I
nd
o
ne
s
ia
n
J
o
urna
l
of
E
lect
rica
l
E
ng
ineering
a
nd
Co
m
pu
t
er
Science
Vo
l.
23
,
No
.
2
,
A
u
g
u
s
t
20
21
,
pp.
8
7
9
~
8
8
9
I
SS
N:
2502
-
4
7
5
2
,
DOI
:
1
0
.
1
1
5
9
1
/ijeecs.v
23
.i
2
.
pp
879
-
8
8
9
879
J
o
ur
na
l
ho
m
ep
a
g
e
:
h
ttp
:
//ij
ee
cs.ia
esco
r
e.
co
m
O
ptima
l
pa
th
disc
o
v
ery
for
two
mo
v
ing
sinks
with
a
co
mm
o
n
junct
io
n
in
a
wi
re
less
sens
o
r
net
wo
rk
Sa
t
is
h
T
u
ng
a
1
,
Sa
da
s
hiv
a
V
.
Cha
k
ra
s
a
l
i
2
,
N
.
Sh
y
la
s
hree
3
,
L
a
t
ha
B
.
N
.
4
,
M
a
m
a
t
ha
A
.
S
.
5
1
De
p
a
rtme
n
t
of
El
e
c
tro
n
ics
&
Tel
e
c
o
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
M
S
Ra
m
a
iah
In
stit
u
te
of
Tec
h
n
o
lo
g
y
,
Be
n
g
a
lu
r
u
,
I
n
d
ia
2
De
p
a
rtme
n
t
o
f
El
e
c
tro
n
ics
&
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
M S
R
a
m
a
iah
In
stit
u
te
o
f
Tec
h
n
o
l
o
g
y
,
Be
n
g
a
lu
r
u
,
I
n
d
ia
3
De
p
a
rtme
n
t
of
El
e
c
tro
n
ics
&
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
RV
C
o
ll
e
g
e
of
En
g
i
n
e
e
rin
g
,
Be
n
g
a
l
u
ru
,
In
d
ia
4
De
p
a
rtme
n
t
of
El
e
c
tro
n
ics
&
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
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g
,
JS
S
A
c
a
d
e
m
y
of
Tec
h
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ica
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Ed
u
c
a
ti
o
n
,
Be
n
g
a
lu
r
u
,
I
n
d
ia
5
De
p
a
rtme
n
t
of
El
e
c
tro
n
ics
&
Co
m
m
u
n
ica
ti
o
n
En
g
in
e
e
rin
g
,
S
t.
J
o
se
p
h
E
n
g
i
n
e
e
rin
g
Co
ll
e
g
e
,
M
a
n
g
a
l
u
ru
,
In
d
ia
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Oct
15
,
2
0
2
0
R
ev
is
ed
J
u
n
1
,
2
0
2
1
Acc
ep
ted
J
u
n
19
,
2
0
2
1
A
n
e
w
a
lg
o
rit
h
m
is
d
e
sc
ri
b
ed
fo
r
d
e
term
in
in
g
th
e
o
p
ti
m
a
l
ro
u
n
d
-
tri
p
p
a
t
h
s
fo
r
two
m
o
v
i
n
g
si
n
k
s
in
a
wire
les
s
se
n
so
r
n
e
two
r
k
.
T
h
e
a
lg
o
rit
h
m
u
se
s
b
in
a
ry
in
teg
e
r
p
ro
g
ra
m
m
in
g
to
se
lec
t
t
wo
non
-
o
v
e
rlap
p
i
n
g
sh
o
rtes
t
p
a
t
h
s
e
x
c
e
p
t
h
a
v
in
g
a
c
o
m
m
o
n
ju
n
c
ti
o
n
n
o
d
e
to
c
o
v
e
r
a
ll
th
e
se
n
so
r
n
o
d
e
s.
Th
e
two
p
a
th
s
a
re
b
a
lan
c
e
d
as
n
e
a
rly
e
q
u
a
l
as
p
o
ss
ib
le.
T
h
a
t
is
th
e
se
n
s
o
r
n
o
d
e
s
a
lo
n
g
each
p
a
th
a
re
e
q
u
a
l
or
d
iffer
by
ju
st
o
n
e
d
e
p
e
n
d
i
n
g
on
wh
e
th
e
r
t
h
e
to
tal
n
u
m
b
e
r
of
se
n
so
r
n
o
d
e
s
e
x
c
lu
d
in
g
t
h
e
j
u
n
c
ti
o
n
n
o
d
e
is
e
v
e
n
or
o
d
d
.
In
t
h
is
m
e
th
o
d
,
b
o
t
h
th
e
p
a
t
h
len
g
th
s
a
re
m
a
d
e
e
q
u
a
l
or
v
e
ry
n
e
a
rly
e
q
u
a
l
w
h
il
e
t
h
e
to
ta
l
len
g
th
is
m
in
imiz
e
d
.
Th
is
i
n
teg
ra
ted
a
p
p
r
o
a
c
h
is
a
n
o
v
e
l
a
n
d
u
n
i
q
u
e
so
l
u
ti
o
n
to
s
o
lv
e
th
e
d
u
a
l
m
o
v
in
g
sin
k
p
a
t
h
p
ro
b
lem
in
a
wire
les
s
se
n
so
r
n
e
tw
o
rk
.
K
ey
w
o
r
d
s
:
B
alan
ce
d
lo
ad
in
g
Dis
jo
in
t
p
ath
s
Par
ticip
atin
g
ed
g
es
Par
ticip
atin
g
n
o
d
es
Sin
g
le
co
m
m
o
n
ju
n
ctio
n
T
wo
m
o
v
in
g
s
in
k
s
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Sh
y
lash
r
ee
N
.
Dep
ar
tm
en
t
of
E
lectr
o
n
ics
&
C
o
m
m
u
n
icatio
n
E
n
g
in
ee
r
i
n
g
R
V
C
o
lleg
e
of
E
n
g
in
ee
r
i
n
g
R
V
Vid
y
an
ik
eth
an
Po
s
t,
8
th
Mile,
My
s
u
r
u
R
o
ad
,
B
en
g
alu
r
u
5
6
0
0
5
9
,
Kar
n
atak
a
,
I
n
d
ia
E
m
ail:
s
h
y
lash
r
ee
n
@
r
v
ce
.
ed
u
.
in
1.
I
NT
RO
D
UCT
I
O
N
In
g
en
e
r
al,
a
wir
eless
s
en
s
o
r
n
etwo
r
k
(
W
SN)
co
n
s
is
ts
of
s
t
atic
s
en
s
o
r
n
o
d
es
an
d
o
n
e
or
more
s
tatic
s
in
k
s
.
T
h
e
s
en
s
o
r
s
s
en
d
th
eir
s
en
s
ed
d
ata
to
th
e
d
esig
n
ated
s
in
k
s
o
v
er
m
u
lti
-
h
o
p
tr
an
s
m
is
s
io
n
.
B
u
t,
in
th
o
s
e
s
itu
atio
n
s
wh
er
e
th
e
s
en
s
o
r
s
ar
e
s
p
r
ea
d
o
v
er
a
wid
e
g
e
o
g
r
ap
h
ic
ar
ea
with
la
r
g
e
in
ter
s
en
s
o
r
d
is
tan
ce
s
,
th
e
s
en
s
o
r
s
an
d
th
e
s
in
k
s
m
ay
n
o
t
be
f
u
lly
co
n
n
ec
ted
be
ca
u
s
e
of
th
e
in
s
u
f
f
icien
t
co
m
m
u
n
icatio
n
r
an
g
e
of
th
e
s
en
s
o
r
n
o
d
es.
T
h
e
n
th
e
m
u
l
ti
-
hop
t
r
an
s
m
is
s
io
n
f
r
o
m
s
e
n
s
o
r
s
to
th
e
s
tatic
s
in
k
s
m
a
y
n
o
t
be
p
o
s
s
ib
le.
In
s
u
ch
a
s
itu
atio
n
,
o
n
e
m
o
b
ile
s
in
k
(
MS)
or
m
o
r
e
MSs
(
m
o
b
ile
co
llecto
r
s
)
ar
e
u
s
ed
to
g
ath
er
d
ata
f
r
o
m
th
e
s
en
s
o
r
s
[1
]
-
[
1
3
]
.
Mo
b
ile
s
in
k
s
p
h
y
s
ically
m
o
v
e
ar
o
u
n
d
th
e
W
SN
an
d
c
o
llect
th
e
d
ata
f
r
o
m
th
e
s
en
s
o
r
s
.
Mo
b
ile
u
n
its
ca
r
r
y
in
g
th
e
s
in
k
can
be
g
r
o
u
n
d
b
ased
or
air
b
o
r
n
e
wh
er
e
u
n
m
an
n
e
d
ae
r
ial
v
e
h
icles
(
UAVs
)
ar
e
u
tili
ze
d
[
1
4
]
-
[
1
7
]
.
Her
e,
we
u
s
e
m
u
ltip
le
s
in
k
s
(
d
ata
co
ll
ec
to
r
s
)
m
o
u
n
ted
on
g
r
o
u
n
d
b
ased
m
o
v
in
g
u
n
its
co
n
tr
o
lled
m
an
u
ally
or
by
r
o
b
o
ts
.
It
is
as
s
u
m
ed
th
at
th
e
g
eo
g
r
ap
h
ical
r
eg
i
o
n
co
v
e
r
ed
by
th
e
W
SN
is
am
en
ab
le
f
o
r
t
h
e
p
h
y
s
ical
n
a
v
ig
atio
n
of
th
e
m
o
b
ile
s
in
k
s
an
d
th
e
y
ca
n
s
m
o
o
th
ly
ap
p
r
o
ac
h
th
e
v
icin
i
ty
of
th
e
in
d
iv
id
u
al
s
en
s
o
r
s
.
Ou
r
p
r
o
p
o
s
ed
m
eth
o
d
d
ete
r
m
in
es
th
e
b
est
p
ath
f
o
r
two
m
o
b
ile
s
in
k
s
to
co
v
er
th
e
W
SN
ar
ea
s
atis
f
y
in
g
th
e
g
iv
en
co
n
s
tr
ain
t
s
.
T
h
e
m
eth
o
d
can
be
ex
te
n
d
e
d
to
h
a
n
d
le
m
u
ltip
le
s
in
k
s
an
d
also
can
o
p
tim
ize
th
e
p
ath
s
of
t
h
e
m
o
v
in
g
s
in
k
s
in
th
e
p
r
esen
ce
of
k
n
o
wn
o
b
s
tacle
s
[
1
8
]
-
[
21]
in
th
e
W
SN
a
r
ea
.
Gen
er
ally
,
th
e
s
ch
ed
u
lin
g
an
d
th
e
m
o
b
ilit
y
of
m
o
b
ile
s
in
k
s
ar
e
d
eter
m
in
is
tically
co
n
tr
o
lled
to
s
u
it
th
e
ap
p
licatio
n
.
T
h
e
m
o
b
ile
s
in
k
s
in
c
r
ea
s
e
th
e
life
of
s
tatic
s
en
s
o
r
s
by
r
e
d
u
cin
g
t
h
e
tr
an
s
m
is
s
io
n
lo
a
d
of
s
en
s
o
r
s
by
r
ed
u
cin
g
th
e
in
ter
m
ed
iate
r
elay
in
g
task
of
t
h
em
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
879
-
8
8
9
880
2.
ST
E
M
M
O
DE
L
,
SY
M
B
O
L
S
AND
DE
F
I
NI
T
I
O
NS
2
.
1
.
M
o
v
ing
s
ink
pa
t
hs
In
our
s
ch
em
e,
we
h
av
e
two
m
an
ag
ed
s
er
v
ice
p
r
o
v
id
er
s
(
MSPs
)
co
v
er
in
g
th
e
s
en
s
o
r
node
g
r
id
p
o
in
ts
of
th
e
en
tire
W
SN.
T
h
e
two
p
ath
s
ar
e
d
esig
n
ated
as
MSP1
an
d
MSP2
.
A
p
ath
is
m
ad
e
up
of
a
s
eq
u
en
ce
of
non
-
r
e
p
ea
tin
g
ed
g
es.
In
t
h
e
p
r
esen
t
s
ch
em
e
o
n
ly
s
tr
aig
h
t
a
n
d
d
iag
o
n
al
ed
g
es
ar
e
allo
we
d
.
As
an
ex
am
p
le,
two
p
ath
s
MSP1
an
d
MSP2
ar
e
s
h
o
wn
in
Fig
u
r
e
1.
Her
e,
MSP
1
an
d
its
ed
g
es
a
r
e
m
ar
k
ed
in
r
ed
w
h
ile
th
o
s
e
of
MSP2
ar
e
m
ar
k
ed
in
b
lu
e.
Fig
u
r
e
1.
T
wo
m
o
v
i
n
g
s
in
k
p
a
th
s
MSP1
an
d
MSP2
L
et
th
e
s
et
of
ed
g
es
f
o
r
m
in
g
MSP1
an
d
MSP2
be
r
ep
r
esen
ted
by
MSP1
_
E
an
d
MSP2
_
E,
r
esp
ec
tiv
ely
.
T
h
e
in
d
iv
id
u
al
e
d
g
es
of
MSP1
_
E
a
n
d
MSP2
_
E
ar
e
r
ep
r
esen
ted
as
(
1
)
an
d
(
2
)
.
1
_
=
[
1
_
(
1
)
,
1
_
(
2
)
,
.
.
.
.
,
1
_
(
)
,
.
.
.
.
,
1
_
(
1
)
]
(
1
)
2
_
=
[
2
_
(
1
)
,
2
_
(
2
)
,
.
.
.
.
,
2
_
(
)
,
.
.
.
.
,
2
_
(
2
)
]
(
2
)
Her
e
1
an
d
2
ar
e
th
e
s
izes
of
MSP1
_
E
an
d
MSP2
_
E,
r
esp
ec
tiv
ely
.
I
n
d
i
v
id
u
al
elem
en
ts
1
_
(
)
′
an
d
2
_
(
)
′
ar
e
th
e
ed
g
es
of
MSP1
_
E
an
d
MSP2
_
E,
r
esp
ec
tiv
ely
.
In
t
h
e
g
r
ap
h
c
o
n
tex
t,
L1
an
d
L2
ar
e
th
e
n
u
m
b
er
of
e
d
g
es
in
MSP1
_
E
an
d
MSP2
_
E,
r
esp
ec
tiv
ely
.
MSP1
_
E
an
d
MSP2
_
E
ar
e
th
e
non
-
o
v
e
r
lap
p
in
g
s
u
b
s
ets
of
th
e
ed
g
e
s
et
E
of
th
e
g
r
ap
h
.
2
.
2
.
I
nd
ex
f
o
rm
a
t
re
presenta
t
io
n
of
M
SP1
_
E
a
nd
M
SP2
_
E
A
s
u
b
s
et
can
be
r
ep
r
esen
ted
in
in
d
e
x
f
o
r
m
at
in
ter
m
s
of
th
e
f
u
ll
s
et.
I
n
d
ex
f
o
r
m
at
of
a
s
u
b
s
et
is
a
b
in
ar
y
v
e
cto
r
of
len
g
th
t
h
at
is
eq
u
iv
alen
t
to
th
e
s
ize
of
th
e
f
u
ll
s
et.
L
et
th
e
b
in
ar
y
v
ec
t
o
r
1
r
ep
r
esen
t
th
e
in
d
ex
f
o
r
m
at
of
MSP1
_
E
.
T
h
en
th
e
s
ize
of
1
is
wh
ich
is
th
e
s
ize
of
E
.
T
h
e
b
in
ar
y
v
ec
to
r
1
is
f
o
r
m
ed
as
f
o
llo
ws.
T
h
e
ℎ
elem
en
t
of
1
is
s
et
to
1,
if
(
)
of
b
elo
n
g
s
to
MSP1
_
E
,
else
it
is
s
et
to
ze
r
o
.
T
h
at
i
s
,
1
(
)
=
{
1
,
if
e
dge
∈
1
_
0
,
othe
r
w
ise
(
3
)
f
or
=
1
to
.
Fro
m
(
3
)
,
it
can
be
s
ee
n
th
at
(
1
)
=
1
.
An
o
th
er
way
of
r
e
p
r
es
en
tin
g
1
is
(
4
)
.
1
(
1
_
(
)
)
=
1
for
=
1
to
1
1
(
ℎ
)
=
0
}
(
4
)
Similar
ly
,
th
e
in
d
ex
f
o
r
m
at
of
MSP2
_
E
r
ep
r
esen
ted
by
2
is
a
b
in
ar
y
v
ec
to
r
of
len
g
th
wh
o
s
e
ℎ
elem
en
t
is
g
iv
en
by
(
5
)
.
2
(
)
=
{
1
,
if
e
d
ge
∈
2
_
0
,
othe
r
wi
s
e
(
5
)
f
o
r
=
1
to
.
Her
e,
(
1
)
=
2
.
An
o
th
er
way
of
r
ep
r
esen
tin
g
2
is
(
6
)
.
2
(
2
_
(
)
)
=
1
for
=
1
to
2
2
(
ℎ
)
=
0
}
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l
p
a
th
d
is
co
ve
r
y
fo
r
tw
o
mo
vin
g
s
in
ks
w
ith
a
co
mmo
n
ju
n
ctio
n
in
a
w
ir
eless
…
(
S
a
tis
h
Tu
n
g
a
)
881
2
.
3
.
Dec
is
io
n
v
ec
t
o
rs
x
1
a
nd
x
2
B
in
ar
y
v
ec
to
r
s
1
an
d
2
ar
e
also
th
e
d
ec
is
io
n
v
ec
to
r
s
in
d
eter
m
in
in
g
MSP1
_
E
an
d
MSP2
_
E
u
s
in
g
an
o
p
tim
izatio
n
p
r
o
g
r
am
.
T
h
i
s
m
ea
n
s
,
o
n
ce
1
an
d
2
ar
e
d
eter
m
in
ed
u
s
in
g
s
ay
th
e
b
in
ar
y
in
teg
er
p
r
o
g
r
am
(
B
I
P)
,
t
h
en
MSP1
_
E
a
n
d
MS
P2
_
E
ar
e
o
b
tain
ed
b
ased
on
(
4
)
a
n
d
(
6
)
.
In
f
ac
t,
we
ca
n
e
x
p
r
ess
MSP1
_
E
an
d
MSP2
_
E
as
(
7
)
.
1
_
=
(
1
)
a
n
d
2
_
=
(
2
)
(
7
)
Her
e,
f
in
d
(
)
is
a
MA
T
L
AB
f
u
n
ctio
n
th
at
g
iv
es
th
e
in
d
ex
lo
ca
tio
n
s
of
1
’
s
in
v
ec
to
r
.
2
.
4
.
M
o
v
ing
s
ink
pa
t
hs
as
t
he
s
eq
uence
of
no
d
es
T
h
e
p
ath
s
MSP1
an
d
MSP2
can
also
be
r
ep
r
esen
ted
as
th
e
s
eq
u
en
ce
s
of
n
o
d
es.
T
h
e
co
r
r
esp
o
n
d
in
g
s
et
of
n
o
d
es
wh
ich
f
o
r
m
MSP1
an
d
MSP2
ar
e
r
ep
r
esen
ted
by
s
ets
MSP1
_
V
an
d
MSP2
_
V
as
(
8
)
an
d
(
9
)
.
1
_
=
[
1
_
(
1
)
,
1
_
(
2
)
,
.
.
.
.
,
1
_
(
)
,
.
.
.
.
,
1
_
(
1
)
]
(
8
)
2
_
=
[
2
_
(
1
)
,
2
_
(
2
)
,
.
.
.
.
,
2
_
(
)
,
.
.
.
.
,
2
_
(
2
)
]
(
9
)
Sin
ce
,
MSP1
an
d
MSP2
ar
e
clo
s
ed
p
ath
s
,
f
o
r
each
p
ath
,
t
h
e
n
u
m
b
e
r
of
ed
g
es
is
eq
u
al
to
th
e
n
u
m
b
er
of
v
er
tices.
T
h
er
ef
o
r
e
,
1
an
d
2
ar
e
th
e
n
u
m
b
e
r
of
v
e
r
tices
in
MSP
1
an
d
MSP2
.
In
(
1
3
)
an
d
(
1
4
)
,
1
_
(
)
′
an
d
2
_
(
)
′
ar
e
th
e
v
er
tices
of
MSP1
_
V
an
d
MSP2
_
V,
r
esp
ec
tiv
el
y
.
2
.
5
.
I
nd
ex
f
o
rm
a
t
re
presenta
t
io
n
of
M
SP1
_
V
a
nd
M
SP2
_
V
I
n
d
ex
f
o
r
m
at
of
MSP1
_
V
is
r
e
p
r
esen
ted
by
th
e
b
i
n
ar
y
v
ec
to
r
s
1
y
as
(
1
0
)
.
1
(
)
=
{
1
,
if
e
dg
e
1
_
0
,
othe
r
wi
s
e
(
1
0
)
f
or
=
1
to
.
T
h
e
len
g
th
of
1
=
=
|
|
wh
er
e
V
is
th
e
v
er
tex
(
n
o
d
e)
s
et
of
th
e
g
r
ap
h
.
Fro
m
(
1
0
)
,
it
can
be
s
ee
n
th
at
(
1
)
=
1
.
An
o
th
e
r
way
of
r
ep
r
esen
tin
g
1
is
(
1
1
)
.
1
(
1
_
(
)
)
=
1
for
=
1
to
1
1
(
ℎ
)
=
0
}
(
1
1
)
Similar
ly
,
th
e
i
n
d
ex
f
o
r
m
at
of
MSP2
_
V
is
r
ep
r
esen
ted
by
t
h
e
b
in
ar
y
v
ec
to
r
2
as
(
1
2
)
:
2
(
)
=
{
1
,
∈
2
_
0
,
othe
r
wi
s
e
(
1
2
)
f
o
r
=
1
to
.
T
h
e
len
g
th
of
2
=
=
|
|
.
Fro
m
(
1
2
)
,
it
can
be
s
ee
n
t
h
at
(
2
)
=
2
.
An
o
th
er
way
of
r
ep
r
esen
tin
g
2
is
(
1
3
)
.
2
(
2
_
(
)
)
=
1
for
=
1
to
2
2
(
ℎ
)
=
0
}
(
1
3
)
2
.
6
.
Dec
is
io
n
v
ec
t
o
rs
y
1
a
nd
y
2
B
in
ar
y
v
ec
to
r
s
1
an
d
2
ar
e
also
t
h
e
d
ec
is
io
n
v
ec
to
r
s
in
d
eter
m
in
in
g
MSP1
_
V
a
n
d
MSP2
_
V
wh
en
an
o
p
tim
izatio
n
p
r
o
g
r
am
is
u
s
ed
to
d
eter
m
in
e
t
h
em
.
T
h
is
m
ea
n
s
,
o
n
ce
1
an
d
2
ar
e
d
eter
m
in
e
d
u
s
in
g
s
ay
th
e
B
I
P
,
th
en
MSP1
_
V
an
d
MSP2
_
V
ar
e
o
b
tain
e
d
u
s
in
g
th
e
MA
T
L
AB
f
in
d
(
…)
f
u
n
ctio
n
as
(
1
4
)
.
1
_
=
(
1
)
2
_
=
(
2
)
(
1
4
)
2
.
7
.
P
a
rt
icipa
t
ing
no
des
a
nd
pa
rt
icipa
t
ing
no
de
s
et
A
node
(
v
er
tex
)
th
at
b
el
o
n
g
s
to
MSP1
_
V
or
MSP2
_
V
is
d
e
f
in
ed
as
a
p
a
r
ticip
atin
g
n
o
d
e.
T
h
at
is
,
a
p
ar
ticip
atin
g
node
∈
{
1
_
}
∪
{
2
_
}
.
T
h
e
p
a
r
ticip
atin
g
n
o
d
e
s
et
is
th
e
co
llectio
n
of
all
t
h
e
p
ar
ticip
atin
g
n
o
d
es.
Par
ticip
a
tin
g
n
o
d
e
s
et,
r
ep
r
esen
ted
by
,
is
g
iv
e
n
by
th
e
u
n
io
n
of
MSP1
_
V
a
n
d
MSP2
_
V
as
:
=
{
1
_
}
∪
{
2
_
}
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
879
-
8
8
9
882
2
.
8
.
Sens
o
r
no
de
v
er
t
ex
s
et
T
h
e
s
e
n
s
o
r
n
o
d
e
s
of
t
h
e
n
e
t
w
o
r
k
a
r
e
r
e
p
r
e
s
e
n
t
e
d
by
t
h
e
s
e
t
.
A
l
l
t
h
e
n
o
d
e
s
(
g
r
i
d
p
o
i
n
t
s
)
n
e
e
d
not
be
s
e
n
s
o
r
n
o
d
e
s
.
P
a
t
h
s
M
S
P
1
a
n
d
M
S
P
2
s
h
o
u
l
d
f
u
l
l
y
c
o
v
e
r
.
T
h
u
s
is
a
s
u
b
s
e
t
of
w
h
i
c
h
in
t
u
r
n
is
a
s
u
b
s
e
t
of
.
2
.
9
.
Co
m
mo
n
no
de
T
h
e
W
SN
h
as
a
s
in
g
le
co
m
m
o
n
n
o
d
e
or
a
ju
n
ctio
n
n
o
d
e
d
e
n
o
ted
by
,
It
is
n
o
r
m
ally
a
n
o
d
e
at
th
e
ce
n
tr
o
id
of
th
e
W
SN
or
v
er
y
n
ea
r
to
it.
T
h
e
g
r
id
p
o
in
t
lo
ca
t
io
n
of
th
e
is
th
e
d
esig
n
e
r
’
s
c
h
o
ice.
m
ay
or
m
ay
not
b
elo
n
g
to
.
In
th
e
e
x
a
m
p
le
of
Fig
u
r
e
1,
n
o
d
e
13
is
t
h
e
an
d
it
b
elo
n
g
s
to
.
T
h
e
p
at
h
s
MSP1
an
d
MSP2
s
h
o
u
ld
co
m
p
u
ls
o
r
ily
v
i
s
it
th
e
n
o
d
es
of
in
clu
d
in
g
.
2
.
1
0
.
P
a
rt
icipa
t
ing
edg
es
a
nd
pa
rt
icipa
t
ing
edg
e
s
et
An
ed
g
e
th
at
b
elo
n
g
s
to
MSP1
_
E
or
MSP2
_
E
is
d
ef
in
ed
as
a
p
ar
ticip
atin
g
ed
g
e.
T
h
at
is
,
ed
g
e
is
a
p
ar
ticip
atin
g
ed
g
e
if
∈
1
_
or
∈
2
_
.
C
o
llectio
n
of
all
th
e
p
ar
ticip
atin
g
ed
g
es
of
th
e
f
o
r
m
s
th
e
p
ar
ticip
atin
g
ed
g
e
s
et
d
en
o
te
d
by
.
T
h
en
,
is
g
iv
en
by
(
1
5
)
.
=
{
1
_
}
∪
{
2
_
}
(
1
5
)
Fro
m
(
3
)
an
d
(
5
)
,
we
know
t
h
at
1
(
)
=
1
if
∈
1
_
an
d
2
(
)
=
1
if
∈
2
_
.
T
h
er
ef
o
r
e,
is
a
p
ar
ticip
atin
g
ed
g
e
if
1
(
)
=
1
or
2
(
)
=
1
.
T
h
is
f
ac
t
can
be
r
ep
r
esen
ted
as
(
1
6
)
.
∈
if
1
(
)
+
2
(
)
=
1
(
1
6
)
2
.
1
1
.
P
a
rt
i
ci
pa
t
ing
deg
re
e
of
a
v
er
t
ex
C
o
n
s
id
er
a
v
er
tex
(
)
of
th
e
MSP
g
r
ap
h
.
T
h
e
n
u
m
b
er
of
ed
g
e
s
co
n
n
ec
ted
to
th
at
v
er
tex
is
d
ef
in
ed
as
th
e
co
n
v
en
tio
n
al
d
eg
r
ee
of
th
at
v
er
tex
.
C
o
n
v
en
tio
n
al
d
eg
r
ee
of
v
e
r
tex
d
en
o
ted
by
(
)
is
g
iv
en
by
:
(
)
=
N
umb
e
r
o
f
e
dge
s
c
on
n
e
c
te
d
to
n
od
e
All
th
e
ed
g
es
of
n
o
d
e
i
m
a
y
n
o
t
p
ar
ticip
ate
in
f
o
r
m
in
g
th
e
MSP.
We
d
ef
in
e
t
h
e
p
ar
ticip
atin
g
d
e
g
r
ee
of
a
n
o
d
e
(
v
er
tex
)
i
,
r
ep
r
esen
ted
by
(
)
as
(
1
7
)
.
(
)
=
N
umb
e
r
of
pa
r
tic
ip
a
tin
g
e
d
ge
s
c
on
n
e
c
te
d
t
o
n
ode
(
1
7
)
B
ased
on
th
is
d
ef
in
itio
n
,
in
Fig
u
r
e
1,
(
3
)
=
2
b
ec
au
s
e
o
n
ly
two
ed
g
es
(
3
,
2)
an
d
(
3
,
9)
of
n
o
d
e
3
p
ar
ticip
ate
in
MSP1
.
Als
o
,
in
Fig
u
r
e
1,
(
1
)
=
0
b
ec
au
s
e
v
er
te
x
1
d
o
es
not
h
o
s
t
an
y
p
ar
ticip
atin
g
e
d
g
e.
2
.
1
2
.
P
a
rt
i
ci
pa
t
ing
edg
e
s
et
of
v
er
t
ices
T
h
o
s
e
ed
g
es
of
th
e
g
r
a
p
h
,
co
n
n
ec
ted
to
v
er
tex
i
f
o
r
m
th
e
co
n
v
en
tio
n
al
ed
g
e
s
et
of
v
er
te
x
an
d
it
is
d
en
o
ted
by
(
)
.
It
is
d
ef
in
ed
as
(
1
8
)
.
(
)
=
{
Those
e
dge
s
c
on
n
e
c
te
d
to
n
ode
}
(
1
8
)
T
h
e
p
ar
ticip
atin
g
ed
g
es
wh
ich
p
ass
th
r
o
u
g
h
n
o
d
e
f
o
r
m
th
e
p
ar
ticip
atin
g
ed
g
e
s
et
of
th
at
n
o
d
e.
T
h
u
s
(
)
wh
ich
d
en
o
tes
th
e
p
ar
ticip
atin
g
ed
g
e
s
et
of
n
o
d
e
is
d
ef
in
ed
as
:
(
)
=
{
Those
pa
r
t
ic
ipa
tin
g
e
dge
s
c
on
n
e
c
te
d
to
n
ode
}
To
d
eter
m
i
n
e
(
)
f
o
r
a
g
iv
e
n
i
,
we
h
av
e
to
co
u
n
t
th
o
s
e
e
d
g
es
wh
i
ch
ar
e
c
o
n
n
ec
te
d
to
v
er
tex
an
d
wh
ich
ar
e
also
p
ar
ticip
atin
g
ed
g
es
(
th
o
s
e
wh
o
b
elo
n
g
to
).
Ob
v
io
u
s
ly
,
t
h
ese
ed
g
es
ar
e
th
e
m
em
b
er
s
of
(
)
.
An
ed
g
e
b
elo
n
g
s
if
(
,
)
=
1
(
p
r
o
p
e
r
ty
of
)
an
d
also
b
elo
n
g
s
if
1
(
)
+
2
(
)
=
1
(
s
e
e
(
1
6
)
)
.
T
h
er
e
f
o
r
e,
∈
(
)
if
(
,
)
=
1
a
n
d
(
1
(
)
+
2
(
)
)
=
1
(
1
9
)
Sin
ce
b
o
th
(
,
)
an
d
1
(
)
+
2
(
)
ar
e
b
i
n
ar
y
v
ar
iab
les,
a
n
d
o
p
er
atio
n
ca
n
be
r
ep
lace
d
by
m
u
ltip
licatio
n
o
p
e
r
atio
n
.
T
h
er
ef
o
r
e,
(
1
9
)
can
be
r
ewr
itten
as
(
2
0
)
.
∈
(
)
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
1
(
2
0
)
f
o
r
=
1
to
.
No
w,
f
o
r
=
1
to
,
co
n
s
id
er
th
e
s
u
m
m
atio
n
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l
p
a
th
d
is
co
ve
r
y
fo
r
tw
o
mo
vin
g
s
in
ks
w
ith
a
co
mmo
n
ju
n
ctio
n
in
a
w
ir
eless
…
(
S
a
tis
h
Tu
n
g
a
)
883
(
)
=
∑
(
,
)
∗
(
1
(
)
+
1
(
)
)
=
1
(
2
1
)
Her
e,
(
,
)
∗
(
1
(
)
+
2
(
)
)
is
a
b
in
ar
y
v
a
r
iab
le
wh
i
ch
can
tak
e
th
e
v
alu
e
1
or
0.
T
h
er
ef
o
r
e
(
2
1
)
im
p
lies
th
at
(
,
)
∗
(
1
(
)
+
2
(
)
)
is
1
f
o
r
(
)
d
is
tin
ct
v
alu
es
of
.
T
h
is
m
ea
n
s
,
f
r
o
m
(
2
0
)
,
t
h
at,
∈
(
)
is
s
atis
f
ied
f
o
r
(
)
d
is
tin
ct
v
alu
e
s
of
out
of
.
T
h
e
r
ef
o
r
e,
th
e
n
u
m
b
er
of
elem
en
ts
in
(
)
is
(
)
.
T
h
er
ef
o
r
e,
(
)
=
|
(
)
|
=
(
)
(
2
2
)
Fro
m
(
2
1
)
an
d
(
2
2
)
,
we
g
et,
(
)
=
∑
(
,
)
∗
(
1
(
)
+
1
(
)
)
=
1
(
2
3
)
3.
DUAL
M
O
VING
S
I
NK
P
A
T
H
DIS
CO
V
E
RY
P
RO
B
L
E
M
Ou
r
o
b
jectiv
e
is
to
f
i
n
d
MSP1
an
d
MSP2
s
atis
f
y
in
g
th
e
f
o
llo
win
g
co
n
s
tr
ain
ts
.
−
B
o
th
MSP1
an
d
MSP2
s
h
o
u
ld
v
is
it
th
e
co
m
m
o
n
n
o
d
e
cn
.
−
T
h
er
e
s
h
o
u
l
d
be
s
in
g
le
c
o
m
m
o
n
n
o
d
e.
−
MSP1
an
d
MSP2
each
s
h
o
u
ld
f
o
r
m
r
o
u
n
d
tr
ip
p
ath
s
v
is
itin
g
ev
er
y
s
en
s
o
r
n
o
d
e
ex
ac
tly
o
n
ce
in
each
tr
ip
,
tr
av
ellin
g
alo
n
g
th
e
e
d
g
es
of
t
h
e
g
r
ap
h
.
−
MSP1
an
d
MSP2
ar
e
to
be
ed
g
e
d
is
jo
in
t.
−
MSP1
an
d
MSP2
s
h
o
u
ld
not
cr
o
s
s
each
o
th
er
.
If
th
e
p
ath
s
cr
o
s
s
,
th
er
e
is
a
p
o
s
s
ib
il
ity
of
th
e
p
h
y
s
ical
co
llis
io
n
of
th
e
m
o
v
in
g
s
in
k
v
eh
icles.
−
MSP1
an
d
MSP2
s
h
o
u
ld
not
cr
o
s
s
th
em
s
elv
es.
T
h
en
th
e
le
n
g
th
of
th
at
p
ath
will
be
u
n
n
e
ce
s
s
ar
ily
lo
n
g
er
co
m
p
ar
ed
to
th
e
non
-
cr
o
s
s
in
g
ca
s
e.
−
MSP1
an
d
MSP2
ar
e
to
be
n
o
d
e
d
is
jo
in
t
ex
ce
p
t
f
o
r
a
c
o
m
m
o
n
n
o
d
e.
−
MSP1
an
d
MSP2
s
h
o
u
ld
n
o
t
h
av
e
an
y
s
u
b
-
to
u
r
s
[
2
2
]
.
−
T
o
tal
len
g
th
of
th
e
tr
i
p
by
MS
P1
an
d
MSP2
s
h
o
u
ld
be
m
in
i
m
u
m
.
−
L
en
g
th
(
MSP1
)
s
h
o
u
ld
be
eq
u
al
or
v
er
y
n
ea
r
l
y
eq
u
al
to
len
g
t
h
(
MSP2
)
.
−
T
h
e
i
n
t
e
r
m
e
d
i
a
te
non
-
s
e
n
s
o
r
v
e
r
t
i
c
es
s
h
o
u
l
d
not
r
e
p
e
a
t
a
l
o
n
g
t
h
e
p
a
t
h
s
t
r
a
v
el
l
e
d
ei
t
h
e
r
by
MS
P
1
or
M
SP
2
.
3
.
1
.
P
ro
po
s
ed
s
o
lutio
n
T
h
e
m
eth
o
d
p
r
o
p
o
s
ed
to
s
o
lv
e
th
e
DM
SP
is
s
im
ilar
to
s
o
lv
in
g
T
SP
[
2
3
]
with
two
s
alesp
eo
p
le
.
As
in
T
SP
[
2
2
]
,
h
er
e
also
we
u
s
e
b
in
ar
y
in
teg
er
p
r
o
g
r
am
m
in
g
[
2
4
]
.
Ou
r
m
aj
o
r
co
n
tr
i
b
u
tio
n
is
to
ex
p
r
ess
th
e
co
n
s
tr
ain
ts
in
th
e
alg
eb
r
aic
f
o
r
m
in
ter
m
s
of
t
h
e
4
d
ec
is
io
n
v
ec
to
r
s
x1,
x
2
,
y1
an
d
y
2
.
4.
F
O
RM
UL
AT
I
O
N
OF
CO
NST
RA
I
NS
T
h
e
co
n
s
tr
ain
ts
of
s
ec
tio
n
3
ar
e
ex
p
r
ess
ed
in
p
r
o
p
er
alg
e
b
r
ai
c
f
o
r
m
ats
s
u
itab
le
f
o
r
th
e
b
in
ar
y
in
teg
er
p
r
o
g
r
a
m
m
in
g
s
o
lv
er
.
We
ass
u
m
e
th
at
MSP1
an
d
MSP2
ar
e
th
e
o
p
tim
u
m
p
ath
s
s
atis
f
y
in
g
th
e
co
n
s
tr
ain
ts
of
s
ec
tio
n
3.
4
.
1
.
Co
ns
t
ra
ints
on
co
m
m
o
n
no
d
e
C
o
n
s
id
er
th
e
co
m
m
o
n
n
o
d
e
cn
th
r
o
u
g
h
wh
ich
MSP1
an
d
MSP2
b
o
th
en
ter
o
n
ce
a
n
d
le
av
e
o
n
ce
.
T
h
u
s
th
e
(
)
=
4
if
is
th
e
co
m
m
o
n
n
o
d
e.
(
See
node
13
in
Fig
u
r
e
1)
No
w,
co
n
s
id
er
o
th
e
r
p
ar
ti
cip
atin
g
n
o
d
es.
Sin
ce
p
ath
s
MSP1
an
d
MSP2
ar
e
clo
s
ed
p
ath
s
with
o
u
t
an
y
s
u
b
l
o
o
p
s
ar
e
t
r
ee
s
eg
m
en
ts
,
a
p
ath
h
as
to
en
ter
a
n
o
n
-
co
m
m
o
n
p
ar
ticip
a
tin
g
n
o
d
e
o
n
ce
an
d
leav
e
also
o
n
ce
.
T
h
er
ef
o
r
e,
th
e
p
ar
ticip
atin
g
d
eg
r
ee
(
)
h
as
to
be
2
if
n
o
d
e
b
elo
n
g
s
{
−
}
(
Set
d
if
f
er
en
ce
)
.
MSP1
an
d
MSP2
do
not
v
is
it
n
o
n
-
p
a
r
ticip
atin
g
n
o
d
es.
T
h
e
r
ef
o
r
e,
th
er
e
is
n
eith
er
an
en
tr
y
nor
an
e
x
it
f
o
r
th
ese
n
o
d
es.
T
h
e
r
ef
o
r
e
,
(
)
=
0
f
o
r
′
wh
ich
do
not
b
elo
n
g
to
.
T
h
ese
p
ar
ticip
a
tin
g
d
eg
r
ee
v
alu
es
ar
e
s
u
r
m
is
ed
as
:
‑
C
ase
1)
No
d
e
is
th
e
co
m
m
o
n
n
o
d
e.
T
h
en
,
(
)
=
4
f
o
r
=
.
‑
C
ase
2)
No
d
e
b
elo
n
g
s
to
PN
ex
ce
p
t
th
e
co
m
m
o
n
n
o
d
e.
T
h
e
n
,
(
)
=
2
f
o
r
∈
{
−
}
.
‑
C
ase
3)
No
d
e
d
o
es
not
b
elo
n
g
to
PN.
T
h
en
,
(
)
=
0
f
o
r
∉
.
Usi
n
g
(
2
3
)
to
r
ep
r
esen
t
(
)
,
th
e
a
b
o
v
e
th
r
ee
ca
s
es
eq
u
atio
n
s
can
be
ex
p
r
ess
ed
as
:
∑
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
4
for
=
=
1
(
2
4
)
∑
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
2
for
∀
∉
{
−
}
=
1
(
2
5
)
∑
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
0
for
∀
∉
=
1
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
879
-
8
8
9
884
No
w,
co
n
s
id
er
th
e
co
m
m
o
n
n
o
d
e
cn
.
It
b
elo
n
g
s
to
b
o
th
MSP1
_
V
an
d
MSP2
_
V.
T
h
er
ef
o
r
e
,
f
r
o
m
(
1
0
)
,
1
(
)
=
1
an
d
f
r
o
m
(
1
2
)
,
2
(
)
=
1
.
T
h
er
ef
o
r
e,
1
(
)
+
2
(
)
=
2
for
=
(
2
7
)
No
w,
co
n
s
id
er
node
i
wh
ich
b
elo
n
g
to
{
1
_
−
}
.
T
h
en
f
r
o
m
(
1
0
)
,
1
(
)
=
1
b
u
t
f
r
o
m
(
1
2
)
,
2
(
)
=
0
b
ec
au
s
e
now
∉
{
2
_
}
b
ec
au
s
e,
{
1
_
−
}
an
d
{
2
_
}
ar
e
d
is
jo
in
t.
T
h
e
r
ef
o
r
e
1
(
)
+
2
(
)
=
1
f
o
r
∈
{
1
_
−
}
.
Similar
ly
,
it
can
be
s
h
o
wn
th
at
1
(
)
=
0
but
2
(
)
=
1
an
d
1
(
)
+
2
(
)
=
1
wh
en
∈
{
2
_
−
}
.
T
h
u
s
,
1
(
)
+
2
(
)
=
1
wh
en
∈
{
{
1
_
−
}
∪
{
2
_
−
}
}
.
Sin
ce
,
∈
{
{
1
_
−
}
∪
{
2
_
−
}
}
is
eq
u
iv
alen
t
to
{
−
}
,
1
(
)
+
2
(
)
=
1
for
∀
∈
{
−
}
(
2
8
)
f
o
r
∉
f
r
o
m
(
1
0
)
an
d
(
1
2
)
,
1
(
)
=
0
an
d
2
(
)
=
0
.
T
h
er
ef
o
r
e,
1
(
)
+
2
(
)
=
0
for
∀
∉
(
2
9
)
C
o
m
p
ar
in
g
th
e
R
HS
of
(
2
4
)
,
(
2
5
)
an
d
(
2
6
)
,
with
(
2
7
)
,
(
2
8
)
an
d
(
2
9
)
,
it
is
clea
r
t
h
at
(
2
4
)
,
(
2
5
)
a
n
d
(
2
6
)
ca
n
be
r
ep
lace
d
by
a
s
in
g
l
e
eq
u
atio
n
as
(
3
0
)
.
∑
(
,
)
=
1
∗
(
1
(
)
+
2
(
)
)
=
2
∗
(
1
(
)
+
2
(
)
)
for
∀
∈
(
3
0
)
4
.
2
.
Co
ns
t
ra
ints
re
g
a
rding
t
he
co
m
m
o
n
no
de
C
o
m
m
o
n
n
o
d
e
is
s
elec
ted
by
th
e
d
esig
n
e
r
an
d
is
k
n
o
wn
a
p
r
io
r
i.
b
elo
n
g
s
to
MSP1
_
V
an
d
MSP2
_
V.
T
h
is
co
n
s
tr
ain
t
is
ex
p
r
ess
ed
as
(
3
1
)
an
d
(
3
2
)
.
1
(
)
=
1
(
3
1
)
2
(
)
=
1
(
3
2
)
4
.
3
.
Co
ns
t
ra
ints o
n sen
s
o
r
no
des
T
h
e
m
o
v
i
n
g
s
in
k
p
ath
,
eith
e
r
MSP1
o
r
MSP2
h
as
to
v
is
it
th
e
s
en
s
o
r
n
o
d
es
r
ep
r
esen
ted
b
y
th
e
s
et
.
T
h
er
ef
o
r
e
th
e
(
)
o
f
th
ese
n
o
d
es
h
as
to
b
e
e
x
ac
tly
two
f
o
r
n
o
n
-
co
m
m
o
n
n
o
d
es
an
d
f
o
u
r
f
o
r
th
e
c
o
m
m
o
n
n
o
d
e.
(
Fo
r
o
th
e
r
n
o
d
es it c
an
b
e
two
o
r
ze
r
o
.
)
T
h
is
co
n
s
tr
ain
t
is
ex
p
r
ess
ed
as (
3
3
)
a
n
d
(
3
4
)
.
∑
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
4
f
o
r
=
=
1
(
3
3
)
∑
(
,
)
∗
(
1
(
)
+
2
(
)
)
=
2
f
o
r
∀
∈
{
−
}
=
1
(
3
4
)
4
.
4
.
No
n
-
cr
o
s
s
ing
cr
it
er
io
n
MSP1
an
d
MSP2
s
h
o
u
ld
n
o
t
cr
o
s
s
ea
ch
o
th
er
o
r
th
em
s
elv
e
s
.
(
T
h
ey
ca
n
m
ee
t
at
th
e
c
o
m
m
o
n
n
o
d
e)
.
Sin
ce
MSP1
an
d
MSP2
ar
e
e
d
g
e
d
is
jo
in
t,
th
e
s
elf
-
cr
o
s
s
in
g
o
f
MSP1
an
d
MSP2
ca
n
o
c
cu
r
o
n
ly
alo
n
g
th
e
d
iag
o
n
al
ed
g
es
o
f
g
r
id
ce
lls
.
W
h
en
a
cr
o
s
s
in
g
o
cc
u
r
s
in
a
g
r
id
c
ell,
b
o
th
th
e
d
iag
o
n
a
l
ed
g
es
ac
t
as
th
e
p
ar
ticip
atin
g
ed
g
es.
L
et
1
an
d
2
b
e
th
e
two
d
ia
g
o
n
al
e
d
g
es o
f
a
s
p
ec
if
ic
g
r
id
ce
ll.
T
h
en
,
f
r
o
m
(
1
6
)
:
1
∈
1
(
1
)
+
2
(
1
)
=
1
2
∈
1
(
2
)
+
2
(
2
)
=
1
If
b
o
th
1
an
d
2
wer
e
to
b
elo
n
g
to
,
th
en
b
o
th
th
e
ab
o
v
e
co
n
d
itio
n
s
h
o
u
l
d
be
tr
u
e.
T
h
en
,
1
(
1
)
+
2
(
1
)
+
1
(
2
)
+
2
(
2
)
=
2
.
To
p
r
ev
en
t
th
is
ev
e
n
t
an
d
to
av
o
id
cr
o
s
s
in
g
,
1
(
1
)
+
2
(
1
)
+
1
(
2
)
+
2
(
2
)
<
2
(
3
5
)
C
o
n
s
tr
ain
t
(
3
5
)
av
o
i
d
s
d
iag
o
n
al
cr
o
s
s
in
g
in
a
s
p
ec
if
ic
g
r
id
ce
ll.
To
ex
te
n
d
t
h
is
to
all
g
r
i
d
ce
lls
,
we
ap
p
ly
c
o
n
s
tr
ain
t
(
3
5
)
to
all
t
h
e
g
r
i
d
ce
lls
in
t
h
e
g
r
ap
h
.
L
et
th
e
g
r
id
ce
lls
of
th
e
g
r
ap
h
be
d
en
o
ted
as
=
[
(
1
)
,
(
2
)
,
.
.
.
.
,
(
)
,
.
.
.
.
,
(
)
]
wh
er
e
is
th
e
to
tal
n
u
m
b
er
of
ce
lls
.
L
et
(
)
.
1
an
d
(
)
.
2
be
th
e
two
d
iag
o
n
al
ed
g
es
of
ce
ll
(
)
f
o
r
=
1
to
.
T
h
en
th
e
ex
ten
s
io
n
of
(
3
5
)
f
o
r
all
th
e
ce
lls
can
be
ex
p
r
ess
ed
as
(
3
6
)
.
1
(
(
)
.
1
)
+
2
(
(
)
.
1
)
+
1
(
(
)
.
2
)
+
2
(
(
)
.
2
)
<
2
(
3
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l
p
a
th
d
is
co
ve
r
y
fo
r
tw
o
mo
vin
g
s
in
ks
w
ith
a
co
mmo
n
ju
n
ctio
n
in
a
w
ir
eless
…
(
S
a
tis
h
Tu
n
g
a
)
885
4
.
5
.
O
bje
ct
iv
e
f
un
ct
io
n
to
be
m
ini
m
ized
T
h
e
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
to
be
m
i
n
i
m
i
z
e
d
in
D
M
S
P
is
t
h
e
t
o
t
a
l
l
e
n
g
t
h
of
t
h
e
m
o
v
i
n
g
s
i
n
k
p
a
t
h
s
M
S
P
1
a
n
d
M
S
P
2
.
In
our
s
c
h
e
m
e
,
t
h
e
h
o
r
i
z
o
n
t
a
l
a
n
d
v
e
r
t
i
c
a
l
(
)
e
d
g
e
l
e
n
g
t
h
s
a
r
e
n
o
r
m
a
l
i
z
e
d
to
1
a
n
d
h
e
n
c
e
t
h
e
l
e
n
g
t
h
of
d
i
a
g
o
n
a
l
e
d
g
e
s
a
r
e
√
2
.
T
h
e
r
e
f
o
r
e
,
t
h
e
t
o
t
a
l
l
e
n
g
t
h
of
M
S
P
1
a
n
d
M
S
P
2
r
e
p
r
e
s
e
n
t
e
d
by
is
g
i
v
e
n
by
(
3
7
)
.
=
1
∗
s
um
(
e
dge
s
of
1
)
+
√
2
s
um
(
dia
gon
a
l
e
d
ge
s
of
1
)
+
1
∗
(
2
)
+
√
2
(
2
)
(3
7
)
is
a
lin
ea
r
f
u
n
ctio
n
of
th
e
d
ec
i
s
io
n
v
ar
iab
les
an
d
it
is
th
e
o
b
j
ec
tiv
e
f
u
n
ctio
n
to
be
m
in
im
ize
d
.
5.
B
I
NA
RY
I
N
T
E
G
E
R
P
RO
G
RAM
F
O
RM
UL
A
T
I
O
N
AND
SO
L
U
T
I
O
N
F
O
R
DM
SP
T
h
e
DM
SP
is
s
o
lv
ed
u
s
in
g
B
I
P
th
at
s
o
lv
es
f
o
r
1
,
2
,
1
an
d
2
to
m
in
im
ize
s
u
b
jecte
d
to
th
e
co
n
s
tr
ain
ts
,
(
3
0
)
to
(
3
4
)
an
d
(
3
6
)
.
All
th
e
c
o
n
s
tr
ain
ts
ar
e
lin
e
ar
an
d
f
r
o
m
(
3
7
)
,
it
can
be
s
ee
n
th
at
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
al
s
o
lin
ea
r
[
2
5
]
.
B
I
P
is
ap
p
lied
iter
ativ
ely
u
n
til
all
th
e
s
u
b
-
to
u
r
s
ar
e
elim
in
at
ed
[
2
3
]
.
B
I
P
g
iv
es
th
e
f
in
al
o
p
tim
u
m
v
alu
es
of
1
,
2
,
1
an
d
2
.
T
h
en
th
e
o
p
tim
u
m
p
ath
s
MSP1
an
d
MSP2
a
r
e
o
b
tain
ed
in
ter
m
s
of
ed
g
es
as
g
iv
en
by
(
4
)
,
(
6
)
an
d
in
ter
m
s
of
n
o
d
es
as
g
iv
en
by
(
1
1
)
,
(
1
3
)
.
DM
SP
alg
o
r
ith
m
is
d
is
cu
s
s
ed
in
th
e
s
ec
tio
n
5
.
1
.
5
.
1
.
DM
SP
a
lg
o
rit
hm
I
n
p
u
ts
:
Gr
id
b
ased
W
SN
with
k
n
o
wn
s
en
s
o
r
n
o
d
e
lo
ca
tio
n
s
.
C
o
m
m
o
n
n
o
d
e
(
)
,
as
s
elec
ted
by
th
e
d
esig
n
er
.
In
g
en
e
r
al,
cn
is
s
elec
ted
to
be
at
th
e
ce
n
ter
of
th
e
W
SN
ar
ea
.
Ou
tp
u
t:
Op
tim
al
p
ath
s
MSP1
an
d
MSP2
.
−
I
d
en
tify
n
o
d
es
an
d
ed
g
es
of
t
h
e
g
r
id
g
r
ap
h
.
−
I
n
itially
s
et
th
e
d
ec
is
io
n
v
ec
to
r
s
1
,
2
an
d
1
an
d
2
as
all
ze
r
o
v
ec
to
r
s
of
len
g
th
an
d
,
r
esp
ec
tiv
ely
.
−
Min
im
ize
th
e
to
tal
len
g
th
as
g
iv
en
by
(
3
7
)
,
s
u
b
jecte
d
to
c
o
n
s
tr
ain
ts
(
3
0
)
,
(
3
1
)
,
(
3
2
)
,
(
3
3
)
,
(
3
4
)
an
d
(
3
6
)
u
s
in
g
B
I
P
.
−
R
ep
ea
t
s
tep
4
u
n
til
all
s
u
b
to
u
r
s
ar
e
elim
in
ated
.
−
Get
th
e
f
in
al
o
p
tim
u
m
v
alu
es
of
1
,
2
,
1
an
d
2
.
−
Get
MSP1
an
d
MSP2
in
ter
m
s
of
ed
g
es
an
d
n
o
d
es
u
s
in
g
(
4
)
,
(
6
)
an
d
(
1
1
)
,
(
1
3
)
.
−
Ov
er
.
E
x
a
m
ple
1
Her
e,
=
8
,
=
6
,
an
d
th
e
c
o
m
m
o
n
n
o
d
e
=
22
.
=
[
22
39
10
23
42
16
46
18
9
44
41
12
7
2
38
8
25
20
34
17
15
3
]
Af
ter
s
o
lv
in
g
th
e
B
I
P
f
o
r
t
h
is
p
r
o
b
lem
,
th
e
r
esu
ltin
g
p
ath
s
MSP1
(
in
r
ed
)
an
d
MSP2
(
in
b
lu
e)
ar
e
s
h
o
w
n
in
Fig
u
r
e
2.
Her
e,
1
_
=
[
2
3
10
11
12
18
17
23
22
16
9
8
7
]
an
d
1
=
13
.
In
Fig
u
r
e
2,
2
_
=
[
15
22
28
34
41
42
47
39
44
38
32
28
20
]
an
d
2
=
14
.
Fro
m
MSP1
_
V
a
n
d
M
SP
2
_
V,
th
e
co
r
r
esp
o
n
d
in
g
p
ath
le
n
g
th
s
can
be
o
b
tain
e
d
b
ased
on
(
3
7
)
.
Fig
u
r
e
2.
Min
im
u
m
len
g
th
d
u
al
m
o
v
in
g
s
in
k
p
ath
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
879
-
8
8
9
886
6.
E
XP
E
R
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M
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N
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L
RE
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T
S
AND
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USS
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O
N
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o
n
s
i
d
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t
h
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f
o
l
l
o
wi
n
g
t
w
o
m
o
d
e
s
o
f
t
h
e
m
o
v
i
n
g
s
i
n
k
u
n
i
t
.
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o
d
e
1
:
T
h
e
m
o
v
i
n
g
s
i
n
k
s
h
a
v
e
o
n
l
y
h
o
r
i
z
o
n
t
a
l
a
n
d
v
e
r
t
i
c
al
m
o
v
em
e
n
t
s
a
l
o
n
g
t
h
e
g
r
i
d
n
o
d
e
s
(
s
e
e
Fi
g
u
r
e
3
(
a
)
)
.
M
o
d
e
2
:
T
h
e
m
o
v
i
n
g
s
i
n
k
s
h
a
v
e
d
i
a
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l
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p
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l
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n
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er
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l
m
o
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e
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e
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ts
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s
e
e
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i
g
u
r
e
3
(
b
)
)
.
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S
D
N
c
a
n
b
e
a
p
p
l
i
e
d
t
o
b
o
t
h
t
h
e
m
o
d
e
s
.
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n
m
o
d
e
1
,
d
i
a
g
o
n
a
l
e
d
g
e
s
a
r
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i
g
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o
r
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d
w
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g
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D
N
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h
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h
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r
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s
e
n
s
o
r
n
o
d
e
s
o
f
t
h
e
g
i
v
en
W
SN
a
r
e
a
,
i
n
m
o
d
e
2
,
is
s
h
o
r
t
e
r
c
o
m
p
a
r
e
d
t
o
t
h
a
t
o
f
m
o
d
e
1
.
E
x
p
e
r
i
m
e
n
t
1
c
o
m
p
a
r
e
s
t
h
e
o
p
t
i
m
a
l
r
o
u
n
d
t
r
i
p
t
r
a
v
e
l
d
i
s
t
a
n
c
e
s
o
f
t
h
e
s
e
t
w
o
m
o
d
es
.
(
a)
(
b
)
Fig
u
r
e
3.
T
h
ese
f
ig
u
r
es a
r
e;
(
a
)
4
-
co
n
n
ec
ted
g
r
id
lay
o
u
t a
n
d
(
b
)
8
-
co
n
n
ec
ted
g
r
id
lay
o
u
t
E
x
perim
ent
1
Her
e,
we
c
o
n
s
id
er
3
W
SNs
wi
th
p
r
o
g
r
ess
iv
ely
i
n
cr
ea
s
in
g
s
izes.
T
h
e
n
u
m
b
er
of
s
en
s
o
r
n
o
d
es
is
tak
en
as
r
o
u
n
d
(
4
5
%
of
n
u
m
b
e
r
of
g
r
id
p
o
in
ts
)
in
each
W
SN.
T
h
e
s
en
s
o
r
n
o
d
es
ar
e
d
is
tr
ib
u
ted
r
a
n
d
o
m
ly
am
o
n
g
th
e
g
r
id
p
o
in
ts
.
T
h
e
o
p
tim
al
len
g
th
s
o
f
MSP1
an
d
MSP2
in
b
o
th
th
e
m
o
d
es
in
all
th
e
3
W
SN
s
ar
e
g
iv
en
in
T
ab
le
1
.
MSP1
an
d
MSP2
ar
e
d
eter
m
in
ed
f
o
r
two
m
o
d
es
w
h
er
e,
4
-
c
o
n
n
ec
tiv
it
y
is
m
ode
1
an
d
8
-
c
o
n
n
ec
ti
v
ity
is
m
ode
2.
T
h
e
o
p
tim
al
p
ath
s
o
b
tain
ed
u
s
in
g
DM
SP
ar
e
s
h
o
wn
in
Fig
u
r
e
s
4
to
6
f
o
r
all
th
e
3
W
SNs
.
Fro
m
T
ab
le
1,
we
s
ee
th
at
th
e
o
p
tim
al
len
g
th
of
p
ath
s
in
m
ode
2
is
s
h
o
r
ter
co
m
p
ar
ed
to
th
o
s
e
of
m
ode
1.
T
ab
le
1
.
Op
tim
al
len
g
th
o
f
M
SP
1
an
d
MSP2
in
two
m
o
d
es f
o
r
1
th
e
5
W
SN’
s
G
r
i
d
s
i
z
e
o
f
W
S
N
Le
n
g
t
h
o
f
M
S
P
1
Le
n
g
t
h
o
f
M
S
P
2
Le
n
g
t
h
o
f
M
S
P
2
M
o
d
e
1
M
o
d
e
2
M
o
d
e
1
M
o
d
e
2
M
o
d
e
1
M
o
d
e
2
5
×
5
1
2
.
0
0
0
0
9
.
6
5
6
0
1
2
.
0
0
0
0
8
.
8
2
8
0
2
4
.
0
0
0
0
1
8
.
4
8
4
0
6
×
6
1
8
.
0
0
0
0
1
1
.
6
5
6
0
1
4
.
0
0
0
0
1
2
.
4
8
4
0
3
2
.
0
0
0
0
2
4
.
1
4
0
0
7
×
7
2
4
.
0
0
0
0
2
0
.
4
8
4
0
1
4
.
0
0
0
0
1
2
.
8
2
8
0
3
8
.
0
0
0
0
3
3
.
3
1
2
0
(
a)
(
b
)
Fig
u
r
e
4
.
Gr
id
s
ize
5
×5
; (
a)
m
o
d
e
1
a
n
d
(
b
)
m
o
d
e
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Op
tima
l
p
a
th
d
is
co
ve
r
y
fo
r
tw
o
mo
vin
g
s
in
ks
w
ith
a
co
mmo
n
ju
n
ctio
n
in
a
w
ir
eless
…
(
S
a
tis
h
Tu
n
g
a
)
887
(
a)
(
b
)
Fig
u
r
e
5
.
Gr
id
s
ize
6
×6
; (
a)
m
o
d
e
1
a
n
d
(
b
)
m
o
d
e
2
(
a)
(
b
)
Fig
u
r
e
6.
Gr
id
s
ize
7
×
7
;
(
a)
m
o
d
e
1
an
d
(
b
)
m
ode
2
7.
CO
NCLU
SI
O
N
A
n
ew
tech
n
iq
u
e
is
p
r
esen
ted
to
d
eter
m
in
e
t
h
e
o
p
tim
al
p
at
h
s
f
o
r
two
m
o
v
in
g
s
in
k
s
with
a
co
m
m
o
n
node
b
etwe
en
t
h
e
two
p
ath
s
.
T
h
e
p
ath
s
can
be
alo
n
g
th
e
h
o
r
izo
n
tal/v
er
tical
ed
g
es
an
d
/
o
r
im
m
ed
iate
d
iag
o
n
al
ed
g
es
b
ased
on
th
e
o
p
tim
ality
cr
iter
io
n
.
T
h
e
p
ath
s
ar
e
so
d
eter
m
in
ed
t
h
at
th
e
two
p
ath
s
do
not
c
r
o
s
s
each
o
th
er
or
o
v
er
lap
e
x
ce
p
t
at
t
h
e
co
m
m
o
n
n
o
d
e.
T
h
e
lin
ea
r
in
t
eg
er
p
r
o
g
r
a
m
is
s
o
lv
ed
u
s
in
g
4
d
ec
is
io
n
v
ec
to
r
s
wh
ich
m
ak
e
th
e
s
p
ec
if
icatio
n
s
of
c
o
n
s
tr
ain
ts
ea
s
y
a
n
d
f
lex
ib
le.
In
t
h
is
m
eth
o
d
,
b
o
th
t
h
e
p
at
h
len
g
th
s
a
r
e
m
a
d
e
eq
u
al
or
v
e
r
y
n
ea
r
ly
eq
u
al
wh
i
le
th
e
to
tal
le
n
g
th
is
m
in
im
ize
d
.
T
h
is
in
te
g
r
ated
ap
p
r
o
ac
h
is
a
n
o
v
el
an
d
u
n
iq
u
e
s
o
lu
tio
n
to
s
o
lv
e
th
e
d
u
al
m
o
v
in
g
s
in
k
p
ath
p
r
o
b
lem
in
a
W
SN
.
RE
F
E
R
E
NC
E
S
[1
]
C.
Tu
n
c
a
,
S.
Isi
k
,
M.
Y.
D
o
n
m
e
z
a
n
d
C.
Ers
o
y
,
"
Distri
b
u
ted
M
o
b
il
e
S
in
k
R
o
u
t
in
g
f
o
r
W
irele
ss
S
e
n
s
o
r
Ne
two
r
k
s:
A
S
u
rv
e
y
,
"
I
EE
E
C
o
mm
u
n
ic
a
ti
o
n
s
S
u
rv
e
y
s
&
T
u
t
o
ria
ls
,
v
o
l.
16,
no.
2,
p
p
.
8
7
7
-
8
9
7
,
S
e
c
o
n
d
Qu
a
rter
2
0
1
4
,
d
o
i:
1
0
.
1
1
0
9
/S
URV
.
2
0
1
3
.
1
0
0
1
1
3
.
0
0
2
9
3
.
[2
]
M.
Di
F
ra
n
c
e
sc
o
,
S.
K.
Da
s,
a
n
d
G.
An
a
sta
si,
“
Da
ta
c
o
ll
e
c
ti
o
n
in
wire
les
s
se
n
so
r
n
e
two
r
k
s
wit
h
m
o
b
il
e
e
lem
e
n
ts:
A
su
rv
e
y
,
”
AC
M
T
r
a
n
s.
S
e
n
s
o
r
Ne
two
rk
s
,
v
o
l
.
8,
n
o
.
1,
p
p
.
1
–
3
1
,
2
0
1
1
.
[3
]
H.
Hu
a
n
g
,
A.
V.
S
a
v
k
i
n
,
M.
Din
g
,
a
n
d
C.
Hu
a
n
g
,
“
M
o
b
il
e
r
o
b
o
ts
in
wire
les
s
se
n
so
r
n
e
two
r
k
s:
A
s
u
rv
e
y
on
tas
k
s,”
Co
mp
u
ter
Ne
tw
o
rk
s
,
v
o
l.
1
4
8
,
pp.
1
–
19,
2
0
1
9
,
doi
:
1
0
.
1
0
1
6
/J.COM
NET.
2
0
1
8
.
1
0
.
0
1
8
.
[4
]
W.
Li
a
n
g
,
J.
Lu
o
,
a
n
d
X.
Xu
,
"
P
ro
lo
n
g
in
g
Ne
two
rk
Li
fe
ti
m
e
v
i
a
a
Co
n
tro
ll
e
d
M
o
b
il
e
S
in
k
in
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
s,"
in
2
0
1
0
IE
EE
Gl
o
b
a
l
T
e
lec
o
mm
u
n
ic
a
ti
o
n
s
Co
n
f
e
re
n
c
e
GLOBE
COM
2
0
1
0
,
2
0
1
0
,
p
p
.
1
-
6,
d
o
i:
1
0
.
1
1
0
9
/G
LOCOM.
2
0
1
0
.
5
6
8
3
0
9
5
.
[5
]
Z.
Wa
n
g
,
S.
Ba
sa
g
n
i,
E.
M
e
lac
h
rin
o
u
d
is,
a
n
d
C.
P
e
tri
o
li
,
“
Ex
p
lo
it
i
n
g
S
i
n
k
M
o
b
i
li
ty
f
o
r
M
a
x
i
m
izin
g
S
e
n
so
r
Ne
two
rk
s
Li
fe
ti
m
e
,
”
Pr
o
c
e
e
d
in
g
s
of
t
h
e
3
8
t
h
An
n
u
a
l
H
a
wa
ii
In
ter
n
a
ti
o
n
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[6
]
H
.
Hu
a
n
g
,
“
P
e
rfo
rm
a
n
c
e
Im
p
ro
v
e
m
e
n
t
by
In
tro
d
u
c
in
g
M
o
b
il
i
ty
in
Wi
re
les
s
C
o
m
m
u
n
ica
ti
o
n
Ne
two
rk
s
,”
a
rXiv:
1
7
1
2
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0
2
4
3
6
,
2
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1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
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J
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&
C
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m
p
Sci,
Vo
l.
23
,
No
.
2
,
Au
g
u
s
t
20
21
:
879
-
8
8
9
888
[7
]
S.
M.
A.
Ak
b
e
r,
et
al
.
,
“
Da
ta
Vo
l
u
m
e
Ba
se
d
Da
ta
G
a
th
e
rin
g
in
WS
Ns
u
sin
g
M
o
b
il
e
Da
ta
Co
ll
e
c
to
r
,
”
in
Pro
c
e
e
d
in
g
s
of
th
e
2
2
n
d
In
ter
n
a
t
io
n
a
l
D
a
ta
b
a
se
E
n
g
i
n
e
e
rin
g
&
A
p
p
li
c
a
ti
o
n
s
S
y
mp
o
si
u
m
on
-
IDE
AS
2
0
1
8
,
2
0
1
8
,
d
oi
:
1
0
.
1
1
4
5
/3
2
1
6
1
2
2
.
3
2
1
6
1
6
6
.
[8
]
S.
Ba
sa
g
n
i,
A.
Ca
ro
si,
C.
P
e
tri
o
li
,
“
M
o
b
i
li
ty
in
wire
les
s
se
n
so
r
n
e
t
wo
rk
s,
”
in
:
Al
g
o
rit
h
ms
a
n
d
Pro
t
o
c
o
ls
fo
r
Ad
Ho
c
and
S
e
n
s
o
r
Ne
two
rk
s
,
Jo
h
n
Wi
ley
&
S
o
n
s,
In
c
.
,
2
0
0
7
.
[9
]
M.
Ko
ç
a
n
d
I.
K
o
rp
e
o
g
l
u
,
“
Co
o
rd
i
n
a
ted
m
o
v
e
m
e
n
t
of
m
u
lt
ip
le
m
o
b
il
e
si
n
k
s
in
a
wire
les
s
se
n
so
r
n
e
two
r
k
f
o
r
imp
ro
v
e
d
li
fe
ti
m
e
,
”
in
EURA
S
IP
J
o
u
rn
a
l
on
W
ire
les
s
Co
mm
u
n
ica
ti
o
n
s
a
n
d
Ne
two
rk
in
g
,
v
o
l.
2
0
1
5
,
n
o
.
1,
2
0
1
5
,
doi
:
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0
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6
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3
6
3
8
-
0
1
5
-
0
4
7
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-
5.
[1
0
]
U.
Ha
rih
a
ra
n
,
“
M
u
lt
i
S
in
k
S
c
h
e
d
u
li
n
g
S
c
h
e
m
e
fo
r
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
s
,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
of
A
d
v
a
n
c
e
d
and
Ap
p
li
e
d
S
c
ien
c
e
s
,
v
o
l.
3
,
n
o
.
2,
p
p
.
1
-
8
,
2
0
1
4
.
[1
1
]
H.
A.
Al‐Be
h
a
d
il
i,
S.
K.
Alwa
n
e
,
Y.
I.
Al‐Ya
sir,
N.
O.
P
a
rc
h
i
n
,
P.
Olley
,
a
n
d
R.
A.
Ab
d
‐Alh
a
m
e
e
d
,
“
Us
e
of
m
u
lt
ip
le
m
o
b
il
e
sin
k
s
in
wire
les
s
se
n
so
r
n
e
two
rk
s
fo
r
larg
e
‐sc
a
le
a
re
a
s,”
IET
W
ire
les
s
S
e
n
so
r
S
y
ste
ms
,
v
o
l.
10,
no.
4,
p
p
.
1
7
5
–
1
8
0
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
4
9
/i
e
t
-
wss.
2
0
1
9
.
0
2
0
8
.
[1
2
]
P.
Z
h
o
n
g
a
n
d
F.
R
u
a
n
,
“
An
e
n
e
rg
y
e
fficie
n
t
m
u
lt
ip
le
m
o
b
il
e
si
n
k
s
b
a
se
d
ro
u
ti
n
g
a
lg
o
r
it
h
m
fo
r
wire
les
s
se
n
so
r
n
e
two
rk
s,”
IOP
Co
n
fer
e
n
c
e
S
e
rie
s:
M
a
ter
ia
ls
S
c
ien
c
e
a
n
d
En
g
in
e
e
rin
g
,
v
o
l.
3
2
3
,
p.
0
1
2
0
2
9
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
8
8
/1
7
5
7
-
8
9
9
x
/
3
2
3
/1
/
0
1
2
0
2
9
.
[1
3
]
W.
Wen
,
C.
-
Y.
Ch
a
n
g
,
S.
Z
h
a
o
,
a
n
d
C.
S
h
a
n
g
,
“
Co
o
p
e
ra
ti
v
e
Da
t
a
Co
ll
e
c
ti
o
n
M
e
c
h
a
n
ism
Us
in
g
M
u
lt
i
p
le
M
o
b
il
e
S
in
k
s
in
Wi
re
les
s
S
e
n
so
r
Ne
two
r
k
s,”
S
e
n
s
o
rs
,
v
o
l.
1
8
,
n
o
.
8,
p.
2
6
2
7
,
2
0
1
8
,
d
o
i:
1
0
.
3
3
9
0
/s1
8
0
8
2
6
2
7
.
[1
4
]
S.
Li
u
,
Z.
Wei,
Z.
G
u
o
,
X.
Yu
a
n
,
a
n
d
Z.
F
e
n
g
,
"
P
e
rfo
rm
a
n
c
e
An
a
ly
sis
of
UAVs
As
siste
d
Da
ta
Co
ll
e
c
ti
o
n
in
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
,
"
in
2
0
1
8
IE
EE
8
7
th
Veh
icu
l
a
r
T
e
c
h
n
o
lo
g
y
Co
n
fer
e
n
c
e
(VT
C
S
p
ri
n
g
)
,
2
0
1
8
,
p
p
.
1
-
5,
d
o
i:
1
0
.
1
1
0
9
/VTCS
p
rin
g
.
2
0
1
8
.
8
4
1
7
6
7
3
.
[1
5
]
A.
M
a
z
a
y
e
v
,
N.
Co
rre
ia,
a
n
d
G.
S
c
h
ü
tz,
“
Da
ta
G
a
th
e
rin
g
in
W
ir
e
les
s
S
e
n
so
r
Ne
two
r
k
s
Us
i
n
g
Un
m
a
n
n
e
d
Ae
rial
Ve
h
icle
s,”
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
of
W
ire
les
s
In
f
o
rm
a
ti
o
n
N
e
two
rk
s
,
v
o
l.
2
3
,
n
o
.
4,
p
p
.
297
–
3
0
9
,
2
0
1
6
,
d
o
i:
1
0
.
1
0
0
7
/s1
0
7
7
6
-
0
1
6
-
0
3
1
9
-
y.
[1
6
]
C.
Lu
o
,
M.
N.
S
a
tp
u
te,
D.
Li,
Y.
Wan
g
,
W.
Ch
e
n
,
a
n
d
W.
W
u
,
"
F
i
n
e
-
G
ra
in
e
d
Traje
c
to
ry
Op
ti
m
iza
ti
o
n
of
M
u
lt
i
p
le
UAVs
fo
r
Eff
icie
n
t
Da
ta
G
a
th
e
rin
g
fro
m
WS
Ns
,
"
IEE
E/
ACM
T
ra
n
sa
c
ti
o
n
s
on
Ne
two
rk
i
n
g
,
v
o
l.
2
9
,
n
o
.
1,
pp.
1
6
2
-
1
7
5
,
F
e
b
.
2
0
2
1
,
d
o
i:
1
0
.
1
1
0
9
/T
NET.
2
0
2
0
.
3
0
2
7
5
5
5
.
[1
7
]
O.
Bo
u
h
a
m
e
d
,
H.
G
h
a
z
z
a
i,
H.
B
e
sb
e
s
a
n
d
Y.
M
a
ss
o
u
d
,
"A
UA
V
-
As
siste
d
Da
ta
Co
ll
e
c
ti
o
n
fo
r
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
s:
Au
t
o
n
o
m
o
u
s
Na
v
ig
a
ti
o
n
a
n
d
S
c
h
e
d
u
li
n
g
,
"
in
IEE
E
Acc
e
ss
,
v
o
l.
8,
p
p
.
1
1
0
4
4
6
-
1
1
0
4
6
0
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
0
9
/ACCES
S
.
2
0
2
0
.
3
0
0
2
5
3
8
.
[1
8
]
K.
C
l
a
r
k
s
o
n
,
S.
K
a
p
o
o
r
,
a
n
d
P.
V
a
i
d
y
a
,
“
R
e
c
t
i
l
i
n
e
a
r
s
h
o
r
t
e
s
t
p
a
t
h
s
t
h
r
o
u
g
h
p
o
l
y
g
o
n
a
l
o
b
s
t
a
c
l
e
s
in
O
(
n
(
l
o
g
n
)
2
)
t
i
m
e
,
”
P
r
o
c
e
e
d
i
n
g
s
of
t
h
e
t
h
i
r
d
a
n
n
u
a
l
s
y
m
p
o
s
i
u
m
on
C
o
m
p
u
t
a
t
i
o
n
a
l
g
e
o
m
e
t
r
y
-
S
C
G
87
,
1987,
d
o
i
:
1
0
.
1
1
4
5
/
4
1
9
5
8
.
4
1
9
8
5
.
[1
9
]
R.
Ku
m
a
r,
T.
Am
g
o
th
a
n
d
D.
D
a
s,
"
Ob
sta
c
le
-
Aw
a
re
Co
n
n
e
c
ti
v
it
y
Estab
li
sh
m
e
n
t
in
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
s,"
IEE
E
S
e
n
so
rs
J
o
u
r
n
a
l
,
v
o
l.
2
1
,
n
o
.
4,
p
p
.
5
5
4
3
-
5
5
5
2
,
15
F
e
b
.
1
5
,
2
0
2
1
,
d
o
i:
1
0
.
1
1
0
9
/JS
EN.
2
0
2
0
.
3
0
3
2
1
4
4
.
[2
0
]
G.
Xie
,
K.
Ota
,
M.
Do
n
g
,
F.
P
a
n
,
a
n
d
A.
Li
u
,
“
En
e
rg
y
-
e
fficie
n
t
ro
u
ti
n
g
fo
r
m
o
b
il
e
d
a
ta
c
o
l
lec
to
rs
in
wire
les
s
se
n
so
r
n
e
two
rk
s
wit
h
o
b
sta
c
les
,
”
Pee
r
-
to
-
Pee
r
Ne
two
rk
in
g
a
n
d
A
p
p
li
c
a
ti
o
n
s
,
v
o
l.
1
0
,
n
o
.
3,
p
p
.
4
7
2
–
4
8
3
,
2
0
1
6
,
doi
:
1
0
.
1
0
0
7
/s1
2
0
8
3
-
0
1
6
-
0
5
2
9
-
1.
[2
1
]
G.
Xie
a
n
d
F.
P
a
n
,
"
Cl
u
ste
r
-
Ba
se
d
Ro
u
ti
n
g
f
o
r
t
h
e
M
o
b
il
e
S
in
k
in
Wi
re
les
s
S
e
n
so
r
Ne
two
rk
s
wi
th
O
b
sta
c
les
,
"
IEE
E
Acc
e
ss
,
v
o
l.
4,
pp.
2
0
1
9
-
2
0
2
8
,
2
0
1
6
,
d
o
i:
1
0
.
1
1
0
9
/ACCE
S
S
.
2
0
1
6
.
2
5
5
8
1
9
6
.
[2
2
]
M.
Dia
b
y
,
“
T
h
e
Trav
e
ll
i
n
g
S
a
le
sm
a
n
P
ro
b
lem
:
A
Li
n
e
a
r
P
ro
g
ra
m
m
in
g
F
o
rm
u
lati
o
n
,
”
W
S
EA
S
T
ra
n
sa
c
ti
o
n
s
on
M
a
t
h
e
ma
ti
c
s
,
v
o
l.
6,
n
o
.
6,
pp.
745
-
7
5
4
,
2
0
0
7
.
[2
3
]
Y.
S
h
u
a
i,
S.
Yu
n
fe
n
g
,
a
n
d
Z.
Ka
i
,
“
An
e
ffe
c
ti
v
e
m
e
th
o
d
f
o
r
so
lv
i
n
g
m
u
lt
i
p
le
tra
v
e
ll
in
g
sa
les
m
a
n
p
r
o
b
lem
b
a
se
d
on
NSG
A
-
II,
”
S
y
ste
ms
S
c
ien
c
e
&
Co
n
tro
l
E
n
g
i
n
e
e
rin
g
,
v
o
l.
7,
n
o
.
2,
p
p
.
1
0
8
–
1
1
6
,
2
0
1
9
,
doi
:
1
0
.
1
0
8
0
/2
1
6
4
2
5
8
3
.
2
0
1
9
.
1
6
7
4
2
2
0
.
[2
4
]
G.
P
a
tak
i,
“
Tea
c
h
in
g
I
n
teg
e
r
P
r
o
g
ra
m
m
in
g
F
o
rm
u
lati
o
n
s
Us
in
g
t
h
e
Trav
e
li
n
g
S
a
les
m
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Ema
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:
sa
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tu
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a
@m
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u
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