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s.
K
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s
:
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©
2
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1
9
In
stit
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te o
f
A
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E
n
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rin
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S
c
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Al
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rig
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C
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p
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A
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:
San
u
T
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d
A
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Scien
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s
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n
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Ko
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.
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ail: t
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1.
I
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as
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o
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[
1
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2
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W
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th
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p
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[
3
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.
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[
4
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.
C
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g
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s
tio
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m
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-
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[
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m
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is
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[
9
]
w
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m
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w
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ap
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m
a
n
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x
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A
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[
9
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A
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2
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w
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Sectio
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3
g
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v
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w
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m
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ass
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Sectio
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4
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I
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s
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5
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co
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p
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th
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s
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d
is
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s
s
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.
Sectio
n
6
g
iv
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s
co
n
cl
u
s
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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1
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n
[
6
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,
th
e
a
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ad
.
T
h
en
th
e
co
n
g
esti
o
n
lev
els
ar
e
p
r
ed
icted
an
d
th
e
l
o
ad
is
p
r
o
p
er
ly
s
h
ar
ed
to
r
ed
u
ce
co
n
g
e
s
tio
n
.
Her
e,
t
h
e
lo
a
d
b
alan
cin
g
is
n
o
t
eq
u
alize
d
o
v
er
t
h
e
tr
a
n
s
m
i
s
s
io
n
p
at
h
s
.
T
AR
A
:
“
T
o
p
o
l
o
g
y
-
Aw
ar
e
R
eso
u
r
ce
A
d
ap
tatio
n
to
A
l
lev
ia
te
C
o
n
g
esti
o
n
i
n
Sen
s
o
r
Net
w
o
r
k
s
”,
is
d
e
s
cr
ib
ed
in
[
9
]
.
Her
e,
ad
d
itio
n
al
n
o
d
es
an
d
lin
k
s
ar
e
b
r
o
u
g
h
t
i
n
to
s
er
v
e
th
e
p
r
ese
n
t
tr
a
f
f
ic.
C
o
n
g
e
s
t
p
r
o
n
e
n
o
d
es
ar
e
p
ar
tiall
y
b
y
p
ass
ed
to
av
o
id
co
n
g
e
s
tio
n
.
T
h
is
is
e
s
s
e
n
tiall
y
a
tr
u
n
ca
ted
m
u
l
ti
-
p
ath
r
o
u
ti
n
g
an
d
lo
ad
b
alan
cin
g
i
s
n
o
t
f
u
ll
y
ad
d
r
ess
ed
.
C
O
D
A
:
“C
o
n
g
e
s
tio
n
D
etec
tio
n
an
d
A
v
o
id
an
ce
in
s
e
n
s
o
r
n
et
w
o
r
k
s
"
,
in
[
1
1
]
u
s
es
clo
s
ed
-
lo
o
p
m
u
lti
-
s
o
u
r
ce
r
eg
u
latio
n
.
I
n
d
esig
n
i
n
g
C
OD
A
,
i
m
p
o
r
tan
ce
i
s
g
iv
e
n
to
e
n
er
g
y
s
a
v
i
n
g
i
n
s
e
n
s
o
r
n
o
d
es.
Her
e,
th
e
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
is
r
elati
v
el
y
h
i
g
h
.
I
n
[
1
2
]
,
th
e
au
t
h
o
r
s
p
r
o
p
o
s
e
E
C
OD
A
:
“
E
n
h
an
ce
d
C
o
n
g
esti
o
n
Dete
ctio
n
a
n
d
Av
o
i
d
an
ce
”.
Her
e,
d
u
al
th
r
es
h
o
ld
b
u
f
f
er
s
ar
e
u
s
ed
f
o
r
co
n
g
esti
o
n
d
etec
tio
n
.
C
h
a
n
n
el
u
t
ilizatio
n
is
o
p
ti
m
ized
b
y
p
r
o
p
er
co
n
tr
o
l
m
ec
h
a
n
i
s
m
.
I
n
t
h
is
ca
s
e,
t
h
e
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
is
h
i
g
h
er
t
h
a
n
C
OD
A
a
n
d
th
e
co
n
tr
o
l
m
ec
h
a
n
is
m
i
s
r
ath
er
co
m
p
lex
.
E
x
ten
s
iv
e
s
u
r
v
e
y
s
o
n
co
n
g
est
io
n
alle
v
iatio
n
tech
n
iq
u
es a
r
e
g
i
v
e
n
in
[
1
3
,
1
4
]
.
3.
NE
T
WO
RK
M
O
DE
L
AND
ASSUM
P
T
I
O
NS
C
o
n
s
id
er
a
W
SN
w
ith
N
h
o
m
o
g
e
n
eo
u
s
s
e
n
s
o
r
n
o
d
es.
W
e
ass
u
m
e
th
e
p
r
ese
n
ce
o
f
a
B
ase
Statio
n
(
B
S)
o
r
Sin
k
t
h
at
co
n
tr
o
ls
th
e
W
SN
a
n
d
co
llect
s
d
ata
f
r
o
m
th
e
s
en
s
o
r
s
.
T
h
e
co
m
m
u
n
icati
o
n
is
m
ai
n
l
y
eit
h
er
f
r
o
m
t
h
e
B
S
to
w
ar
d
s
th
e
s
e
n
s
o
r
n
o
d
es o
r
v
ice
-
v
er
s
a.
B
u
t a
n
y
n
o
d
e
ca
n
ac
t a
s
a
s
o
u
r
ce
as
w
e
ll a
s
a
d
es
tin
a
tio
n
.
B
ec
au
s
e
o
f
th
e
l
i
m
ited
tr
an
s
m
is
s
io
n
r
a
n
g
e
o
f
i
n
d
i
v
id
u
al
s
en
s
o
r
n
o
d
es,
th
e
m
u
lti
-
h
o
p
co
m
m
u
n
icatio
n
i
s
ad
o
p
ted
b
etw
ee
n
t
h
e
s
o
u
r
ce
an
d
t
h
e
d
est
in
at
io
n
.
T
h
e
i
n
ter
m
ed
iate
s
e
n
s
o
r
n
o
d
es
ac
t
as
r
ela
y
n
o
d
es.
T
h
e
f
o
llo
w
i
n
g
a
s
s
u
m
p
t
io
n
s
ar
e
m
ad
e
ab
o
u
t th
e
W
SN.
a.
Sen
s
o
r
n
o
d
es a
r
e
h
o
m
o
g
e
n
eo
u
s
an
d
s
tatic.
b.
Sen
s
o
r
s
h
av
e
l
i
m
ited
b
atter
y
en
er
g
y
.
c.
T
h
e
B
S h
as su
f
f
icie
n
t p
o
w
er
a
n
d
r
u
n
s
th
e
p
r
o
p
o
s
ed
ce
n
tr
alize
d
alg
o
r
ith
m
.
3
.
1
.
Wirele
s
s
s
en
s
o
r
net
w
o
rk
a
s
a
g
ra
ph
T
h
e
W
SN
is
r
ep
r
esen
ted
b
y
a
p
lan
ar
g
r
ap
h
G
(
V
,
E
)
w
h
er
e
V
is
t
h
e
v
er
tex
s
et
o
f
N
n
o
d
es
an
d
E
i
s
th
e
ed
g
e
s
et.
T
h
e
s
e
n
s
o
r
n
o
d
es
ar
e
id
en
tifie
d
an
d
r
ep
r
esen
te
d
b
y
t
h
e
v
er
tice
s
1
,
2
,
.
.
,
N
.
T
h
e
v
er
tex
o
r
n
o
d
e
s
et
V
is
g
i
v
en
b
y
,
V
=
[
1
,
2
,
.
.
.
N
−
1
,
N
]
(
1
)
T
h
e
ed
g
e
s
et
E
i
s
t
h
e
co
llec
tio
n
o
f
al
l
th
e
lin
k
s
o
f
t
h
e
n
et
w
o
r
k
.
E
d
g
e
ele
m
en
t
e
(
i
,
j
)
r
ep
r
esen
ts
th
e
ed
g
e
b
et
w
ee
n
n
o
d
e
i
an
d
j
f
o
r
all
i
an
d
j
in
th
e
r
an
g
e
1
to
N
.
T
h
e
ed
g
e
v
alu
e
e
(
i
,
j
)
is
s
et
to
1
if
n
o
d
e
i
an
d
j
ar
e
w
it
h
i
n
t
h
e
tr
a
n
s
m
i
s
s
io
n
r
an
g
e
o
f
ea
c
h
o
t
h
er
.
Ot
h
er
w
is
e,
e
(
i
,
j
)
is
s
et
to
∞.
T
h
er
ef
o
r
e,
e(
i
,
j
)
=
1
m
ea
n
s
n
o
d
es
i
an
d
j
ar
e
o
n
e
-
h
o
p
n
e
ig
h
b
o
r
s
an
d
t
h
er
e
is
co
n
n
ec
ti
v
it
y
b
et
w
ee
n
t
h
e
m
a
n
d
e
(
i
,
j
)
=
∞
m
ea
n
s
,
i
an
d
j
ca
n
n
o
t
co
m
m
u
n
icate
d
ir
ec
tly
.
On
l
y
co
n
n
ec
ti
n
g
ed
g
es
w
ill
b
e
s
h
o
w
n
in
t
h
e
g
r
ap
h
.
On
e
h
o
p
n
eig
h
b
o
r
n
o
d
es
ar
e
also
ca
lled
ad
j
ac
e
n
t
n
o
d
es.
Her
e,
b
id
ir
ec
tio
n
al
li
n
k
s
ar
e
ass
u
m
ed
b
et
w
ee
n
o
n
e
-
h
o
p
n
ei
g
h
b
o
r
s
.
T
h
er
ef
o
r
e,
e
(
i
,
j
)
=
e
(
j
,
i
)
.
W
e
tak
e
e
(
i
,
i
)
=
∞
to
av
o
id
s
elf
-
lo
o
p
s
.
T
h
e
co
llectio
n
o
f
e
(
i
,
j
)
’
s
f
o
r
m
th
e
ad
j
ac
en
c
y
o
r
co
n
n
ec
ti
v
it
y
m
atr
ix
f
o
r
th
e
g
r
a
p
h
o
f
th
e
n
et
w
o
r
k
.
3
.
2
.
P
a
t
h f
ro
m
t
he
s
o
urce
t
o
t
he
des
t
ina
t
io
n
A
p
ath
f
r
o
m
a
s
o
u
r
ce
n
o
d
e
s
to
a
d
esti
n
atio
n
n
o
d
e
t
i
s
a
s
eq
u
e
n
ce
o
f
n
o
n
-
r
ep
ea
tin
g
ad
j
ac
en
t
(
o
n
e
h
o
p
)
n
o
d
es
s
tar
tin
g
f
r
o
m
s
an
d
en
d
in
g
at
t.
No
n
r
ep
etiti
o
n
o
f
n
o
d
es
ass
u
r
es
t
h
at
th
e
p
ath
is
f
r
ee
o
f
lo
o
p
s
.
A
d
j
ac
en
c
y
o
f
n
o
d
es
a
lo
n
g
t
h
e
p
ath
as
s
u
r
e
s
co
n
ti
n
u
o
u
s
co
n
n
ec
ti
v
it
y
f
r
o
m
t
h
e
s
o
u
r
ce
to
th
e
d
esti
n
a
tio
n
.
T
h
er
e
ca
n
b
e
s
ev
er
al
p
ath
s
f
r
o
m
s
to
t
in
a
g
i
v
en
g
r
ap
h
(
n
et
wo
r
k
)
.
3
.
3
.
M
e
a
s
ure
o
f
co
ng
estio
n lev
el
a
t
a
no
de
Sev
er
al
m
etr
ics
ar
e
u
s
ed
to
m
ea
s
u
r
e
t
h
e
co
n
g
esti
o
n
le
v
el
o
r
th
e
d
eg
r
ee
o
f
co
n
g
e
s
tio
n
at
a
n
o
d
e
(
Ak
y
i
ld
iz
et
al.
,
2
0
0
2
)
.
W
ith
o
u
t
a
n
y
lo
s
s
o
f
g
e
n
er
alit
y
,
w
e
t
ak
e
t
h
e
q
u
e
u
e
len
g
t
h
o
f
p
ac
k
et
s
at
a
g
i
v
e
n
n
o
d
e
as
th
e
m
ea
s
u
r
e
o
f
th
e
co
n
g
e
s
ti
o
n
lev
el
at
t
h
at
n
o
d
e.
I
t
is
ass
u
m
ed
t
h
at
t
h
e
s
izes
o
f
b
u
f
f
er
s
at
n
o
d
es
ar
e
s
u
f
f
icie
n
tl
y
l
ar
g
e
s
o
t
h
at
t
h
er
e
is
n
o
lo
s
s
o
f
p
ac
k
et
s
in
a
n
y
q
u
e
u
e
d
u
e
to
o
v
er
f
lo
w
.
I
t
i
s
also
ass
u
m
ed
th
a
t
th
e
q
u
e
u
e
len
g
t
h
s
ch
a
n
g
e
r
elat
iv
el
y
s
lo
w
l
y
w
it
h
r
esp
ec
t
to
ti
m
e
s
o
th
a
t
d
u
r
i
n
g
t
h
e
ca
lc
u
lati
o
n
an
d
r
ed
is
co
v
er
y
o
f
th
e
o
p
ti
m
a
l p
ath
s
,
t
h
e
q
u
e
u
e
len
g
t
h
s
r
e
m
ai
n
n
e
ar
l
y
co
n
s
ta
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
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I
n
t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
8
0
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4
8
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I
n
g
e
n
er
al,
th
e
co
n
g
e
s
tio
n
lev
els
o
f
t
h
e
s
e
n
s
o
r
s
n
o
d
es
r
e
m
ai
n
al
m
o
s
t
s
a
m
e
i
n
a
s
ess
io
n
.
T
h
e
ce
n
tr
alize
d
co
n
tr
o
ller
,
B
S
co
llects
th
i
s
i
n
f
o
r
m
atio
n
p
er
i
o
d
ically
.
T
h
is
p
er
io
d
d
ep
en
d
s
o
n
th
e
ap
p
licatio
n
s
an
d
ch
ar
ac
ter
is
tic
s
o
f
t
h
e
n
et
w
o
r
k
.
T
h
e
p
r
esen
t
co
n
g
est
io
n
lev
el
o
f
n
o
d
e
i
is
r
ep
r
esen
te
d
b
y
s
y
m
b
o
l
f
o
r
i
=
1
to
N
.
T
h
e
co
n
g
esti
o
n
ar
r
ay
f
o
r
th
e
e
n
tire
W
SN is
w
r
it
te
n
as,
=
[
1
,
2
,
…
,
,
…
,
]
(
2
)
3
.
4
.
Co
ng
estio
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els a
lo
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t
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On
ce
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s
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k
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w
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f
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r
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h
e
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d
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n
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all
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s
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p
ath
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et
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ter
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ter
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h
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o
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g
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p
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ted
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h
at
is
,
th
e
co
r
r
esp
o
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g
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m
e
n
ts
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ad
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y
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atr
i
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a
s
,
(
,
−
1
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,
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=
1
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)
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o
r
k
=
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to
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+
1
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I
n
(
4
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,
,
0
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an
d
,
(
)
+
1
=
.
T
h
e
(
4
)
s
im
p
l
y
m
ea
n
s
th
at
an
y
t
w
o
ad
j
ac
en
t
n
o
d
es
in
P
j
ar
e
w
it
h
in
t
h
e
co
m
m
u
n
icati
o
n
r
an
g
e
o
f
ea
ch
o
th
er
.
T
h
e
C
o
n
g
e
s
tio
n
ar
r
a
y
(
o
r
v
ec
to
r
)
o
f
a
p
ath
is
t
h
e
s
eq
u
e
n
c
e
o
f
th
e
co
n
g
e
s
tio
n
le
v
el
s
o
f
th
e
n
o
d
es
alo
n
g
t
h
at
p
ath
.
Fo
r
th
e
p
ath
s
p
ec
if
ied
b
y
(
3
)
,
th
e
ar
r
ay
t
h
at
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ep
r
esen
ts
th
e
co
n
g
es
tio
n
le
v
e
ls
is
r
ep
r
esen
ted
b
y
CL
as,
=
[
,
,
1
,
,
2
,
…
,
,
,
…
,
,
(
)
,
]
(
5
)
Her
e,
th
e
s
o
u
r
ce
an
d
th
e
d
esti
n
atio
n
n
o
d
es
ar
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f
ix
ed
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s
p
ec
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ied
)
f
o
r
all
p
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s
ib
le
p
ath
s
f
r
o
m
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Sin
ce
t
h
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p
ac
k
et
s
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t
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n
g
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o
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is
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o
t
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elev
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t
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th
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el
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m
s
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t
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h
er
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r
e,
ter
m
Q
t
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ca
n
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e
ig
n
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r
ed
.
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n
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n
in
g
t
h
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e
f
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tiv
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C
o
n
g
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n
Vec
to
r
f
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th
e
p
u
r
p
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s
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f
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eter
m
i
n
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g
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p
ti
m
al
p
at
h
,
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e
e
x
cl
u
d
e
f
r
o
m
(
5
)
.
T
h
e
r
esu
ltin
g
e
f
f
ec
t
iv
e
co
n
g
est
io
n
v
ec
to
r
is
,
=
[
,
,
1
,
,
2
,
…
,
,
,
…
,
,
(
)
]
(
6
)
Her
e,
,
is
t
h
e
co
n
g
es
tio
n
lev
el
o
f
n
o
d
e
,
in
a
p
r
o
p
er
u
n
it
a
n
d
k
v
ar
ies
f
r
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m
1
to
L
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.
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h
at
is
,
,
=
,
.
T
h
u
s
,
∈
.
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x
a
m
p
le
1
:
T
o
d
em
o
n
s
tr
ate
th
e
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o
r
m
atio
n
s
o
f
’
s
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d
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s
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a
s
im
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l
e
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et
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k
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s
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wn
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Fi
g
u
r
e
1
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e,
s
o
u
r
ce
s
=
1
a
n
d
th
e
d
e
s
tin
a
tio
n
t
=
5
w
it
h
n
u
m
b
er
o
f
n
o
d
es
N
=
5
an
d
t
h
e
n
u
m
b
e
r
o
f
d
is
ti
n
ct
p
at
h
s
,
M
=
4
.
C
o
n
g
es
tio
n
at
s
o
u
r
ce
is
tak
en
a
s
0
,
w
h
ich
w
i
ll b
e
ex
p
l
ain
ed
later
.
T
h
e
p
ath
s
f
r
o
m
1
to
5
an
d
th
ei
r
co
n
g
esti
o
n
lev
el
s
ar
e,
=
[
1
,
2
,
5
]
.
=
[
Q
1
, Q
2
]
=
[
0
,
4
0
]
.
=
[
1
,
2
,
4
,
5
]
.
=
[
Q
1
,
Q
2
, Q
4
]
=
[
0
,
4
0
,
2
0
]
.
=
[
1
,
3
,
4
,
5
]
.
=
[
Q
1
, Q
3
, Q
4
]
=
[
0
,
3
0
,
2
0
]
.
=
[
1
,
3
,
4
,
2
,
5
]
.
= [
Q1
,
Q3
,
Q
4
, Q
2
]
=
[
0
,
3
0
,
2
0
,
4
0
]
.
F
ig
u
r
e
1
.
Net
w
o
r
k
w
i
th
5
n
o
d
e
s
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:
2
0
8
8
-
8708
C
o
n
g
esti
o
n
b
o
ttlen
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k
a
vo
id
r
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u
tin
g
in
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s
en
s
o
r
n
etw
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ks (
S
a
n
u
Th
o
ma
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)
4807
3
.
5
.
M
a
x
i
m
u
m
co
ng
estio
n
lev
el
o
f
a
pa
t
h
T
h
e
m
a
x
i
m
u
m
co
n
g
e
s
tio
n
le
v
el
o
f
p
ath
P
j
,
r
ep
r
esen
ted
b
y
v
ar
iab
le
R
j
,
is
d
ef
in
ed
as
th
e
m
ax
i
m
u
m
o
f
ar
r
ay
.
T
h
at
is
,
=
(
)
(
7
)
T
h
e
(
7
)
also
ca
n
b
e
ex
p
r
ess
ed
as,
=
∈
{
1
:
(
)
}
(
,
)
(
8
)
T
h
is
g
i
v
es
t
h
e
m
ax
i
m
u
m
o
f
,
o
v
er
k
in
t
h
e
r
an
g
e
1
to
L
(
j
)
.
T
h
u
s
R
j
is
d
eter
m
in
ed
b
y
f
i
n
d
in
g
th
e
m
ax
i
m
u
m
o
f
th
e
co
n
g
e
s
tio
n
le
v
els
o
f
n
o
d
es
f
o
r
m
i
n
g
t
h
e
p
ath
ex
c
lu
d
i
n
g
th
e
s
o
u
r
ce
an
d
t
h
e
d
esti
n
atio
n
n
o
d
es.
I
n
E
x
a
m
p
le
1
,
R
1
=
4
0
.
R
2
=
4
0
.
R
3
=
3
0
.
R
4
=
4
0
.
3
.
6
.
M
ini
m
u
m
a
m
o
ng
Rj
’
s
L
et
R
b
e
t
h
e
ar
r
a
y
f
o
r
m
ed
b
y
R
j
’
s
f
o
r
j
=
1
,
2
,
.
.
.
,
M
as,
=
[
1
,
2
,
…
,
,
…
,
]
(
9
)
I
n
E
x
a
m
p
le
1
,
=
[
40
,
40
,
30
,
40
]
.
Ou
r
o
b
j
ec
tiv
e
is
to
f
in
d
t
h
at
i
n
d
ex
j
,
s
a
y
J
,
w
h
er
e
R
J
is
t
h
e
m
in
i
m
u
m
o
f
th
e
ar
r
a
y
R
.
T
h
is
ca
n
b
e
s
tated
as,
=
∈
{
1
:
}
(
)
(
1
0
)
I
n
E
x
a
m
p
le
1
,
th
e
m
i
n
(
R
)
o
cc
u
r
s
at
in
d
e
x
lo
ca
tio
n
3
.
T
h
er
ef
o
r
e
J
=
3
,
R
J
=3
0
an
d
th
e
o
p
tim
al
p
ath
i
s
P
J
=
P
3
.
Su
b
s
ti
tu
t
in
g
f
o
r
R
j
f
r
o
m
(
8
)
in
(
1
0
)
,
w
e
g
et,
=
∈
{
1
:
}
(
∈
{
1
:
(
)
}
(
,
)
)
(
1
1
)
On
ce
J
i
s
o
b
tain
ed
,
th
e
co
r
r
esp
o
n
d
in
g
m
i
n
i
m
u
m
a
m
o
n
g
R
j
’
s
is
R
J
(
t
h
e
J
th
ele
m
e
n
t
o
f
ar
r
a
y
R
)
a
n
d
it
ca
n
b
e
ex
p
r
ess
ed
as,
=
(
[
1
,
2
,
…
,
]
)
=
min
(
)
(
1
2
)
On
ce
J
is
k
n
o
w
n
,
t
h
e
o
p
ti
m
al
p
ath
f
r
o
m
s
to
t
i
s
P
J
as
s
p
e
cif
ied
i
n
(
3
)
.
T
h
is
p
ath
i
s
d
es
ig
n
a
ted
as
OP
(
t
)
.
T
h
e
v
alu
es
o
f
J
,
P
J
an
d
R
J
f
o
r
a
g
iv
e
n
s
o
u
r
ce
s
d
ep
en
d
o
n
th
e
d
e
s
ti
n
atio
n
t
.
T
h
er
ef
o
r
e,
w
e
d
esi
g
n
ate
J
as
g
i
v
en
b
y
(
1
0
)
as
J
(
t
)
an
d
th
e
co
r
r
esp
o
n
d
in
g
m
in
i
m
i
s
e
d
m
a
x
i
m
u
m
co
n
g
es
tio
n
le
v
el
v
alu
e
R
J
as
f
(
t
)
.
T
h
en
w
e
r
e
w
r
ite
(
1
0
)
an
d
(
1
2
)
as,
(
)
=
∈
{
1
:
}
(
)
(
1
3
)
(
)
=
(
)
=
(
[
1
,
2
,
…
,
]
)
(
1
4
)
T
h
at
is
,
f
(
t
)
ca
n
b
e
w
r
itte
n
as,
(
)
=
min
∈
{
1
:
}
(
)
=
min
(
)
(
1
5
)
W
h
en
w
e
s
elec
t
t
h
e
o
p
ti
m
al
p
ath
OP
(
t
)
,
th
e
r
elati
v
el
y
h
i
g
h
er
co
n
g
e
s
tio
n
le
v
el
n
o
d
es
ar
e
av
o
id
ed
w
h
ile
tr
a
v
elli
n
g
f
r
o
m
s
to
t
.
Th
e
va
r
ia
b
le
f
(
t
)
fr
o
m
(
1
5
)
,
r
ep
r
esen
ts
th
e
ma
ximu
m
co
n
g
esti
o
n
leve
l
o
f
p
a
th
OP
(
t
)
fr
o
m
s
to
t
.
3
.
7
.
O
bje
ct
iv
e
T
h
e
o
b
j
ec
tiv
e
is
to
d
eter
m
i
n
e
f
(
t
)
an
d
th
e
o
p
ti
m
al
p
ath
OP
(
t
)
f
o
r
a
g
i
v
en
s
an
d
f
o
r
all
t
’
s
i
n
(
t
∈
{1
:
N
}
\
s
)
.
W
e
d
esig
n
ate
t
h
i
s
p
ath
as
t
h
e
C
o
n
g
e
s
tio
n
B
o
ttl
en
ec
k
No
d
e
A
v
o
id
P
ath
(
C
B
N
A
P
)
an
d
d
esig
n
ate
th
e
m
e
th
o
d
to
d
eter
m
in
e
C
B
N
A
P
as th
e
C
B
N
A
P
alg
o
r
ith
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
8
0
4
-
4
8
1
4
4808
4.
DE
T
E
RM
I
NAT
I
O
N
O
F
CB
NAP
4
.
1
.
E
x
ha
us
t
iv
e
s
ea
rc
h
m
et
ho
d
I
n
g
en
er
al,
f
o
r
a
g
iv
e
n
W
SN,
b
y
k
n
o
w
i
n
g
its
to
p
o
lo
g
y
,
w
e
ca
n
en
u
m
er
ate
all
p
o
s
s
ib
le
p
ath
s
f
r
o
m
a
g
iv
e
n
s
o
u
r
ce
n
o
d
e
s
to
a
d
e
s
tin
a
tio
n
n
o
d
e
t.
A
lo
n
g
ea
ch
p
ath
,
w
e
ca
n
f
i
n
d
th
at
n
o
d
e
w
h
ich
h
as
t
h
e
h
i
g
h
e
s
t
co
n
g
es
tio
n
le
v
el
a
m
o
n
g
all
th
e
n
o
d
es
o
f
t
h
at
p
at
h
.
T
h
is
g
i
v
es
t
h
e
m
a
x
i
m
u
m
co
n
g
e
s
tio
n
lev
el
o
f
th
a
t
p
ath
.
Af
ter
d
eter
m
i
n
in
g
th
e
m
ax
i
m
u
m
co
n
g
es
tio
n
lev
e
l
o
f
ea
ch
p
ath
f
r
o
m
s
to
t
,
w
e
ca
n
s
elec
t
th
at
p
ath
w
h
ich
h
a
s
th
e
least
m
ax
i
m
u
m
co
n
g
e
s
tio
n
lev
el
v
al
u
e.
B
u
t
th
i
s
m
et
h
o
d
is
NP
h
ar
d
,
b
ec
au
s
e
th
e
n
u
m
b
e
r
o
f
p
o
s
s
ib
le
p
ath
s
in
cr
ea
s
es
ex
p
o
n
e
n
tia
ll
y
as
N
in
cr
ea
s
es.
T
h
er
ef
o
r
e,
th
e
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
i
n
g
ap
p
r
o
ac
h
is
ad
o
p
ted
to
s
o
lv
e
th
is
p
r
o
b
le
m
.
4
.
2
.
Dy
na
m
ic
pro
g
ra
m
m
i
ng
a
pp
ro
a
ch
As
u
s
u
al,
t
h
e
s
o
u
r
ce
n
o
d
e
is
d
en
o
ted
b
y
s
.
L
et
t
b
e
an
y
o
t
h
er
n
o
d
e
r
ea
c
h
ab
le
f
r
o
m
s
w
i
th
OP
(
t
)
a
s
th
e
o
p
ti
m
al
p
ath
f
r
o
m
s
to
t
an
d
f(
t)
as
t
h
e
m
i
n
i
m
i
ze
d
m
ax
i
m
u
m
co
n
g
e
s
tio
n
lev
el
v
alu
e
o
f
t
h
at
p
ath
.
L
et
OP
(
t
)
=
[
v
0,
v
1
,
…,
v
n
]
w
h
er
e
v
0
=
s
a
n
d
v
n
=
t
.
T
h
e
n
,
b
y
k
n
o
w
i
n
g
f
(
v
0
)
,
th
e
Dyn
a
mic
P
r
o
g
r
a
mmin
g
m
et
h
o
d
s
o
lv
e
s
,
f
(
v
1
)
in
ter
m
s
o
f
f
(
v
0
),
f
(
v
2
)
in
ter
m
s
o
f
f
(
v
1
)
,
…,
f
(
v
n
)
in
ter
m
s
o
f
f
(
v
n
−1
)
.
T
h
e
s
u
b
-
o
p
ti
m
al
p
r
o
b
lem
s
ar
e
s
o
lv
ed
r
ec
u
r
s
iv
e
l
y
.
4
.
2
.
1
.
E
f
f
ec
t
iv
e
co
ng
estio
n a
t
s
o
urc
e
s
W
h
atev
er
t
h
e
ac
t
u
al
co
n
g
es
tio
n
le
v
el
at
s
,
all
t
h
e
p
ath
s
h
av
e
to
s
tar
t
f
r
o
m
s
.
T
h
er
e
is
n
o
o
th
er
o
p
tio
n
.
T
h
e
co
n
g
esti
o
n
le
v
el
Q
s
is
co
m
m
o
n
f
o
r
all
p
ath
s
s
tar
ti
n
g
f
r
o
m
s
.
T
h
er
ef
o
r
e,
f
o
r
th
e
p
u
r
p
o
s
e
co
m
p
ar
is
o
n
an
d
ca
lcu
latio
n
o
f
t
h
e
co
n
g
e
s
tio
n
l
ev
els o
f
t
h
e
p
ath
s
,
ef
f
ec
ti
v
e
Q
s
is
s
et
to
ze
r
o
as,
Q
s
=
0
(
1
6
)
T
h
e
m
i
n
i
m
ized
m
a
x
i
m
u
m
v
al
u
e
o
f
Q
s
is
al
s
o
0
.
T
h
er
ef
o
r
e
th
e
co
r
r
esp
o
n
d
in
g
f
(
s
)
=
0
.
4
.
2
.
2
.
f
(
t
)
v
a
lues
f
o
r
a
o
ne
-
ho
p neig
h
bo
urs
o
f
s
On
e
h
o
p
n
ei
g
h
b
o
u
r
s
o
f
s
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
Her
e,
t
1
, t
2
,
…,
t
K
ar
e
th
e
o
n
e
h
o
p
n
ei
g
h
b
o
u
r
s
o
f
s
.
Fig
u
r
e
2
.
On
e
h
o
p
n
ei
g
h
b
o
u
r
s
o
f
s
Sin
ce
,
t
1
is
d
ir
ec
tl
y
co
n
n
ec
te
d
to
s
,
p
ath
(
s
,
t
1
)
i
s
a
s
in
g
le
lin
k
(
s
in
g
le
h
o
p
)
p
ath
.
T
h
e
m
i
n
i
m
u
m
a
s
w
el
l
as
th
e
m
a
x
i
m
u
m
co
n
g
e
s
tio
n
lev
e
l o
f
p
ath
(
s
,
t
1
)
is
Q
s
it
s
elf
w
h
i
ch
is
ze
r
o
as g
i
v
e
n
b
y
(
1
6
)
.
T
h
er
ef
o
r
e,
f
(
t
1
)
=
Q
s
= 0
(
1
7
)
T
h
is
r
elatio
n
h
o
ld
s
g
o
o
d
ev
e
n
w
h
e
n
w
e
h
a
v
e
a
t
w
o
h
o
p
p
ath
f
r
o
m
s
to
t
1
th
r
o
u
g
h
a
n
i
n
ter
m
ed
iat
e
n
o
d
e
i
as
s
h
o
w
n
i
n
Fi
g
u
r
e
4
.
Her
e
,
w
e
h
a
v
e
t
w
o
p
at
h
s
(
s
,
t
1
)
an
d
(
s
,
i
,
t
1
)
.
T
h
e
co
r
r
es
p
o
n
d
in
g
m
a
x
i
m
u
m
co
n
g
es
tio
n
le
v
els
ar
e
.
Fo
r
p
ath
P
1
=
(
s
,
t
1
)
,
R
1
=
ma
x
(
Q
s
)
=
Q
s
=
0
.
Fo
r
p
ath
P
2
=
(
s
,
i
,
t
1
),
R
2
=
m
ax
(
[
Q
s
,
Q
i
]
)
=
m
ax
(
0
,
Q
i
)
=
Q
i
.
T
h
e
m
in
i
m
i
s
ed
m
a
x
i
m
u
m
v
al
u
e
f
(
t
1
)
is
,
f
(
t
1
)
=
m
in
(
R
1
,
R
2
)
=
m
i
n
(
0
,
Q
i
)
)
=
0
(
1
8
)
T
h
e
(
1
8
)
h
o
ld
s
g
o
o
d
ev
en
w
h
en
th
er
e
ar
e
ad
d
itio
n
al
m
u
lt
i
-
h
o
p
p
ath
s
to
t
1
f
r
o
m
s
.
Si
m
ilar
r
elatio
n
h
o
ld
s
g
o
o
d
f
o
r
t
2
,
t
3
,
…,
t
K
w
h
ic
h
h
a
v
e
o
n
e
h
o
p
co
n
n
ec
ti
v
it
y
w
it
h
s
,
as
f
(
t
2
)
=
f
(
t
3
)
=
…
=
f
(
t
K
)
=
0
(
1
9
)
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o
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o
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h
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(
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1
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ca
n
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e
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m
b
in
ed
to
s
tate
an
i
m
p
o
r
ta
n
t p
r
o
p
er
ty
o
f
f
(
.
)
as
f
o
llo
w
s
.
P
ro
pert
y
1
:
W
h
en
a
n
o
d
e
i
b
elo
n
g
s
to
th
e
o
n
e
h
o
p
n
eig
h
b
o
u
r
s
et
o
f
s
,
t
h
e
n
,
f
(
i
)
=
0
f
o
r
i
∈
o
n
e
h
o
p
n
eig
h
b
o
u
r
s
o
f
s
(
2
0
)
T
h
u
s
,
(
)
’
s
o
f
o
n
e
h
o
p
n
e
ig
h
b
o
u
r
s
o
f
s
ar
e
d
ir
ec
tl
y
ca
lcu
lated
u
s
in
g
(
2
0
)
.
L
et
th
e
o
n
e
h
o
p
n
e
ig
h
b
o
u
r
s
o
f
s
b
e
g
r
o
u
p
ed
in
to
a
s
et
d
esi
g
n
ated
as
A
0
.
T
h
at
is
,
A
0
=
{o
n
e
h
o
p
n
ei
g
h
b
o
u
r
s
o
f
s
}
(
2
1
)
T
h
en
,
f
o
r
i
∈
A
0
,
th
e
v
a
lu
es
f
(
i
)
’
s
ar
e
0
as
g
i
v
en
b
y
(
2
0
)
.
Star
tin
g
f
r
o
m
t
h
e
k
n
o
w
n
v
a
lu
e
s
o
f
f
(
i
)
’
s
(
f
o
r
i
∈
A
0
),
th
e
v
al
u
e
s
o
f
(
)
’
s
o
f
o
th
er
n
o
d
es (
i
∉
A
0
)
ar
e
ca
lcu
lated
u
s
i
n
g
th
e
p
r
in
cip
le
o
f
d
y
n
a
m
ic
p
r
o
g
r
a
m
m
in
g
.
4
.
3
.
Ca
lcula
t
io
n o
f
f
(
t
)
by
dy
na
m
ic
pro
g
ra
m
m
i
ng
f
o
r
a
ny
t
A
ll
th
e
n
o
d
es
o
f
t
h
e
n
et
w
o
r
k
ar
e
g
r
o
u
p
ed
in
to
t
w
o
d
i
s
j
o
in
t
s
ets
d
esi
g
n
ated
as
A
a
n
d
B
.
S
et
A
h
o
ld
s
th
o
s
e
n
o
d
es
w
h
o
s
e
f
(
i
)
’
s
h
av
e
b
ee
n
alr
ea
d
y
ca
lc
u
lated
a
n
d
ar
e
k
n
o
w
n
.
T
h
u
s
t
h
e
o
p
ti
m
a
l
p
ath
s
OP
(
i)
’
s
ar
e
k
n
o
w
n
f
o
r
i
∈
A
.
No
d
es
in
s
et
B
h
o
ld
s
t
h
o
s
e
n
o
d
es
w
h
o
s
e
f
(
i
)
’
s
ar
e
n
o
t
k
n
o
w
n
a
n
d
y
et
to
b
e
ca
lcu
lated
.
T
h
er
ef
o
r
e
B
=
{[
1
:
N
]
–
A
}
A
=
{No
d
es
w
h
o
s
e
f
(
i)
’
s
h
a
v
e
alr
ea
d
y
b
ee
n
ca
lc
u
lated
an
d
k
n
o
w
n
}
(
2
2
)
B
=
{No
d
es
w
h
o
s
e
f
(
i)
’
s
h
a
v
e
y
et
to
b
e
ca
lcu
lated
an
d
to
b
e
r
ef
i
n
ed
}
(
2
3
)
Un
k
n
o
w
n
an
d
u
n
ca
lc
u
lated
f
(
i
)
’
s
ar
e
i
n
it
ialized
to
∞
s
o
th
at
t
h
e
y
ar
e
ex
cl
u
d
ed
w
h
ile
ca
lc
u
l
atin
g
th
e
m
i
n
i
m
u
m
as e
x
p
lai
n
ed
later
.
4
.
3
.
1
.
I
nitia
liza
t
io
n o
f
f
(
i)
’
s
T
h
e
ca
lcu
latio
n
o
f
f
(
i
)
’
s
f
o
r
all
i
’
s
is
an
iter
ativ
e
p
r
o
ce
s
s
.
I
n
itiall
y
,
t
h
e
o
n
e
h
o
p
n
o
d
es
o
f
s
ar
e
ca
lcu
lated
to
g
et
A
0.
T
h
e
f
(
i
)
’
s
f
o
r
i
∈
A
0
,
ar
e
s
et
to
0
an
d
f
(
i
)
’
s
f
o
r
i
∉
A
0
,
ar
e
s
et
to
∞.
T
h
ese
ar
e
th
e
i
n
itia
l
v
alu
e
s
o
f
f
(
i
)
’
s
.
I
n
itializa
tio
n
o
p
er
atio
n
s
ca
n
b
e
ca
lled
a
s
iter
atio
n
0
.
Fo
r
th
e
f
ir
s
t
iter
atio
n
,
t
h
e
p
r
ev
io
u
s
iter
atio
n
is
ta
k
e
n
as
iter
atio
n
0
.
T
h
e
v
alu
e
s
o
f
f
(
i)
’
s
f
o
r
ite
r
atio
n
0
ar
e
th
e
in
itia
l
v
al
u
es
w
h
ic
h
ar
e
alr
ea
d
y
k
n
o
w
n
.
I
n
th
e
f
ir
s
t
iter
atio
n
,
c
o
n
s
id
er
a
tar
g
et
n
o
d
e
t
th
at
b
elo
n
g
s
to
B.
No
w
(
)
is
∞.
L
et
M
b
e
th
e
n
u
m
b
er
o
n
e
h
o
p
n
eig
h
b
o
u
r
n
o
d
es
of
t
w
h
ic
h
ar
e
a
ls
o
m
e
m
b
er
s
o
f
s
e
t
A
.
L
et
t
h
ese
n
o
d
es
b
e
d
en
o
te
d
b
y
i
1
,
i
2
,
…,
i
M
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
3
.
T
h
at
is
i
k
∈
A
a
n
d
e
(
i
k
,
t
)
=
1
.
I
f
M
=
0
,
th
e
n
t
h
e
n
ex
t
n
o
d
e
f
r
o
m
s
et
B
is
ta
k
en
a
s
t
an
d
ag
ain
M
i
s
d
eter
m
in
ed
.
T
h
is
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
t
il
M
b
ec
o
m
es
g
r
ea
ter
t
h
an
ze
r
o
.
I
n
g
e
n
er
al
t
h
es
e
n
eig
h
b
o
u
r
n
o
d
es
w
ill
b
e
all
ar
o
u
n
d
t.
B
u
t
f
o
r
t
h
e
p
u
r
p
o
s
e
o
f
ea
s
e
o
f
e
x
p
la
n
atio
n
,
t
h
e
y
ar
e
s
h
o
w
n
i
n
a
s
in
g
le
co
lu
m
n
to
th
e
le
f
t o
f
t
.
C
o
n
g
es
tio
n
lev
el
Q
i,
k
o
f
i
k
ar
e
also
m
a
r
k
ed
in
Fi
g
u
r
e
3
f
o
r
k
=
1
to
M
.
Fig
u
r
e
3
.
Mu
lti
h
o
p
p
ath
s
f
o
r
n
o
d
e
t
I
n
Fi
g
u
r
e
3
,
co
n
s
id
er
th
e
p
at
h
[
s
–
i
k
–
t
]
.
I
t
is
m
ad
e
u
p
o
f
[
s
–
i
k
]
in
ca
s
ca
d
e
w
ith
[
i
k
–
t
].
Her
e,
p
ath
[
s
–
i
k
]
is
th
e
o
p
tim
al
p
ath
,
b
ec
au
s
e
(
)
h
as
alr
ea
d
y
b
ee
n
ca
lcu
lated
an
d
is
k
n
o
w
n
.
(
)
Giv
e
s
th
e
m
a
x
i
m
u
m
co
n
g
esti
o
n
alo
n
g
[
s
–
i
k
]
.
T
h
e
co
n
g
e
s
tio
n
le
v
e
l
co
n
tr
ib
u
ted
f
r
o
m
n
o
d
e
i
k
to
p
ath
[
i
k
–
t
]
i
s
Q
i,
k
.
T
h
er
ef
o
r
e,
th
e
o
v
er
all
m
ax
i
m
u
m
co
n
g
esti
o
n
lev
e
l a
lo
n
g
th
e
p
ath
[
s
–
i
k
–
t
]
,
is
g
iv
e
n
b
y
,
ma
x
[
−
−
]
=
(
)
=
(
(
)
,
,
)
(
2
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
8
0
4
-
4
8
1
4
4810
Her
e
all
i
k
’
s
b
elo
n
g
to
A
.
Usi
n
g
(
2
4
)
,
(
)
′
ar
e
ca
lcu
lated
f
o
r
all
i
k
’
s
f
o
r
k
=
1
t
o
M
.
T
h
en
,
th
e
m
i
n
i
m
ized
m
ax
i
m
u
m
f
o
r
th
is
p
at
h
,
in
t
h
e
p
r
esen
t iter
atio
n
i
s
r
ep
r
esen
ted
b
y
g
(
t)
an
d
it is
ca
lc
u
lated
as,
(
)
=
min
k
=
1
:
M
(
(
)
)
(
2
5
)
Su
b
s
ti
tu
t
in
g
f
o
r
(
)
in
(
2
5
)
r
o
m
(
2
4
)
,
(
)
=
min
k
=
1
:
M
(
(
(
)
,
,
)
)
(
2
6
)
On
ce
g
(
t
)
is
ca
lcu
lated
,
it
i
s
co
m
p
ar
ed
w
ith
th
e
ex
i
s
ti
n
g
v
al
u
e
o
f
f
(
t
)
(
f
r
o
m
t
h
e
p
r
ev
io
u
s
i
ter
atio
n
)
a
n
d
th
e
p
r
esen
t
f
(
t
)
is
u
p
d
ated
o
n
l
y
if
g
(
t)
is
le
s
s
t
h
an
f
(
t)
.
T
h
at
is
,
(
)
=
{
(
)
if
(
)
<
(
)
,
(
)
othe
r
w
ise
(
2
7
)
No
w
t
i
s
r
e
m
o
v
ed
f
r
o
m
B
a
n
d
ad
d
ed
to
A
.
Set
A
g
r
o
w
s
a
n
d
B
co
n
tr
ac
t
s
.
No
w
n
e
x
t
t
f
r
o
m
B
is
ta
k
e
n
u
p
an
d
f
(
t
)
f
o
r
th
i
s
t
i
s
u
p
d
ated
as
g
i
v
e
n
b
y
(
2
7
)
.
On
ce
all
th
e
ele
m
e
n
ts
in
B
ar
e
co
v
er
ed
,
(
B
g
o
es
e
m
p
t
y
)
,
th
e
p
r
esen
t
iter
atio
n
i
s
o
v
er
an
d
th
e
n
e
x
t
iter
atio
n
s
tar
ts
.
I
n
t
h
e
n
e
x
t
iter
atio
n
,
s
a
m
e
p
r
o
ce
s
s
as
i
n
f
ir
s
t
iter
atio
n
r
ep
ea
ts
b
u
t
w
i
th
t
h
e
u
p
d
ated
s
et
o
f
f
(
i
)
’
s
.
4
.
3
.
2
.
Sto
pp
ing
cr
it
er
io
n
Du
r
in
g
s
u
cc
e
s
s
i
v
e
i
ter
atio
n
s
,
f
(
t
)
’
s
a
r
e
u
p
d
ated
ac
co
r
d
in
g
to
(
2
7
)
.
T
o
ex
p
r
ess
t
h
is
i
n
a
co
m
p
ac
t
f
o
r
m
,
let
th
e
co
llectio
n
o
f
all
f
(
t
)
’
s
f
o
r
t
=
1
to
N
f
o
r
a
g
iv
en
s
,
b
e
r
ep
r
es
en
ted
b
y
t
h
e
ar
r
a
y
F
as,
=
[
(
1
)
,
(
2
)
,
…
,
(
)
]
(
2
8
)
T
h
en
,
F
is
u
p
d
ated
in
s
u
cc
es
s
iv
e
iter
at
io
n
s
.
T
h
e
th
eo
r
etica
l
m
a
x
i
m
u
m
n
u
m
b
er
o
f
iter
ati
o
n
s
is
(
N
−
1
)
[
1
5
]
.
I
n
p
r
ac
tice,
if
F
d
o
es
n
o
t
ch
an
g
e
f
r
o
m
th
e
p
r
ev
io
u
s
to
th
e
p
r
esen
t
iter
atio
n
,
th
e
n
F
w
il
l
n
o
t
ch
an
g
e
in
f
u
r
t
h
er
iter
atio
n
s
to
o
.
A
f
ter
t
h
is
,
th
e
p
r
o
ce
s
s
ca
n
b
r
ea
k
o
u
t
o
f
t
h
e
iter
atio
n
lo
o
p
a
n
d
th
er
e
is
n
o
n
ee
d
to
co
m
p
lete
th
e
(
N
−
1
)
th
eo
r
etica
l
i
ter
atio
n
s
.
T
o
f
ac
ilit
ate
th
e
ter
m
i
n
atio
n
o
f
t
h
e
iter
atio
n
s
,
t
h
e
v
al
u
e
o
f
F
at
t
h
e
e
n
d
o
f
th
e
p
r
ev
io
u
s
i
ter
atio
n
is
s
to
r
e
d
in
F
old
.
At
th
e
en
d
o
f
t
h
e
p
r
esen
t
iter
atio
n
,
th
e
u
p
d
ated
F
is
co
m
p
ar
ed
to
F
old
.
I
f
F
=
F
ol
d
,
th
e
iter
atio
n
lo
o
p
is
ter
m
in
a
ted
.
T
h
e
o
p
tim
a
l
p
ath
is
o
b
tain
ed
u
s
i
n
g
t
h
e
p
r
ed
ec
ess
o
r
v
ec
to
r
p
r
ed
o
f
s
ize
N
as
u
s
u
al
[
1
5
]
.
Dete
r
m
i
n
atio
n
o
f
f
(
t
)
’
s
a
n
d
t
h
e
p
r
ed
v
ec
to
r
is
d
escr
ib
ed
in
Alg
o
r
it
h
m
1
.
T
h
is
i
s
b
asi
ca
ll
y
a
ce
n
tr
alize
d
alg
o
r
ith
m
.
B
u
t
ca
n
b
e
co
n
v
er
t
ed
in
to
its
eq
u
iv
ale
n
t
d
i
s
tr
ib
u
t
ed
alg
o
r
ith
m
.
T
h
e
alg
o
r
ith
m
i
s
a
m
o
d
i
f
icatio
n
o
f
B
ell
m
an
-
Fo
r
d
s
h
o
r
test
p
ath
al
g
o
r
ith
m
[
1
5
]
.
Alg
o
rit
h
m
CB
NAP
I
np
ut
s
:
N
=
No
.
o
f
n
o
d
es in
t
h
e
W
SN.
E
=
E
d
g
e
co
n
n
ec
ti
v
it
y
(
A
d
j
ac
en
c
y
)
m
atr
ix
.
Q
=
C
o
n
g
esti
o
n
lev
el
v
ec
to
r
f
o
r
all
n
o
d
es.
s
=
So
u
r
ce
n
o
d
e.
O
utput
s
:
OP
(
t
)
=
Op
tim
a
l p
ath
f
r
o
m
s
t
o
,
t
f
o
r
t
=1
to
N
f
(
t
)
=
Min
i
m
ized
m
ax
i
m
u
m
co
n
g
es
tio
n
le
v
el
o
f
p
ath
OP
(
t
)
f
o
r
t
=
1
to
N
.
1.
I
n
itialize
all
f
(
t
)
’
s
to
∞ a
n
d
p
r
e
d
(
t
)
’
s
to
0
as,
Fo
r
t
=
1
t
o
N
,
f
(
t
)
=
∞;
p
r
ed
(
t
)
=
0
; E
n
d
f
o
r
t
2.
Set
f
(
s
)
=
0
;
T
ak
e
A
0
=
[
s
]
//s
tar
t
w
it
h
3.
Get
th
e
o
n
e
h
o
p
n
eig
h
b
o
u
r
s
o
f
s
a
n
d
ca
lcu
late
f
(
t
)
’
s
f
o
r
th
e
m
as,
Fo
r
t
=
1
to
N
I
f
e
(
s
,
t
)
=1
,
f
(
t
)
=
0
; p
r
ed
(
t
)
=
s
;
A
0
= [
A
0
,
t]
; E
n
d
i
f
E
n
d
f
o
r
t
//S
et
A
0
is
r
ea
d
y
4.
T
ak
e
s
et
A
=
A0
,
T
ak
e
B
=
[
1
:
N
]−
A
5.
Sto
r
e
f
(
t
)
’
s
f
o
r
t
∈
{1
:
N
}
in
ar
r
ay
F
a
s
,
F
= [
f
(
1
)
,
f
(
2
)
,
…,
f
(
N
)
]
// I
n
itializat
io
n
o
v
er
.
First i
ter
atio
n
s
tar
ts
.
Set
F
old
=
F
//s
av
e
F
i
n
F
o
ld
.
6.
Fo
r
h
=
1
to
N
−
1
//f
ir
s
t iter
ati
o
n
.
//
h
is
t
h
e
iter
atio
n
co
u
n
t.
Fo
r
ea
ch
t
in
B
w
h
ile
B
i
s
n
o
t
e
m
p
t
y
Fo
r
i
=
1
to
N
// Ne
ig
h
b
o
u
r
n
o
d
es o
f
t
R
(
i
)
=
∞
//in
itial v
a
lu
e
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:
2
0
8
8
-
8708
C
o
n
g
esti
o
n
b
o
ttlen
ec
k
a
vo
id
r
o
u
tin
g
in
w
ir
eles
s
s
en
s
o
r
n
etw
o
r
ks (
S
a
n
u
Th
o
ma
s
)
4811
if
(
i
= =
t
)
co
n
tin
u
e;
i
f
(
e
(
i
,
t
)
=
=
∞)
co
n
tin
u
e
;
ca
lcu
late
R
(
i
)
f
r
o
m
(
2
4
)
a
s
,
(
)
=
(
(
)
,
)
en
d
f
o
r
i
7.
Fin
d
t
h
e
m
i
n
i
m
u
m
o
f
th
e
ar
r
a
y
R
as,
[
g
(
t
)
,
i
n
d
ex
]
=
min
(
R
)
;
I
f
g
(
t
)
=
=
∞
co
n
tin
u
e
e
n
d
if
8.
if
g
(
t
)
<
f
(
t
)
,
f
(
t
)
=
g
(
t
)
;
p
r
ed
(
t
)
=
in
d
ex
;
en
d
i
f
en
d
f
o
r
t
9.
Get
th
e
u
p
d
ated
ar
r
a
y
F
f
o
r
t
=
1
to
N
as,
F
= [
f
(
1
)
,
f
(
2
)
,
…,
f
(
N
)
]
;
I
f
F
= =
F
old
B
r
ea
k
(
Go
to
1
1
)
en
d
if
10.
Sto
r
e
F
in
Fo
ld
f
o
r
th
e
co
m
p
ar
is
o
n
i
n
th
e
n
ex
t iter
atio
n
as,
F
o
ld
=
F;
E
n
d
f
o
r
h
//en
d
o
f
h
lo
o
p
11.
Ov
er
On
ce
p
r
ed
(
t
)
is
r
ea
d
y
f
o
r
t
=1
to
N
,
th
e
co
r
r
esp
o
n
d
in
g
OP
(
t
)
’
s
ar
e
ea
s
il
y
o
b
tain
ed
[
1
5
]
u
s
in
g
t
h
e
f
u
n
c
tio
n
g
et
_
T
S(…)
as g
iv
e
n
b
elo
w
.
f
u
n
ctio
n
T
S =
g
et_
T
S(p
r
ed
,
t,
s
)
T
S=[
t]
; w
h
ile
t~=
s
,
T
S=[
T
S
,
p
r
ed
(
t)
]
;t=p
r
ed
(
t)
;en
d
Vec
to
r
TS
g
i
v
es t
h
e
p
at
h
f
r
o
m
t
to
s
.
P
ath
OP
(
t
)
w
h
ic
h
i
s
t
h
e
p
ath
f
r
o
m
s
to
t i
s
o
b
tain
ed
b
y
r
ev
er
s
i
n
g
th
e
s
eq
u
e
n
ce
TS
.
A
l
g
o
r
ith
m
C
B
NA
P
in
ass
o
ciatio
n
w
it
h
f
u
n
ctio
n
g
et
_
T
S(…)
g
iv
e
s
f
(
t
)
’
s
an
d
th
e
C
o
n
g
es
tio
n
B
o
ttlen
ec
k
No
d
e
Av
o
id
P
ath
s
,
OP
(
t
)
’
s
,
f
r
o
m
s
to
all
o
th
er
n
o
d
es.
On
ce
f
(
t
)
’
s
ar
e
d
eter
m
i
n
ed
f
o
r
t
=
1
to
N
f
o
r
a
g
i
v
en
s
,
th
o
s
e
h
i
g
h
co
n
g
esti
o
n
le
v
el
n
o
d
es
w
h
o
s
e
Q
’s
ar
e
g
r
ea
ter
th
a
n
ma
x
(
F
)
ar
e
ex
clu
d
ed
f
r
o
m
p
ar
ticip
atin
g
as
i
n
ter
m
ed
iate
n
o
d
es
in
th
e
r
o
u
tin
g
p
r
o
ce
s
s
in
th
e
p
r
esen
t
s
e
s
s
io
n
.
T
h
u
s
th
e
s
e
b
o
ttlen
ec
k
n
o
d
es
ar
e
av
o
id
ed
ac
tin
g
as
in
ter
med
ia
te
n
o
d
es
d
u
r
in
g
t
h
e
d
is
co
v
er
y
o
f
th
e
o
p
ti
m
al
p
ath
.
Her
e,
O
P
(
t)
’
s
ar
e
th
e
o
p
ti
m
al
p
ath
s
f
r
o
m
B
S
to
s
en
s
o
r
s
an
d
th
e
r
ev
er
s
e
o
f
OP
(
t)
’
s
p
r
o
v
id
e
th
e
o
p
ti
m
al
p
ath
s
f
r
o
m
ea
c
h
s
en
s
o
r
to
B
S.
E
x
a
m
p
le
1
:
A
n
et
w
o
r
k
w
it
h
1
0
n
o
d
es,
is
r
ep
r
esen
ted
as
a
n
u
n
d
ir
ec
ted
g
r
ap
h
a
s
s
h
o
w
n
in
F
ig
u
r
e
4
.
No
d
es
ar
e
s
h
o
w
n
i
n
b
lac
k
.
C
o
n
g
e
s
tio
n
l
ev
els
at
n
o
d
es
ar
e
s
h
o
w
n
in
r
ed
.
T
h
e
n
o
d
e
lo
ca
tio
n
s
i
n
Fig
u
r
e
4
ar
e
n
o
t
e
x
ac
t
p
h
y
s
ical
lo
ca
tio
n
s
.
T
h
e
y
ar
e
j
u
s
t
r
ep
r
esen
tat
iv
e
f
o
r
v
i
s
u
al
id
en
ti
f
icatio
n
.
T
h
e
co
n
n
ec
ti
v
i
t
y
a
m
o
n
g
n
o
d
es
is
r
ep
r
esen
ted
b
y
th
e
co
n
n
ec
ted
lin
k
s
.
I
n
Fig
u
r
e
4
,
s
=1
.
T
h
e
p
r
esen
t
co
n
g
e
s
tio
n
lev
el
s
,
w
it
h
Q
s
=
0
,
ar
e
g
iv
e
n
as
,
Q
=
[
0
,
7
0
,
1
1
,
1
1
0
,
1
5
,
4
0
,
8
0
,
2
,
3
0
,
1
2
]
;
Fig
u
r
e
4
.
Gr
ap
h
la
y
o
u
t
f
o
r
ex
a
m
p
le
2
Af
ter
r
u
n
n
i
n
g
C
B
N
A
P
,
t
h
e
r
e
s
u
lt
in
g
f
(
t
)
a
n
d
p
r
ed
(
t
)
v
al
u
es
ar
e
s
h
o
w
n
in
T
ab
le
1
,
f
o
r
t
=
1
to
1
0
.
Fo
r
lack
o
f
s
p
ac
e,
co
lu
m
n
h
ea
d
in
g
Up
d
ate
i
s
r
ep
r
esen
ted
b
y
Ud
an
d
t
h
e
v
ar
iab
le
p
r
ed
(
t
)
b
y
P
(
t
)
i
n
T
ab
le
1
.
W
e
ca
n
s
ee
th
e
u
p
d
ated
v
alu
es
o
f
f
(
t
)
af
ter
ea
ch
u
p
d
ate.
Af
ter
u
p
d
ate
9
,
th
e
F
v
ec
to
r
is
s
a
m
e
as
t
h
at
o
f
u
p
d
ate
8
.
T
h
at
is
,
F
=
F
ol
d
an
d
t
h
en
t
h
e
p
r
o
ce
s
s
co
n
v
er
g
e
s
.
I
n
t
h
is
e
x
a
m
p
le,
th
e
m
a
in
o
u
ter
lo
o
p
s
tar
tin
g
at
s
tep
8
o
f
C
B
N
A
P
alg
o
r
ith
m
ter
m
in
ate
s
af
ter
3
iter
atio
n
s
.
Her
e,
m
a
x
(
F)
=
1
5
an
d
th
e
b
o
ttlen
ec
k
n
o
d
es
h
av
i
n
g
Q
v
a
lu
e
s
g
r
ea
ter
t
h
an
1
5
ar
e
n
o
d
es
2
,
4
,
6
,
7
,
9
.
T
h
ese
n
o
d
es
ar
e
ex
c
lu
d
ed
f
r
o
m
ac
ti
n
g
as
in
ter
m
ed
iate
n
o
d
es
in
an
y
o
p
ti
m
al
p
at
h
o
r
ig
in
a
tin
g
f
r
o
m
s
.
Fro
m
T
ab
le
2
,
it
ca
n
b
e
cle
ar
l
y
s
ee
n
th
at
n
o
d
es
2
,
4
,
6
,
7
,
9
a
r
e
ab
s
e
n
t
as
in
ter
m
e
d
iate
n
o
d
es
in
all
th
e
o
p
ti
m
al
p
at
h
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
4
8
0
4
-
4
8
1
4
4812
T
ab
le
1
.
Valu
es o
f
P
(
t
)
an
d
f
(
t
)
af
ter
s
u
cc
e
s
s
i
v
e
u
p
d
ates
Ud
t
1
2
3
4
5
6
7
8
9
10
1
P
(
t
)
0
1
1
1
-
-
-
-
-
-
f
(
t
)
0
0
0
0
∞
∞
∞
∞
∞
∞
2
P
(
t
)
0
1
1
1
3
-
-
-
-
-
f
(
t
)
0
0
0
0
11
∞
∞
∞
∞
∞
3
P
(
t
)
0
1
1
1
3
3
-
-
-
-
f
(
t
)
0
0
0
0
11
11
∞
∞
∞
∞
4
P
(
t
)
0
1
1
1
3
3
5
-
-
-
f
(
t
)
0
0
0
0
11
11
15
∞
∞
∞
5
P
(
t
)
0
1
1
1
3
3
5
5
-
-
f
(
t
)
0
0
0
0
11
11
15
15
∞
∞
6
P
(
t
)
0
1
1
1
3
3
5
5
6
-
f
(
t
)
0
0
0
0
11
11
15
15
40
∞
7
P
(
t
)
0
1
1
1
3
3
5
5
6
8
f
(
t
)
0
0
0
0
11
11
15
15
40
15
8
P
(
t
)
0
1
1
1
3
3
5
5
10
8
f
(
t
)
0
0
0
0
11
11
15
15
15
15
9
P
(
t
)
0
1
1
1
3
3
5
5
10
8
f
(
t
)
0
0
0
0
11
11
15
15
15
15
T
ab
le
2
.
Op
tim
al
OP
(
t)
’s
an
d
f
(
t)
’s
s
t
O
p
t
i
mal
p
a
t
h
O
P(
t
)
f
(
t
)
P
(
t
)
1
2
1
→
2
0
1
1
3
1
→
3
0
1
1
4
1
→
4
0
1
1
5
1
→
3
→
5
11
3
1
6
1
→
3
→
6
11
3
1
7
1
→
3
→
5
→
7
15
5
1
8
1
→
3
→
5
→
8
15
5
1
9
1
→
3
→
5
→
8
→1
0
→
9
1
5
10
1
10
1
→
3
→
5
→
8
→
1
0
15
8
5.
CO
M
P
ARIS
O
N
WI
T
H
O
T
H
E
R
M
E
T
H
O
DS
C
o
n
g
esti
o
n
av
o
id
r
o
u
te
ca
n
b
e
d
eter
m
i
n
ed
b
y
th
e
s
i
m
p
le
‘
G
R
E
E
DY
’
m
et
h
o
d
.
T
h
e
b
asic
i
d
ea
h
er
e
is
,
s
tar
tin
g
f
r
o
m
t
h
e
s
o
u
r
ce
,
to
s
elec
t
t
h
e
least
co
n
g
ested
n
e
ig
h
b
o
r
n
o
d
e
as
t
h
e
n
e
x
t
f
o
r
w
ar
d
in
g
n
o
d
e
u
n
til
th
e
f
i
n
al
d
esti
n
atio
n
i
s
r
ea
ch
ed
.
Gr
ee
d
y
m
et
h
o
d
is
i
n
v
ar
ia
b
ly
s
u
b
-
o
p
ti
m
al,
b
ec
au
s
e
it
w
il
l
n
o
t
f
o
r
esee
a
ll
p
o
s
s
ib
le
alter
n
ati
v
es.
B
u
t
it
is
f
ast.
An
o
t
h
er
av
ai
lab
le
s
o
lu
tio
n
is
to
u
s
e
‘
T
A
R
A’
[
9
]
to
alle
v
iate
co
n
g
e
s
tio
n
i
n
W
SNs
.
Ou
r
Me
t
h
o
d
C
B
NA
P
i
s
co
m
p
ar
ed
to
‘
T
A
R
A’
an
d
‘
G
R
E
E
DY
’
m
et
h
o
d
s
.
5
.
1
.
T
i
m
e
co
m
p
lex
it
y
T
h
e
tim
e
co
m
p
le
x
it
y
o
f
C
B
NA
P
is
O
(
N
3
)
[
1
5
]
.
T
h
e
ex
p
er
i
m
en
tal
co
m
p
letio
n
ti
m
e
ta
k
en
to
g
et
th
e
o
p
ti
m
u
m
r
es
u
lt
f
o
r
s
u
cc
e
s
s
iv
e
v
al
u
es
o
f
N
is
s
h
o
w
n
in
t
h
e
g
r
ap
h
o
f
Fi
g
u
r
e
5
.
Her
e,
t
h
e
n
u
m
b
er
o
f
ed
g
e
s
an
d
th
e
ad
j
ac
en
c
y
m
atr
i
x
ar
e
r
an
d
o
m
l
y
g
e
n
er
ated
.
T
h
e
co
n
g
e
s
tio
n
lev
el
v
al
u
es
o
f
n
o
d
e
s
ar
e
ch
o
s
e
n
u
s
i
n
g
u
n
i
f
o
r
m
r
an
d
o
m
d
is
tr
ib
u
tio
n
.
Fro
m
Fi
g
u
r
e
5
,
it
ca
n
b
e
s
ee
n
th
at,
th
e
ti
m
e
tak
e
n
to
g
e
n
er
ate
th
e
o
p
ti
m
al
s
o
lu
tio
n
in
cr
ea
s
es
as
t
h
e
n
u
m
b
er
o
f
n
o
d
es
in
cr
ea
s
es.
T
h
e
GR
E
E
DY
m
et
h
o
d
is
f
aster
c
o
m
p
ar
ed
to
C
B
NA
P
w
h
ile
T
AR
A
i
s
s
lo
w
er
.
T
h
e
ti
m
e
s
av
ed
i
n
C
B
NA
P
i
s
a
b
o
u
t
1
5
-
2
0
%
w
h
e
n
t
h
e
n
u
m
b
er
o
f
n
o
d
es
is
i
n
th
e
r
an
g
e
1
6
0
-
1
8
0
.
5
.
2
.
L
o
a
d B
a
la
nce
I
nd
ex
L
o
ad
b
alan
ci
n
g
i
s
a
n
ef
f
ec
t
iv
e
tech
n
iq
u
e
f
o
r
co
n
g
e
s
tio
n
co
n
tr
o
l
[
1
6
-
2
0
]
.
C
B
NA
P
s
elec
ts
p
ath
w
it
h
lo
w
er
co
n
g
e
s
tio
n
lev
el
s
.
T
h
er
ef
o
r
e,
w
h
en
co
m
m
u
n
icatio
n
ta
k
es
p
lace
u
s
in
g
th
is
p
ath
,
t
h
e
o
v
er
all
lo
ad
b
alan
ce
i
m
p
r
o
v
es
b
ec
a
u
s
e
o
n
l
y
t
h
e
l
ess
co
n
g
e
s
ted
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RE
F
E
R
E
NC
E
S
[1
]
I.
A
k
y
il
d
iz,
e
t
a
l.
,
“
A
S
u
rv
e
y
o
n
S
e
n
so
r
Ne
tw
o
rk
s
,
”
IEE
E
Co
mm
u
n
i
c
a
ti
o
n
s M
a
g
a
zin
e
,
v
ol
.
4
0
,
p
p
.
1
0
2
-
1
1
4
,
2
0
0
2
.
[2
]
R
.
S
h
a
rm
a
a
n
d
N
.
T
.
S
.
Ku
m
a
r,
“
Re
v
ie
w
p
a
p
e
r
o
n
w
irele
ss
se
n
s
o
r
n
e
tw
o
rk
s
,
”
Pro
c
.
o
f
th
e
In
tl
.
C
o
n
f.
o
n
Rec
e
n
t
T
re
n
d
s
in
Co
m
p
u
ti
n
g
a
n
d
C
o
mm
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
–
RT
CCE
,
p
p
.
2
5
5
-
2
5
8
,
2
0
1
3
.
[3
]
B.
Hu
ll
,
e
t
a
l.
,
“
M
it
ig
a
ti
n
g
c
o
n
g
e
stio
n
in
w
irele
ss
s
e
n
so
r
n
e
two
rk
s
,”
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Emb
e
d
d
e
d
Ne
two
rk
e
d
S
e
n
so
r
S
y
ste
ms
,
M
a
ry
lan
d
,
2
0
0
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.