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E
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Science
Vo
l.
10
,
No
.
2
,
May
201
8
,
p
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.
7
3
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2
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4752
I
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J
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Vo
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10
,
No
.
2
,
May
2018
:
7
3
3
–
7
4
0
734
Fig
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e
r
elate
d
w
o
r
k
.
Sec
tio
n
I
I
I
p
r
o
v
id
es
t
h
e
p
r
o
b
le
m
f
o
r
m
u
latio
n
an
d
o
u
r
p
r
o
p
o
s
ed
r
o
u
tin
g
alg
o
r
it
h
m
.
Si
m
u
la
tio
n
r
esu
lt
s
ar
e
p
r
esen
ted
in
Sectio
n
I
V.
Sectio
n
V
co
n
cl
u
d
es t
h
e
p
ap
er
.
Fig
u
r
e
2
.
E
x
a
m
p
le
o
f
a
P
air
o
f
L
i
n
k
-
d
is
j
o
in
t
L
i
g
h
tp
at
h
s
w
i
th
Min
i
m
u
m
Sp
atial
Dis
ta
n
ce
2.
RE
L
AT
E
D
WO
RK
Dis
aster
s
ar
e
in
e
v
itab
le,
a
n
d
ca
n
d
is
r
u
p
t
th
e
n
et
w
o
r
k
s
er
v
i
ce
s
s
i
g
n
if
ican
t
l
y
[
6
]
.
Du
r
i
n
g
th
e
r
ec
en
t
y
ea
r
s
,
a
lo
t
o
f
w
o
r
k
h
a
s
b
ee
n
co
n
d
u
cted
to
ad
d
r
ess
th
e
is
s
u
e
o
f
d
is
aster
v
u
ln
er
ab
ili
ties
w
it
h
d
if
f
er
en
t
p
er
s
p
ec
tiv
es
li
k
e
n
at
u
r
al
d
is
aster
s
,
elec
tr
o
m
ag
n
etic
p
u
ls
e,
w
ea
p
o
n
s
o
f
m
as
s
d
estru
ctio
n
attac
k
s
,
s
p
ec
if
ic
g
eo
g
r
ap
h
ical
lo
ca
tio
n
s
a
n
d
r
eg
io
n
-
a
w
ar
e
n
et
w
o
r
k
au
g
m
e
n
tatio
n
to
d
is
co
u
r
s
e
th
e
in
f
l
u
en
ce
o
f
a
r
eg
io
n
al
f
ail
u
r
es
[
7
,
8
-
19
]
.
T
h
e
i
m
p
ac
t
o
f
f
a
ilu
r
e
e
v
e
n
ts
o
n
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e
t
w
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’
s
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er
v
ice
s
a
n
d
ca
p
ac
it
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ca
n
b
e
d
eter
m
i
n
ed
f
r
o
m
th
e
n
et
w
o
r
k
g
eo
g
r
ap
h
y
.
Dik
b
i
y
ik
et
al.
[
9
]
,
p
r
o
p
o
s
ed
s
o
lu
ti
o
n
s
to
p
r
ev
en
t
co
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ec
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n
f
ail
u
r
es
f
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o
m
d
is
a
s
ter
s
th
r
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h
p
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ac
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ap
p
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e
d
a
m
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es
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n
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s
ca
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in
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ail
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r
es
ar
e
esti
m
ated
as
s
p
ec
if
ic
ev
e
n
t
s
lik
e
f
lo
o
d
s
,
h
u
r
r
ican
e
s
,
ea
r
th
q
u
a
k
e
s
,
an
d
o
cc
u
r
r
in
g
in
s
p
ec
if
ic
g
eo
g
r
ap
h
ical
lo
ca
tio
n
s
.
I
n
[
1
1
]
,
Neu
m
a
y
er
et
al.
p
r
esen
ted
th
e
g
eo
g
r
ap
h
ic
-
b
ase
d
f
ailu
r
e
as
g
e
n
er
alize
d
m
i
n
-
c
u
t
an
d
m
a
x
-
f
lo
w
p
r
o
b
le
m
s
,
wh
er
e
a
r
iv
al
tr
ies
to
Evaluation Warning : The document was created with Spire.PDF for Python.
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N:
2502
-
4752
Ma
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lly
S
p
a
tia
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-
Dis
jo
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t Lig
h
tp
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in
O
p
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l Netw
o
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ks
(
M.
W
a
q
a
r
A
s
h
r
a
f
)
735
r
ed
u
ce
th
e
n
et
w
o
r
k
co
n
n
ec
ti
v
it
y
b
y
m
u
l
tip
le
attac
k
s
.
T
h
e
y
p
r
o
p
o
s
ed
p
o
ly
n
o
m
ia
l
-
t
i
m
e
alg
o
r
it
h
m
f
o
r
th
e
g
eo
g
r
ap
h
ic
m
i
n
-
c
u
t p
r
o
b
le
m
a
n
d
s
ev
er
al
ap
p
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h
es f
o
r
th
e
g
eo
g
r
ap
h
ic
m
a
x
-
f
lo
w
p
r
o
b
le
m
s
.
I
q
b
al
et
al.
[
1
4
]
co
n
s
id
er
ed
th
e
g
eo
g
r
ap
h
ical
i
n
f
o
r
m
atio
n
o
f
n
et
w
o
r
k
n
o
d
es
a
n
d
l
in
k
s
a
n
d
i
n
clu
d
e
th
e
n
o
tio
n
o
f
ti
m
e
-
b
ased
d
is
aster
i
m
p
ac
t,
f
o
r
f
in
d
i
n
g
t
h
e
r
is
k
p
r
o
f
ile
o
f
d
i
f
f
er
en
t
n
et
w
o
r
k
ar
ea
s
at
d
i
f
f
er
e
n
t
ti
m
es.
T
h
e
r
atio
n
ale
is
th
at
s
o
m
e
d
is
aster
s
,
lik
e
h
u
r
r
ican
e
s
,
m
a
y
tr
av
er
s
e
d
if
f
er
en
t
n
et
w
o
r
k
ar
ea
at
d
if
f
er
en
t
ti
m
es
.
T
h
ey
t
h
en
p
r
o
v
id
ed
p
o
ly
n
o
m
i
al
-
ti
m
e
alg
o
r
it
h
m
s
to
ass
es
s
t
h
e
m
o
s
t
v
u
l
n
er
ab
le
n
et
w
o
r
k
c
o
n
n
ec
tio
n
s
.
I
q
b
al
et
al.
[
1
5
]
also
p
r
o
p
o
s
ed
f
ast
r
u
n
n
i
n
g
al
g
o
r
ith
m
s
f
o
r
d
etec
tin
g
s
p
atia
ll
y
-
clo
s
e
d
f
ib
er
s
a
n
d
g
r
o
u
p
in
g
t
h
e
m
u
s
i
n
g
th
e
m
i
n
i
m
u
m
n
u
m
b
er
o
f
d
i
s
t
in
ct
r
is
k
g
r
o
u
p
s
.
Ag
r
a
w
al
et
al.
[
1
6
]
,
p
r
o
p
o
s
ed
a
s
ch
e
m
e
r
ef
er
r
ed
to
as
th
e
Seis
m
ic
Z
o
n
e
Aw
ar
e
No
d
e
R
elo
ca
tio
n
(
S
Z
A
N
R
)
,
b
ased
o
n
th
e
in
f
o
r
m
atio
n
o
n
s
eis
m
ic
zo
n
es
b
y
m
eteo
r
o
lo
g
ical
d
ep
ar
t
m
e
n
t
s
a
n
d
o
th
er
s
i
m
ilar
a
g
e
n
cies.
R
e
s
u
lt
s
s
h
o
w
ed
t
h
at
s
i
g
n
i
f
ican
t
en
h
a
n
ce
m
en
t
i
n
t
h
e
n
et
w
o
r
k
s
u
r
v
i
v
ab
ilit
y
ca
n
b
e
attain
ed
i
n
ev
e
n
t
s
o
f
ea
r
t
h
q
u
ak
e
s
t
h
r
o
u
g
h
p
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o
m
p
tl
y
m
in
u
te
c
h
an
g
es
in
t
h
e
n
et
w
o
r
k
to
p
o
lo
g
y
.
So
u
s
a
et
al.
[
1
9
]
a
d
d
r
ess
ed
a
s
i
m
ilar
p
r
o
b
le
m
to
th
is
p
ap
er
,
th
e
p
ath
g
eo
-
d
i
v
er
s
i
f
icatio
n
p
r
o
b
lem
,
w
h
er
e
a
d
e
m
a
n
d
b
et
w
ee
n
t
w
o
n
et
w
o
r
k
n
o
d
es
is
s
u
p
p
o
r
ted
b
y
a
p
air
o
f
g
eo
g
r
ap
h
icall
y
-
s
ep
ar
ated
p
ath
s
o
f
a
m
i
n
i
m
u
m
d
i
s
ta
n
ce
.
T
h
e
y
p
r
o
p
o
s
ed
an
I
L
P
to
s
o
lv
e
th
e
p
r
o
b
lem
.
I
n
t
h
e
s
a
m
e
co
n
te
x
t,
W
an
g
et
al.
[
2
0
]
p
r
esen
ted
a
g
eo
g
r
ap
h
ic
a
w
a
r
e
r
o
u
te
s
elec
tio
n
al
g
o
r
ith
m
f
o
r
f
i
n
d
in
g
alter
n
ati
v
e
p
ath
s
w
it
h
ap
p
r
o
p
r
iate
g
eo
g
r
ap
h
ical
s
ep
ar
atio
n
,
r
ef
er
r
ed
to
as
th
e
p
r
o
x
im
it
y
f
ac
to
r
.
C
o
n
tr
ar
y
to
th
e
ir
w
o
r
k
,
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
is
b
ased
o
n
th
e
Yen
’
s
al
g
o
r
ith
m
[
2
1
]
,
s
u
ch
th
a
t
th
e
r
u
n
n
in
g
ti
m
e
an
d
ac
cu
r
ac
y
o
f
o
u
r
alg
o
r
ith
m
ca
n
b
e
tu
n
ed
b
ased
o
n
th
e
s
elec
ted
K
v
al
u
e.
I
L
P
ar
e
o
f
ten
to
o
ti
m
e
-
co
n
s
u
m
i
n
g
an
d
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
p
r
o
v
id
e
t
h
e
m
ea
n
s
f
o
r
r
e
d
u
cin
g
t
h
e
r
u
n
n
in
g
ti
m
e
f
o
r
f
in
d
i
n
g
a
v
ia
b
le
s
o
lu
tio
n
to
th
e
p
r
o
b
le
m
,
alb
eit
w
it
h
lo
w
er
o
p
tim
a
lit
y
.
Ho
w
e
v
er
,
w
h
en
k
is
u
n
b
o
u
n
d
ed
,
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
w
ill
al
w
a
y
s
f
in
d
th
e
m
o
s
t
o
p
ti
m
al
s
o
lu
tio
n
.
3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
AND
P
RO
P
O
SE
D
A
L
G
O
RIT
H
M
L
et
a
n
u
n
d
ir
ec
ted
g
r
ap
h
G
(
N
,
L
)
r
ep
r
e
s
en
t
s
a
p
h
y
s
ical
n
et
w
o
r
k
,
w
h
e
r
e
N
=
{
n
1
,
n
2
,
n
3
,
⋯
,
n
N
}
is
t
h
e
s
et
o
f
|
N
|
n
o
d
es
an
d
L
=
{
l
1
,
l
2
,
l
3
,
⋯
,
l
M
}
is
t
h
e
s
et
o
f
|
M
|
u
n
d
ir
ec
ted
lin
k
s
r
ep
r
esen
ti
n
g
b
id
ir
ec
tio
n
al
o
p
tica
l
f
ib
er
s
.
P
=
{
P
1
,
P
2
,
P
3
,
⋯
,
P
k
}
is
th
e
s
et
o
f
ca
n
d
id
ate
s
h
o
r
test
li
g
h
tp
a
th
s
f
r
o
m
s
o
u
r
c
e
n
o
d
e
s
to
d
esti
n
atio
n
n
o
d
e
t
an
d
w
=
{
w
1
,
w
2
,
w
3
,
⋯
,
w
k
}
is
th
e
s
et
o
f
co
r
r
esp
o
n
d
in
g
p
ath
w
eig
h
t
s
.
(
P
u
,
P
v
)
th
en
r
ep
r
esen
ts
th
e
li
n
k
-
d
is
j
o
in
t p
air
o
f
lig
h
tp
at
h
s
w
i
th
co
r
r
esp
o
n
d
in
g
p
ath
w
ei
g
h
t p
air
(
w
u
,
w
v
).
1.
P
r
o
v
is
io
n
in
g
o
f
Di
s
j
o
in
t P
air
w
it
h
Ma
x
i
m
ized
Min
i
m
u
m
Sp
atial
Dis
ta
n
ce
(
DP
MM
SD)
P
r
o
b
lem
:
2.
Fin
d
a
p
air
o
f
lin
k
-
d
is
j
o
in
t
lig
h
tp
ath
s
(
,
)
b
et
w
ee
n
t
w
o
s
p
ec
if
ic
n
et
w
o
r
k
n
o
d
es
s
u
c
h
th
at
th
e
m
i
n
i
m
u
m
s
p
atia
l d
is
tan
ce
b
et
w
ee
n
th
e
l
ig
h
tp
at
h
s
is
m
a
x
i
m
i
ze
d
.
W
e
p
r
o
p
o
s
ed
th
e
DP
MM
SD
alg
o
r
ith
m
in
th
e
co
n
te
x
t
o
f
t
h
e
m
e
n
tio
n
ed
p
r
o
b
le
m
.
T
h
e
al
g
o
r
ith
m
i
s
d
iv
id
ed
in
to
t
w
o
p
ar
ts
.
T
h
e
f
ir
s
t
p
ar
t
o
f
th
e
alg
o
r
it
h
m
f
i
n
d
s
K
n
u
m
b
er
o
f
s
h
o
r
test
p
at
h
s
b
e
t
w
ee
n
n
o
d
es
s
a
n
d
t
in
t
h
e
g
i
v
e
n
n
et
w
o
r
k
(
u
s
i
n
g
Y
en
’
s
al
g
o
r
ith
m
[
2
1
]
)
.
Oth
er
k
-
s
h
o
r
test
p
at
h
r
o
u
ti
n
g
al
g
o
r
ith
m
s
m
a
y
a
ls
o
b
e
u
s
ed
in
s
tead
.
T
h
e
s
ec
o
n
d
p
ar
t
o
f
t
h
e
al
g
o
r
ith
m
p
r
o
ce
ed
s
f
r
o
m
l
in
e
3
to
li
n
e
1
1
.
L
in
e
5
co
n
f
i
r
m
s
w
h
et
h
er
a
p
air
(
,
)
o
f
s
h
o
r
test
li
g
h
tp
ath
s
is
li
n
k
-
d
is
j
o
in
ted
.
I
f
p
air
(
,
)
is
li
n
k
-
d
is
j
o
in
ted
,
t
h
en
th
e
co
r
r
esp
o
n
d
in
g
m
i
n
i
m
u
m
s
p
atial
d
is
tan
ce
(
m
s
d
)
an
d
th
e
a
v
er
ag
e
m
in
i
m
u
m
s
p
atial
d
is
tan
ce
(
m
s
d
A
v
g
)
o
f
th
e
p
air
is
co
m
p
u
ted
in
li
n
e
7
u
s
i
n
g
A
l
g
o
r
ith
m
3
(
a
m
o
d
if
ied
f
o
r
m
o
f
t
h
e
alg
o
r
ith
m
p
r
o
p
o
s
ed
in
[
1
5
]
t
o
d
et
ec
t
s
p
atiall
y
-
clo
s
ed
f
ib
er
s
,
b
ased
o
n
t
h
e
u
s
e
o
f
k
-
d
tr
ee
an
d
k
n
ea
r
es
t
n
ei
g
h
b
o
r
s
ea
r
ch
[
22
-
24
]
)
.
I
n
s
o
m
e
ca
s
es,
m
u
l
tip
le
li
n
k
-
d
is
j
o
in
t
p
air
s
m
a
y
h
av
e
s
a
m
e
m
ax
i
m
u
m
v
al
u
e
o
f
m
i
n
i
m
u
m
s
p
atial
d
is
ta
n
ce
.
Hen
ce
,
we
in
tr
o
d
u
ce
an
o
th
e
r
s
u
p
p
o
r
tin
g
d
ec
is
io
n
v
ar
iab
le,
t
h
e
a
v
er
ag
e
m
i
n
i
m
u
m
s
p
atial
d
is
tan
ce
(
m
s
d
Av
g
)
t
h
at
r
ep
r
ese
n
ts
th
e
q
u
a
n
titati
v
e
d
is
j
o
in
tn
es
s
b
et
w
ee
n
t
h
e
lig
h
tp
ath
s
,
a
s
a
tieb
r
ea
k
er
.
L
i
n
e
8
-
1
1
s
elec
ted
t
h
e
l
in
k
-
d
is
j
o
in
t
p
air
o
f
lig
h
tp
at
h
s
b
ased
o
n
m
s
d
an
d
m
s
d
A
v
g
v
al
u
es
w
it
h
m
ax
i
m
ized
m
i
n
i
m
u
m
s
p
atial
d
is
tan
ce
.
Alg
o
r
ith
m
1
:
Pro
v
isio
n
i
n
g
o
f
Dis
jo
in
t
Pa
ir wi
th
M
a
x
imize
d
M
in
im
u
m S
p
a
ti
a
l
Dist
a
n
c
e
(
DPM
M
S
D)
Inp
u
t:
A
n
a
d
jac
e
n
c
y
m
a
tri
x
G
o
f
th
e
n
e
tw
o
rk
,
so
u
rc
e
n
o
d
e
s
,
d
e
sti
n
a
ti
o
n
n
o
d
e
t
,
d
e
sire
d
n
u
m
b
e
r
o
f
sh
o
rtes
t
p
a
t
h
s
K
a
n
d
g
e
o
d
e
ti
c
lo
c
a
ti
o
n
s d
a
ta i
n
t
h
e
f
o
rm
o
f
(
1
,
1
)
a
n
d
(
2
,
2
)
f
o
r
e
a
c
h
f
ib
e
r
se
g
m
e
n
t.
O
u
t
p
u
t:
A
p
a
ir
o
f
li
n
k
-
d
isjo
in
t
li
g
h
tp
a
th
s w
it
h
m
a
x
i
m
iz
e
d
m
in
i
m
u
m
sp
a
ti
a
l
d
istan
c
e
.
1:
mmsd
:=
-
1
,
mm
sd
Av
g
:=
-
1
2:
F
in
d
K
s
h
o
rtes
t
li
g
h
tp
a
t
h
s
=
{
1
,
2
,
3
,
⋯
,
}
a
n
d
w
e
i
g
h
ts
=
{
1
,
2
,
3
,
⋯
,
}
f
ro
m
s
to
t
u
sin
g
Ye
n
’s
a
lg
o
rit
h
m
.
3:
fo
r
u
fr
o
m
1
to
K
-
1
4:
fo
r
v
fr
o
m
u
+
1
to
K
5:
m
a
tch
e
d
:=
L
in
k
M
a
tch
in
g
(
,
)
u
sin
g
A
lg
o
rit
h
m
2
.
6:
if
p
a
ir
(
,
)
n
o
t
ma
tch
e
d
i.
e
.
d
isj
o
in
ted
p
a
ir
7:
[
msd
,
ms
d
Avg
]
:=
Co
m
p
u
ti
n
g
th
e
m
in
im
u
m
sp
a
ti
a
l
d
istan
c
e
(
msd
)
a
n
d
a
v
e
ra
g
e
m
sd
o
f
d
isjo
in
t
p
a
ir
(
,
)
u
sin
g
A
lg
o
rit
h
m
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
10
,
No
.
2
,
May
2018
:
7
3
3
–
7
4
0
736
8:
if
mmsd
<
ms
d
a
n
d
mm
sd
Avg
<
ms
d
Avg
9:
mmsd
:=
msd
10:
mm
sd
Avg
:=
ms
d
Avg
11:
Co
n
stra
i
n
e
d
P
a
ir
:=
(
,
)
Alg
o
r
ith
m
2
:
L
in
k
M
a
tch
in
g
Al
g
o
rith
m
Inp
u
t:
A
p
a
ir
o
f
li
g
h
tp
a
th
s
(
,
)
.
O
u
t
p
u
t:
I
f
a
n
y
li
n
k
o
f
a
li
g
h
tp
a
th
m
a
tch
e
d
w
it
h
a
n
y
li
n
k
o
f
li
g
h
tp
a
th
th
e
n
re
tu
r
n
tr
u
e
e
lse
fa
lse
.
1:
m
a
tch
e
d
:=
f
a
lse
2:
fo
r
e
a
c
h
f
ib
e
r
li
n
k
s
in
li
g
h
t
p
a
th
3:
fo
r
e
a
c
h
f
ib
e
r
li
n
k
s
in
li
g
h
t
p
a
th
4:
if
=
=
5:
m
a
tch
e
d
:=
tru
e
6:
re
tu
rn
Alg
o
r
ith
m
3
:
Co
mp
u
ti
n
g
th
e
M
in
imu
m S
p
a
ti
a
l
Dist
a
n
c
e
f
o
r a
L
in
k
-
Disjo
in
t
Pa
ir u
si
n
g
k
-
d
T
re
e
Inp
u
t:
A
p
a
ir
o
f
li
n
k
-
d
isjo
i
n
t
li
g
h
tp
a
t
h
s
(
=
∑
1
,
=
∑
1
)
su
c
h
th
a
t
∈
is
th
e
f
ib
e
r
se
g
m
e
n
t
a
ss
o
c
iate
d
w
it
h
tw
o
f
ib
e
r
p
o
in
ts
(
1
,
1
)
a
n
d
(
2
,
2
)
o
f
k
n
o
w
n
g
e
o
d
e
ti
c
lo
c
a
ti
o
n
s
f
ro
m
a
f
ib
e
r
li
n
k
,
a
n
d
∈
is
th
e
f
ib
e
r
se
g
m
e
n
t
a
ss
o
c
iate
d
w
it
h
tw
o
f
ib
e
r
p
o
i
n
ts
(
1
,
1
)
a
n
d
(
2
,
2
)
o
f
k
n
o
w
n
g
e
o
d
e
ti
c
lo
c
a
ti
o
n
s
f
ro
m
a
f
ib
e
r
li
n
k
.
G
i
v
e
n
se
t
a
n
d
a
re
th
e
f
ib
e
rs
jo
in
i
n
g
th
e
in
term
e
d
iar
y
n
o
d
e
s
w
h
il
e
t
ra
v
e
rsin
g
th
e
p
a
th
s
f
ro
m
sta
rt
n
o
d
e
to
d
e
stin
a
ti
o
n
n
o
d
e
.
O
u
t
p
u
t:
M
in
im
u
m
sp
a
ti
a
l
d
istan
c
e
(
msd
)
a
n
d
a
v
e
ra
g
e
m
in
i
m
u
m
sp
a
ti
a
l
d
istan
c
e
(
ms
d
Avg
)
b
e
tw
e
e
n
th
e
li
g
h
t
p
a
th
s
o
f
d
isjo
i
n
t
p
a
ir
(
,
)
.
1:
S
u
p
p
o
se
f
o
r
th
e
li
g
h
tp
a
t
h
s
,
msd
:=
∞
,
to
t
a
lP
o
in
ts
:=
0
,
ms
d
S
u
m
:=
0
,
ms
d
Avg
:=
0
2:
fo
r
e
a
c
h
f
ib
e
r
3:
fo
r
e
a
c
h
se
g
m
e
n
t
4:
C
o
m
p
u
te t
h
e
se
g
m
e
n
t
m
id
p
o
in
t
.
In
se
rt
f
ib
e
r
se
g
m
e
n
t
jo
i
n
in
g
p
o
i
n
ts
(
1
,
1
)
,
(
2
,
2
)
a
n
d
in
t
o
t
h
e
k
-
d
tree
Q
5:
fo
r
e
a
c
h
f
ib
e
r
6:
fo
r
e
a
c
h
se
g
m
e
n
t
7:
C
o
m
p
u
te t
h
e
se
g
m
e
n
t
m
id
p
o
in
t
.
8:
F
in
d
n
e
a
re
st n
e
ig
h
b
o
r
d
istan
c
e
{d
1
,
d
2
,
d
3
}
o
f
p
o
in
ts
(
1
,
1
)
,
(
2
,
2
)
a
n
d
u
sin
g
k
NN
se
a
rc
h
a
n
d
k
-
d
tree
Q,
h
o
w
e
v
e
r
ig
n
o
re
so
u
rc
e
a
n
d
d
e
stin
a
ti
o
n
n
o
d
e
s.
9:
d
:=
mi
n
imu
m
o
f{d
1
, d
2
, d
3
}
10:
if
msd
>
d
11:
ms
d
:=
d
12:
ms
d
S
u
m
:=
ms
d
S
u
m
+
d
13:
to
t
a
lP
o
in
ts
:=
to
t
a
lP
o
in
ts
+
1
14:
ms
d
Avg
:=
ms
d
S
u
m
/
to
t
a
lP
o
in
ts
Fo
r
g
eo
-
ca
lc
u
latio
n
s
o
v
er
a
g
r
ea
t
-
cir
cle
(
i.e
.
f
i
n
d
i
n
g
d
is
ta
n
ce
,
m
id
-
p
o
in
t,
in
ter
m
ed
iate
p
o
in
t
etc.
)
b
et
w
ee
n
t
w
o
lat
itu
d
e
a
n
d
lo
n
g
itu
d
e
p
o
in
t
s
,
w
e
u
s
ed
t
h
e
f
o
r
m
u
lae
g
iv
e
n
in
[
25
]
.
W
e
also
ex
clu
d
e
ce
r
tain
f
ib
er
p
ar
ts
(
w
ith
in
an
e
x
clu
s
io
n
d
is
t
an
ce
f
r
o
m
th
e
s
o
u
r
ce
a
n
d
t
h
e
d
esti
n
atio
n
n
o
d
es)
f
r
o
m
th
e
d
i
s
tan
ce
co
m
p
u
tatio
n
.
E
x
clu
s
io
n
d
i
s
tan
ce
(
δ)
i
s
t
h
e
r
ad
iu
s
o
f
t
h
e
cir
cu
lar
r
eg
io
n
f
o
r
w
h
ic
h
t
h
e
s
o
u
r
ce
n
o
d
e,
d
esti
n
a
tio
n
n
o
d
e
an
d
en
clo
s
ed
f
ib
er
p
ar
ts
ar
e
ass
u
m
ed
s
af
e.
T
h
e
m
in
i
m
u
m
s
p
atial
d
is
tan
ce
w
i
ll b
e
m
ea
s
u
r
ed
af
te
r
th
is
d
is
ta
n
ce
.
T
h
e
u
p
p
er
b
o
u
n
d
ti
m
e
co
m
p
le
x
it
y
o
f
Yen
’s
A
l
g
o
r
ith
m
i
s
(
3
)
[
2
1
]
w
h
er
e
K
is
t
h
e
n
u
m
b
er
o
f
s
h
o
r
test
p
ath
s
an
d
N
is
th
e
n
u
m
b
er
o
f
n
o
d
es.
Hen
ce
,
t
h
e
w
o
r
s
t
-
ca
s
e
ti
m
e
co
m
p
lex
it
y
o
f
o
u
r
p
r
o
p
o
s
ed
alg
o
r
ith
m
i
s
(
2
2
2
)
,
w
h
er
e
L
is
t
h
e
n
u
m
b
er
o
f
to
t
al
f
ib
er
lin
k
s
an
d
is
th
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
f
ib
er
s
e
g
m
en
t
s
p
er
f
ib
er
.
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
W
e
s
i
m
u
late
th
e
p
er
f
o
r
m
a
n
c
e
o
f
o
u
r
al
g
o
r
ith
m
u
s
in
g
t
h
e
E
u
r
o
p
ea
n
n
e
t
w
o
r
k
.
P
er
f
o
r
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Hu
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S
.
S
h
a
k
y
a
,
"
IC
T
I
m
p
le
m
e
n
tatio
n
a
n
d
In
f
ra
stru
c
tu
re
De
p
lo
y
m
e
n
t
A
p
p
ro
a
c
h
f
o
r
Ru
ra
l
Ne
p
a
l,
"
in
Rec
e
n
t
A
d
v
a
n
c
e
s in
In
fo
rm
a
t
io
n
a
n
d
C
o
mm
u
n
ica
ti
o
n
T
e
c
h
n
o
lo
g
y
2
0
1
6
,
e
d
:
S
p
rin
g
e
r
,
2
0
1
6
.
[5
]
F
Iq
b
a
l
a
n
d
F
.
A
.
Ku
i
p
e
rs,
“
Disj
o
in
t
p
a
t
h
s
in
n
e
tw
o
rk
s”
,
W
il
e
y
En
c
y
c
lo
p
a
e
d
ia
o
f
El
e
c
trica
l
a
n
d
El
e
c
tro
n
ics
En
g
i
n
e
e
rin
g
,
2
0
1
5
.
[6
]
J.
Ra
k
,
D.
Hu
tch
iso
n
,
E.
Ca
ll
e
,
T
.
G
o
m
e
s,
M
.
G
u
n
k
e
l,
P
.
S
m
it
h
,
e
t
a
l.
,
"
RE
COD
IS
:
Res
il
ien
t
Co
mm
u
n
ica
ti
o
n
S
e
rv
ice
s
Pro
tec
ti
n
g
En
d
-
u
se
r
Ap
p
li
c
a
ti
o
n
s
fro
m
Disa
ste
r
-
b
a
se
d
Fa
il
u
re
s
,
"
in
2
0
1
6
1
8
th
I
n
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
T
ra
n
sp
a
re
n
t
Op
t
ica
l
Ne
tw
o
rk
s (ICT
ON
)
,
2
0
1
6
.
[7
]
S
.
T
ra
jan
o
v
sk
i,
F
.
A
.
Ku
ip
e
rs,
A
.
Ili
ć
,
J.
Cro
w
c
ro
f
t,
a
n
d
P
.
V
a
n
M
i
e
g
h
e
m
,
"
F
in
d
in
g
c
rit
ica
l
re
g
io
n
s
a
n
d
re
g
io
n
-
d
isjo
i
n
t
p
a
th
s i
n
a
n
e
tw
o
rk
,
"
IEE
E/
ACM
T
ra
n
s
a
c
ti
o
n
s o
n
Ne
two
rk
i
n
g
(
T
ON),
vo
l.
2
3
,
p
p
.
9
0
8
-
9
2
1
,
2
0
1
5
.
[8
]
F
.
Dik
b
iy
ik
,
A
.
S
.
Re
a
z
,
M
.
De
L
e
e
n
h
e
e
r,
a
n
d
B.
M
u
k
h
e
rjee
,
"
M
in
imizin
g
th
e
d
isa
ste
r
risk
in
o
p
ti
c
a
l
tele
c
o
m
n
e
two
rk
s
,
"
in
Op
t
ica
l
F
ib
e
r
C
o
m
m
u
n
ica
ti
o
n
Co
n
f
e
re
n
c
e
,
2
0
1
2
.
[9
]
F
.
Dik
b
iy
ik
,
M
.
T
o
rn
a
to
re
,
a
n
d
B.
M
u
k
h
e
rjee
,
"
M
in
im
izin
g
th
e
r
isk
f
ro
m
d
isa
ste
r
f
a
il
u
re
s
in
o
p
ti
c
a
l
b
a
c
k
b
o
n
e
n
e
tw
o
rk
s,"
J
o
u
rn
a
l
o
f
L
i
g
h
tw
a
v
e
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
3
2
,
p
p
.
3
1
7
5
-
3
1
8
3
,
2
0
1
4
.
[1
0
]
P
.
K.
A
g
a
r
w
a
l,
A
.
Ef
r
a
t,
S
.
K.
G
a
n
ju
g
u
n
te,
D.
Ha
y
,
S
.
S
a
n
k
a
ra
ra
m
a
n
,
a
n
d
G
.
Z
u
ss
m
a
n
,
"
T
h
e
re
sili
e
n
c
e
o
f
W
DM
n
e
tw
o
rk
s
to
p
ro
b
a
b
i
li
stic
g
e
o
g
ra
p
h
ica
l
f
a
il
u
re
s,"
IEE
E/
ACM
T
ra
n
sa
c
ti
o
n
s
o
n
Ne
two
rk
i
n
g
(
T
ON)
,
v
o
l.
2
1
,
p
p
.
1
5
2
5
-
1
5
3
8
,
2
0
1
3
.
[1
1
]
S
.
Ne
u
m
a
y
e
r,
A
.
Ef
ra
t,
a
n
d
E.
M
o
d
ia
n
o
,
"
G
e
o
g
ra
p
h
ic
m
a
x
-
f
lo
w
a
n
d
m
in
-
c
u
t
u
n
d
e
r
a
c
ircu
lar
d
isk
f
a
il
u
re
m
o
d
e
l,
"
Co
mp
u
ter
Ne
two
rk
s
,
v
o
l.
7
7
,
p
p
.
1
1
7
-
1
2
7
,
2
0
1
5
.
[1
2
]
S.
Ne
u
m
a
y
e
r
a
n
d
E.
M
o
d
ian
o
,
"
Ne
two
rk
re
li
a
b
il
it
y
wit
h
g
e
o
g
ra
p
h
ica
ll
y
c
o
rr
e
la
ted
fa
i
lu
re
s
,
"
in
INFOCOM,
2
0
1
0
P
ro
c
e
e
d
in
g
s IE
EE
,
2
0
1
0
.
[1
3
]
B.
M
u
k
h
e
rjee
,
M
.
Ha
b
ib
,
a
n
d
F
.
Dik
b
iy
ik
,
"
N
e
t
w
o
rk
a
d
a
p
tab
il
it
y
f
ro
m
d
isa
ste
r
d
isru
p
ti
o
n
s
a
n
d
c
a
sc
a
d
in
g
f
a
il
u
re
s,"
IEE
E
Co
mm
u
n
ic
a
t
io
n
s
M
a
g
a
zin
e
,
v
o
l.
5
2
,
p
p
.
2
3
0
-
2
3
8
,
2
0
1
4
.
[1
4
]
F
.
Iq
b
a
l
a
n
d
F
.
Ku
i
p
e
rs,
"
S
p
a
t
io
tem
p
o
r
a
l
risk
-
a
v
e
rs
e
ro
u
ti
n
g
,
"
in
2
0
1
6
IEE
E
Co
n
f
e
re
n
c
e
o
n
Co
m
p
u
ter
Co
m
m
u
n
ica
ti
o
n
s W
o
rk
sh
o
p
s (IN
F
OCO
M
W
KSHP
S
),
2
0
1
6
.
[1
5
]
F
.
Iq
b
a
l,
S
.
T
ra
jan
o
v
sk
i,
a
n
d
F
.
K
u
ip
e
rs,
"
De
tec
ti
o
n
o
f
sp
a
ti
a
l
ly
-
c
lo
se
fi
b
e
r
se
g
me
n
ts
in
o
p
ti
c
a
l
n
e
tw
o
rk
s
,
"
2
0
1
6
1
2
t
h
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
o
n
th
e
De
sig
n
o
f
Re
li
a
b
le Co
m
m
u
n
ica
ti
o
n
Ne
tw
o
rk
s (DRCN
),
2
0
1
6
.
[1
6
]
A
.
Ag
ra
w
a
l,
P
.
S
h
a
rm
a
,
V
.
Bh
a
ti
a
,
a
n
d
S
.
P
ra
k
a
sh
,
"
S
u
rv
iv
a
b
il
it
y
I
m
p
ro
v
e
m
e
n
t
A
g
a
in
st
Earth
q
u
a
k
e
s
in
Ba
c
k
b
o
n
e
Op
t
ica
l
Ne
tw
o
rk
s Us
in
g
Ac
tu
a
l
S
e
ism
ic Z
o
n
e
In
f
o
rm
a
ti
o
n
,
"
a
rX
iv p
re
p
rin
t
a
rX
iv
:
1
7
0
3
.
0
2
3
5
8
,
2
0
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
10
,
No
.
2
,
May
2018
:
7
3
3
–
7
4
0
740
[1
7
]
Y.
Aw
a
ji
,
H.
F
u
ru
k
a
wa
,
S
.
Xu
,
M
.
S
h
iraiw
a
,
N.
W
a
d
a
,
a
n
d
T
.
T
su
rit
a
n
i,
"
Re
sili
e
n
t
o
p
ti
c
a
l
n
e
tw
o
rk
tec
h
n
o
l
o
g
ies
f
o
r
Ca
tas
tro
p
h
ic Disa
ste
rs,"
J
o
u
rn
a
l
o
f
Op
ti
c
a
l
C
o
mm
u
n
ic
a
ti
o
n
s a
n
d
Ne
two
rk
in
g
,
v
o
l
.
9
,
p
p
.
A
2
8
0
-
A
2
8
9
,
2
0
1
7
.
[1
8
]
C.
G
a
ld
a
m
e
z
a
n
d
Z.
Ye
,
"
Res
il
ien
t
v
irtu
a
l
n
e
tw
o
rk
ma
p
p
i
n
g
a
g
a
in
st
la
rg
e
-
sc
a
le
re
g
i
o
n
a
l
f
a
il
u
re
s
,
"
in
W
irele
ss
a
n
d
Op
t
ica
l
Co
m
m
u
n
ica
ti
o
n
C
o
n
f
e
re
n
c
e
(
W
OCC),
2
0
1
7
.
[1
9
]
A
.
d
e
S
o
u
sa
,
D.
S
a
n
to
s,
a
n
d
P
.
M
o
n
teir
o
,
"
De
ter
min
a
ti
o
n
o
f
th
e
M
in
imu
m
C
o
st
P
a
ir o
f
D
-
Ge
o
d
ive
rs
e
Pa
th
s
,
"
in
1
3
t
h
In
tern
a
ti
o
n
a
l
Co
n
f
e
re
n
c
e
De
sig
n
o
f
Re
li
a
b
le Co
m
m
u
n
ica
ti
o
n
Ne
tw
o
rk
s
,
2
0
1
7
.
[2
0
]
J.
W
a
n
g
,
J.
Big
h
a
m
,
a
n
d
C.
P
h
il
li
p
s,
"
A
G
e
o
g
ra
p
h
ica
l
P
r
o
x
im
it
y
Aw
a
r
e
M
u
lt
i
-
p
a
t
h
Ro
u
ti
n
g
M
e
c
h
a
n
ism
f
o
r
Re
sili
e
n
t
Ne
tw
o
rk
in
g
,
"
IEE
E
Co
mm
u
n
ica
ti
o
n
s
L
e
tt
e
rs
,
2
0
1
7
.
[2
1
]
J.
Y.
Ye
n
,
"
F
in
d
in
g
th
e
k
sh
o
rte
st
lo
o
p
les
s
p
a
th
s
i
n
a
n
e
tw
o
rk
,
"
M
a
n
a
g
e
me
n
t
S
c
ien
c
e
,
v
o
l.
1
7
,
p
p
.
7
1
2
-
7
1
6
,
1
9
7
1
.
[2
2
]
J.
L
.
Be
n
tl
e
y
,
"
M
u
lt
id
im
e
n
sio
n
a
l
b
in
a
ry
se
a
r
c
h
tree
s
u
se
d
f
o
r
a
ss
o
c
iativ
e
se
a
rc
h
in
g
,
"
Co
mm
u
n
ica
ti
o
n
s
o
f
th
e
ACM
,
v
o
l.
1
8
,
p
p
.
5
0
9
-
5
1
7
,
1
9
7
5
.
[2
3
]
J.
H.
F
ried
m
a
n
,
J.
L
.
Be
n
tl
e
y
,
a
n
d
R.
A
.
F
in
k
e
l,
"
A
n
a
lg
o
rit
h
m
f
o
r
fin
d
i
n
g
b
e
st
m
a
tch
e
s
in
lo
g
a
rit
h
m
i
c
e
x
p
e
c
ted
ti
m
e
,
"
ACM
T
ra
n
sa
c
ti
o
n
s o
n
M
a
t
h
e
ma
ti
c
a
l
S
o
ft
wa
re
(
T
OM
S
)
,
v
o
l.
3
,
p
p
.
2
0
9
-
2
2
6
,
1
9
7
7
.
[2
4
]
R.
P
a
n
ig
ra
h
y
,
"
A
n
i
m
p
ro
v
e
d
a
lg
o
rit
h
m
f
in
d
in
g
n
e
a
re
st
n
e
ig
h
b
o
r
u
sin
g
k
d
-
tree
s,"
LAT
IN
2
0
0
8
:
T
h
e
o
re
ti
c
a
l
In
fo
rm
a
t
ics
,
p
p
.
3
8
7
-
3
9
8
,
2
0
0
8
.
[2
5
]
Ca
lcu
late
d
istan
c
e
,
b
e
a
rin
g
a
n
d
m
o
re
b
e
twe
e
n
L
a
ti
tu
d
e
/L
o
n
g
it
u
d
e
p
o
in
ts.
A
v
a
il
a
b
le:
h
tt
p
:/
/w
ww
.
m
o
v
a
b
le
-
ty
p
e
.
c
o
.
u
k
/sc
rip
ts/l
a
tl
o
n
g
.
h
t
ml
[2
6
]
S
.
V
e
r
b
ru
g
g
e
,
D.
Co
ll
e
,
P
.
De
m
e
e
ste
r,
R.
Hu
e
lse
r
m
a
n
n
,
a
n
d
M
.
Ja
e
g
e
r,
"
Ge
n
e
ra
l
a
v
a
il
a
b
il
it
y
mo
d
e
l
fo
r
mu
lt
il
a
y
e
r
tr
a
n
sp
o
rt n
e
two
rk
s
,
"
i
n
5
th
In
ter
n
a
ti
o
n
a
l
W
o
rk
sh
o
p
o
n
De
sig
n
o
f
Re
li
a
b
le
Co
m
m
u
n
ica
ti
o
n
Ne
tw
o
rk
s
(DRCN
2
0
0
5
),
2
0
0
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.