip
le
p
iece
s
o
f
e
v
id
e
n
ce
.
L
et'
s
co
n
s
id
er
an
ex
am
p
le
o
f
a
s
ec
o
n
d
B
N.
Fig
u
r
e
6
s
h
o
ws
a
n
etwo
r
k
co
n
tain
in
g
2
0
v
er
tices.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
2
1
8
1
-
2
1
9
1
2188
Fig
u
r
e
6
.
L
e
v
el
p
ar
titi
o
n
in
g
co
n
s
id
er
in
g
d
-
s
ep
ar
atio
n
Of
p
ar
ticu
lar
in
ter
est
ar
e
v
er
ti
ce
s
E
1
an
d
E
2
,
wh
ich
p
o
s
s
ess
a
co
n
v
e
r
g
in
g
co
n
n
ec
tio
n
,
d
eter
m
in
in
g
th
e
ex
is
ten
ce
o
f
d
-
s
ep
ar
atio
n
in
ce
r
tain
ca
s
es.
W
h
en
co
n
s
id
er
in
g
a
s
ce
n
ar
io
wh
er
e
v
er
tic
es
A4
an
d
C
3
h
av
e
r
ec
eiv
ed
e
v
id
en
ce
,
th
e
lev
el
p
ar
titi
o
n
in
g
will
b
e
as
f
o
llo
ws:
At
th
e
ze
r
o
lev
el
ar
e
v
er
tice
s
A4
,
C
3
,
an
d
B
4
,
wh
er
e
th
e
f
ir
s
t
two
v
er
tices
h
av
e
r
ec
eiv
ed
ev
id
e
n
ce
,
an
d
B
4
is
n
o
t
co
n
n
ec
ted
to
th
e
v
er
tices
g
en
er
ated
b
y
v
er
tices
A4
an
d
C
3
th
r
o
u
g
h
c
o
n
v
er
g
in
g
c
o
n
n
ec
tio
n
s
in
E
1
an
d
E
2
.
T
h
e
f
ir
s
t
lev
el
in
cl
u
d
es
v
er
tices
A3
,
C
4
,
C
2
,
an
d
B
3
.
T
h
e
s
ec
o
n
d
lev
el
co
n
s
is
ts
o
f
v
er
tices
A2
,
C
1
,
an
d
B
2
.
T
h
e
th
ir
d
lev
el
i
n
clu
d
es
v
er
tices
A1
an
d
B
1
.
Ver
tices
D1
an
d
E
1
r
ep
r
esen
t
th
e
f
o
u
r
th
lev
el,
t
h
e
f
if
th
lev
el
b
y
v
er
tices
D2
an
d
E
2
,
th
e
s
ix
th
lev
el
in
clu
d
es
D3
an
d
E
3
,
an
d
th
e
s
ev
en
th
lev
el
co
n
s
is
ts
o
f
v
er
tices
D4
an
d
E
4
.
T
h
e
f
o
llo
win
g
o
r
d
er
o
f
ca
lcu
latin
g
th
e
v
er
tices
in
th
e
B
N
ca
n
b
e
p
r
o
p
o
s
ed
:
A3
-
>
C
4
-
>
C
2
-
>
B
3
-
>
A2
-
>
C
1
-
>
B
2
-
>
A1
-
>
B
1
-
>
D1
-
>
E
1
-
>
D2
-
>
E
2
-
>
D3
-
>
E
3
-
>
D4
-
>
E
4
.
T
h
e
B
ay
esian
b
lan
k
ets
f
o
r
th
e
v
er
tices
will
b
e
as
f
o
llo
ws:
th
e
b
lan
k
et
f
o
r
v
e
r
tex
A3
will
b
e
{A4
,
A
2
};
th
e
b
la
n
k
et
f
o
r
v
er
tex
C
4
will
b
e
{C3
};
th
e
b
la
n
k
et
f
o
r
v
er
tex
C
2
will
b
e
{C3
,
C
1
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
B
3
will
b
e
{B4
,
B
2
};
th
e
b
lan
k
et
f
o
r
v
er
tex
A
2
will
b
e
{A3
,
A1
};
t
h
e
b
lan
k
et
f
o
r
v
er
tex
C
1
will
b
e
{C2
,
A1
};
th
e
b
lan
k
et
f
o
r
v
er
tex
B
2
will
b
e
{B3
,
B
1
,
E
2
,
E
1
};
th
e
b
lan
k
et
f
o
r
v
er
tex
A1
will
b
e
{A2
,
C
1
,
D1
,
E
1
,
B
1
};
th
e
b
lan
k
et
f
o
r
v
er
tex
B
1
will
b
e
{B2
,
E
1
,
A1
};
th
e
b
lan
k
et
f
o
r
v
er
tex
D
1
will
b
e
{A1
,
D2
};
th
e
b
lan
k
et
f
o
r
v
er
tex
E
1
will
b
e
{A1
,
B
1
,
E
2
,
B
2
};
th
e
b
la
n
k
et
f
o
r
v
er
tex
D2
will
b
e
{D1
,
D
3
};
th
e
b
lan
k
e
t
f
o
r
v
er
tex
E
2
will
b
e
{B2
,
E
1
,
E
3
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
D3
will
b
e
{D2
,
D4
};
th
e
b
lan
k
et
f
o
r
v
e
r
tex
E
3
will
b
e
{E
2
,
E
4
};
t
h
e
b
lan
k
et
f
o
r
v
er
te
x
D4
will
b
e
{D3
}
;
an
d
th
e
b
lan
k
et
f
o
r
v
er
tex
E
4
will
b
e
{E
3
}.
T
h
e
ar
ticle
ex
p
lo
r
es
th
e
p
o
s
s
ib
ilit
ies
o
f
u
s
in
g
th
e
Ma
r
k
o
v
p
r
o
p
er
ty
to
s
im
p
lif
y
co
m
p
u
tatio
n
s
in
B
ay
esian
n
etwo
r
k
s
,
wh
ich
in
tr
o
d
u
ce
s
n
ew
ch
allen
g
es
wh
ile
s
o
lv
in
g
a
n
u
m
b
er
o
f
ex
is
tin
g
p
r
o
b
lem
s
.
Sp
ec
if
ically
,
it
r
eq
u
ir
es
ju
s
tific
atio
n
f
o
r
a
p
p
ly
in
g
th
e
Ma
r
k
o
v
p
r
o
p
er
ty
,
ad
ap
tatio
n
o
f
ex
is
tin
g
p
r
o
b
a
b
ilit
y
tab
les
d
esp
ite
th
eir
in
co
n
v
e
n
ien
t
s
tr
u
ctu
r
es,
a
n
d
p
r
o
p
er
ju
s
tific
atio
n
f
o
r
u
s
in
g
B
ay
es
'
th
eo
r
em
.
I
t
is
ess
en
tial
to
p
r
o
v
e
th
at
in
t
h
e
p
r
esen
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o
f
m
u
ltip
le
p
iece
s
o
f
ev
id
en
ce
a
n
d
c
h
an
g
es
in
th
e
d
ir
ec
tio
n
o
f
s
o
m
e
ed
g
es,
cy
cles d
o
n
o
t a
r
is
e
an
d
to
in
v
esti
g
ate
p
o
ten
tial c
o
n
tr
a
d
ictio
n
s
in
B
ay
esian
n
etwo
r
k
s
th
at
m
ay
o
cc
u
r
d
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e
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I
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8
7
0
8
Ma
r
ko
v
p
r
o
ce
s
s
es in
B
a
ye
s
ia
n
n
etw
o
r
k
co
mp
u
ta
tio
n
(
A
s
s
em
S
h
a
ya
k
h
meto
va
)
2189
to
in
co
r
r
ec
t
o
r
in
c
o
m
p
atib
le
r
e
ce
ip
t
o
f
m
u
ltip
le
p
iece
s
o
f
ev
id
en
ce
,
o
f
f
e
r
in
g
s
o
lu
tio
n
s
to
th
ese
is
s
u
es.
Desp
ite
th
e
ch
allen
g
es,
th
e
a
p
p
r
o
ac
h
u
n
d
e
r
c
o
n
s
id
er
atio
n
ap
p
ea
r
s
to
b
e
q
u
ite
p
r
o
m
is
in
g
an
d
war
r
an
ts
f
u
r
th
e
r
in
v
esti
g
atio
n
.
T
h
e
ef
f
ec
tiv
en
e
s
s
o
f
u
s
in
g
B
ay
esian
n
etwo
r
k
s
lar
g
ely
d
e
p
en
d
s
o
n
s
elec
tin
g
th
e
co
r
r
ec
t
c
o
n
ce
p
t
f
o
r
q
u
e
r
y
in
g
th
e
n
etwo
r
k
an
d
ef
f
icien
t
p
r
o
p
a
g
atio
n
m
eth
o
d
s
,
esp
ec
ially
in
th
e
p
r
esen
ce
o
f
m
u
ltip
le
p
iece
s
o
f
ev
id
en
ce
.
T
h
e
c
o
m
p
lex
an
d
e
x
ten
s
iv
e
to
p
o
lo
g
y
o
f
B
ay
esian
n
etwo
r
k
s
ca
n
s
ig
n
if
ican
tl
y
in
cr
ea
s
e
co
m
p
u
tatio
n
tim
e,
an
d
m
an
y
ex
is
tin
g
alg
o
r
i
th
m
s
cu
r
r
en
tl
y
u
s
e
a
n
ap
p
r
o
ac
h
b
ased
o
n
r
ep
r
esen
tin
g
th
e
o
r
ig
in
al
n
etwo
r
k
as
a
ju
n
ctio
n
t
r
ee
.
T
h
is
m
eth
o
d
h
as
s
ev
er
al
a
d
v
an
tag
es,
s
u
ch
as
u
n
iv
er
s
ality
,
o
b
tain
in
g
ac
cu
r
ate
p
r
o
b
ab
ilit
y
v
alu
es,
an
d
h
i
g
h
-
s
p
ee
d
im
p
lem
en
tatio
n
o
f
alg
o
r
ith
m
s
in
co
d
e.
Ho
we
v
er
,
th
is
ap
p
r
o
ac
h
also
h
as
lim
itatio
n
s
,
in
clu
d
in
g
d
if
f
icu
lties
in
co
m
p
u
tatio
n
s
f
o
r
s
p
ec
if
ic
to
p
o
lo
g
ies
an
d
co
m
p
lex
ity
i
n
u
n
d
er
s
tan
d
i
n
g
an
d
d
ev
elo
p
in
g
alg
o
r
ith
m
s
.
As
a
r
esu
lt,
m
a
n
y
d
e
v
elo
p
er
s
a
r
e
s
ee
k
in
g
way
s
to
s
im
p
lify
alg
o
r
ith
m
s
an
d
im
p
r
o
v
e
th
eir
ef
f
icien
cy
,
h
ig
h
lig
h
tin
g
th
e
n
e
ed
f
o
r
n
ew,
c
o
r
r
ec
t
p
ar
ad
i
g
m
s
f
o
r
w
o
r
k
in
g
with
B
ay
esian
n
etwo
r
k
s
.
On
e
s
u
ch
d
ir
ec
tio
n
is
a
r
etu
r
n
to
t
h
e
id
e
a
o
f
Ma
r
k
o
v
ch
ain
s
,
wh
er
e
t
h
e
in
f
o
r
m
atio
n
in
a
n
o
d
e
d
ep
e
n
d
s
o
n
ly
o
n
t
h
e
s
tate
o
f
n
eig
h
b
o
r
in
g
n
o
d
es,
wh
ich
s
im
p
lifie
s
alg
o
r
ith
m
s
an
d
in
cr
ea
s
es
th
eir
s
p
ee
d
.
I
t
i
s
es
s
en
tial
to
co
n
s
id
er
th
e
o
r
d
er
o
f
n
o
d
e
co
m
p
u
tatio
n
s
an
d
th
e
n
ee
d
f
o
r
iter
atio
n
s
i
n
th
e
p
r
esen
ce
o
f
ev
id
e
n
ce
.
C
o
n
tr
o
llin
g
th
e
d
-
s
ep
ar
atio
n
o
f
n
o
d
es
an
d
u
s
in
g
th
e
Ma
r
k
o
v
b
lan
k
et
also
p
lay
a
cr
u
cial
r
o
le
in
im
p
r
o
v
i
n
g
th
e
ac
cu
r
ac
y
o
f
ca
lcu
latio
n
s
,
alth
o
u
g
h
th
e
y
m
ay
co
m
p
licate
th
e
p
r
o
ce
s
s
.
T
h
u
s
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
to
d
ev
elo
p
in
g
alg
o
r
ith
m
s
f
o
r
B
ay
esian
n
etwo
r
k
s
r
eq
u
ir
es
f
u
r
th
er
in
v
esti
g
atio
n
an
d
p
r
ac
tical
test
in
g
to
ass
ess
its
ef
f
ec
tiv
en
ess
in
r
ea
l
-
wo
r
ld
co
n
d
itio
n
s
.
4.
CO
NCLU
SI
O
N
T
h
is
ar
ticle
ex
am
in
es
th
e
p
o
te
n
tial
o
f
u
s
in
g
Ma
r
k
o
v
p
r
o
ce
s
s
es
to
s
im
p
lify
B
ay
esian
n
etwo
r
k
s
(
B
Ns)
co
m
p
u
tatio
n
s
.
Desp
ite
th
e
o
b
v
io
u
s
ad
v
a
n
tag
es,
s
u
ch
as
s
p
ee
d
in
g
u
p
ca
lcu
latio
n
s
an
d
s
im
p
lify
in
g
alg
o
r
ith
m
s
,
in
tr
o
d
u
cin
g
t
h
e
Ma
r
k
o
v
p
r
o
p
er
ty
in
to
B
ay
esian
n
etwo
r
k
s
also
in
tr
o
d
u
ce
s
s
ev
er
al
n
ew
ch
allen
g
es.
T
h
ese
in
clu
d
e
th
e
n
ee
d
to
ju
s
tify
th
e
ap
p
licatio
n
o
f
Ma
r
k
o
v
p
r
o
p
er
ties
,
ad
ap
t
ex
is
tin
g
p
r
o
b
a
b
ilit
y
tab
les
to
n
ew
s
tr
u
ctu
r
es,
an
d
co
r
r
ec
tl
y
ap
p
ly
B
ay
es'
th
eo
r
em
.
Ad
d
itio
n
ally
,
it
is
im
p
o
r
tan
t
to
p
r
o
v
e
t
h
a
t
n
o
c
y
cles
ar
is
e
in
th
e
p
r
esen
ce
o
f
m
u
ltip
le
p
iec
es
o
f
ev
id
en
ce
an
d
ch
an
g
es
in
th
e
d
ir
ec
tio
n
o
f
ce
r
tain
ed
g
es
an
d
to
in
v
esti
g
ate
p
o
s
s
ib
le
co
n
tr
ad
ictio
n
s
th
at
m
ay
o
cc
u
r
wh
en
m
u
ltip
le
p
iece
s
o
f
ev
id
e
n
ce
ar
e
r
ec
eiv
ed
i
n
co
m
p
atib
le.
Nev
er
th
eless
,
th
e
ap
p
r
o
ac
h
u
n
d
er
co
n
s
id
er
atio
n
is
p
r
o
m
is
in
g
an
d
r
eq
u
ir
es
f
u
r
th
er
r
esear
ch
,
esp
ec
ially
in
co
m
p
lex
an
d
lar
g
e
B
N
to
p
o
lo
g
ies.
T
h
e
p
r
ac
tical
ap
p
licatio
n
o
f
th
ese
m
eth
o
d
s
co
u
ld
s
ig
n
if
ican
tly
im
p
r
o
v
e
th
e
ef
f
icien
c
y
o
f
wo
r
k
in
g
with
B
ay
esian
n
etwo
r
k
s
,
p
ar
ticu
lar
ly
in
p
r
o
ce
s
s
in
g
d
ata
with
m
u
ltip
le
u
n
ce
r
tain
ties
.
T
h
e
p
r
o
p
o
s
ed
al
g
o
r
ith
m
s
an
d
ap
p
r
o
ac
h
es
n
ee
d
d
etailed
test
in
g
an
d
o
p
tim
izat
io
n
f
o
r
u
s
e
in
r
ea
l
-
wo
r
ld
co
n
d
itio
n
s
,
wh
ich
will a
llo
w
th
eir
to
tal
p
r
ac
tical
v
alu
e
to
b
e
r
ea
lized
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
is
p
ap
er
was w
r
itten
u
n
d
er
g
r
an
t A
P1
9
6
7
9
1
4
2
“
Sear
ch
f
o
r
o
p
tim
al
s
o
lu
tio
n
s
in
B
ay
esia
n
n
etwo
r
k
s
in
m
o
d
els
with
lin
ea
r
c
o
n
s
tr
a
in
ts
an
d
lin
ea
r
f
u
n
ctio
n
als.
D
ev
elo
p
m
en
t
o
f
alg
o
r
ith
m
s
an
d
p
r
o
g
r
am
s
”
(
2
0
2
3
-
2
0
2
5
)
o
f
t
h
e
Min
is
tr
y
o
f
E
d
u
c
atio
n
an
d
Scien
ce
o
f
th
e
R
ep
u
b
lic
o
f
Kaz
ak
h
s
tan
.
RE
F
E
R
E
NC
E
S
[
1
]
J.
K
.
G
h
o
s
h
,
“
P
r
o
b
a
b
i
l
i
st
i
c
n
e
t
w
o
r
k
s
a
n
d
e
x
p
e
r
t
s
y
st
e
ms:
e
x
a
c
t
c
o
m
p
u
t
a
t
i
o
n
a
l
m
e
t
h
o
d
s
f
o
r
B
a
y
e
si
a
n
n
e
t
w
o
r
k
s,”
I
n
t
e
rn
a
t
i
o
n
a
l
S
t
a
t
i
st
i
c
a
l
Re
v
i
e
w
,
v
o
l
.
7
6
,
n
o
.
2
,
p
p
.
3
0
6
–
3
0
7
,
J
u
l
.
2
0
0
8
,
d
o
i
:
1
0
.
1
1
1
1
/
j
.
1
7
5
1
-
5
8
2
3
.
2
0
0
8
.
0
0
0
5
4
_
8
.
x
.
[
2
]
F
.
J.
R
a
d
e
r
mac
h
e
r
,
“
P
r
o
b
a
b
i
l
i
s
t
i
c
r
e
a
s
o
n
i
n
g
i
n
i
n
t
e
l
l
i
g
e
n
t
sy
st
e
ms:
n
e
t
w
o
r
k
s
o
f
p
l
a
u
si
b
l
e
i
n
f
e
r
e
n
c
e
,
”
S
I
A
M
Re
v
i
e
w
,
v
o
l
.
3
2
,
n
o
.
4
,
p
p
.
7
0
4
–
7
0
7
,
D
e
c
.
1
9
9
0
,
d
o
i
:
1
0
.
1
1
3
7
/
1
0
3
2
1
5
5
.
[
3
]
L.
E.
S
u
c
a
r
,
“
B
a
y
e
si
a
n
n
e
t
w
o
r
k
s
:
r
e
p
r
e
s
e
n
t
a
t
i
o
n
a
n
d
i
n
f
e
r
e
n
c
e
,
”
i
n
P
r
o
b
a
b
i
l
i
s
t
i
c
G
ra
p
h
i
c
a
l
M
o
d
e
l
s
,
S
p
r
i
n
g
e
r
I
n
t
e
r
n
a
t
i
o
n
a
l
P
u
b
l
i
s
h
i
n
g
,
2
0
2
0
,
p
p
.
1
1
1
–
1
5
1
.
[
4
]
J.
B
a
z
,
P
.
A
l
o
n
so
,
J.
M
.
P
e
ñ
a
,
a
n
d
R
.
P
é
r
e
z
-
F
e
r
n
á
n
d
e
z
,
“
G
a
u
ssi
a
n
M
a
r
k
o
v
r
a
n
d
o
m fie
l
d
s
a
n
d
t
o
t
a
l
l
y
p
o
si
t
i
v
e
m
a
t
r
i
c
e
s
,
”
J
o
u
rn
a
l
o
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AP
9
6
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1
4
2
p
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“
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p
ro
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”
(2
0
2
3
-
2
0
2
5
).
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r
re
se
a
rc
h
in
tere
sts
in
c
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e
d
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v
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l
o
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m
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,
d
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ta
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in
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,
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rti
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in
tell
ig
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c
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,
a
n
d
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a
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D.
,
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ro
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Artifi
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tell
ig
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d
Bi
g
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ta
a
t
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-
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ra
b
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Ka
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k
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ti
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y
.
S
h
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c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
a
se
m
sh
a
y
a
k
h
m
e
to
v
a
@m
a
il
.
r
u
.
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