IKN-CF: An Approach to Identify Key Nodes in Inter-Domain Routing Systems Based on Cascading Failures

. 2021 Nov 2;23(11):1456. doi: 10.3390/e23111456

Algorithm 1 DBR

Input: Predecessor

p r e d l i s t

, successors

s u c c l i s t

, complex network G,

s o u r c e

t a r g e t

, forward business relationships

f c r l i s t

, reverse business relationships

r c r l i s t

Output: The

o p t i m a l p a t h

between the source node and the target node.

1:
$f o r w a r d_f r i n g e . a d d (s o u r c e)$
2:
$r e v e r s e_f r i n g e . a d d (t a r g e t)$
3:
while $f o r w a r d_f r i n g e$ $a n d$ $r e v e r s e_f r i n g e$ do
4:
if $l e n (f o r w a r d_f r i n g e)$ $< =$ $l e n (r e v e r s e_f r i n g e)$ then
5:
$t h i s_l e v e l$ ← $f o r w a r d_f r i n g e$ , $f o r w a r d_f r i n g e = []$
6:
for v∈ $t h i s_l e v e l$ do
7:
for w ∈ $N e i g h b o u r [v]$ do
8:
if w∉ $p r e d$ then
9:
k← $r e a d_b u s i n e s s r e l a t i o n s h i p (G, v, w)$
10:
if ( $f c r l i s t [v] = 1$ ) or ( $f c r l i s t [v] = - 1$ $a n d$ $k = - 1$ ) or ( $f c r l i s t [v] = 0$ $a n d$ $k = - 1$ ) then
11:
$f o r w a r d_f r i n g e . a d d (w)$
12:
$p r e d [w]$ ← v
13:
$d [w]$ ← k
14:
else
15:
$w \leftarrow v$
16:
end if
17:
end if
18:
if $w \in s u c c$ then
19:
if ( $f c r l i s t [w] = 1$ ) or ( $f c r l i s t [w] = - 1$ $a n d$ $p [w] = 1$ ) or ( $f c r l i s t [w] = 0$ $a n d$ $p [w] = 1$ ) then
20:
$o p t i m a l p a t h \leftarrow p r e d + s u c c$
21:
end if
22:
end if
23:
end for
24:
end for
25:
else
26:
$t h i s_l e v e l \leftarrow r e v e r s e_f r i n g e$ , $r e v e r s e_f r i n g e = []$
27:
for $v \in t h i s_l e v e l$ do
28:
for $w \in N e i g h b o u r [v]$ do
29:
if $w \notin s u c c$ then
30:
$j \leftarrow r e a d_b u s i n e s s r e l a t i o n s h i p (G, v, w)$
31:
if ( $r c r l i s t [v] = 1$ ) or ( $r c r l i s t [v] = - 1$ $a n d$ $j = - 1$ ) or ( $r c r l i s t [v] = 0$ $a n d$ $j = - 1$ ) then
32:
$s u c c [w] \leftarrow v$
33:
$r e v e r s e_f r i n g e . a d d (w)$
34:
$p [w] \leftarrow j$
35:
else
36:
$w \leftarrow v$
37:
end if
38:
end if
39:
if $w \in s u c c$ then
40:
if ( $r c r l i s t [w] = 1$ ) or ( $r c r l i s t [w] = - 1$ $a n d$ $f c r l i s t [w] = 1$ ) or ( $r c r l i s t [w] = 0$ $a n d$ $f c r l i s t [w] = 1$ ) then
41:
$o p t i m a l p a t h \leftarrow p r e d + s u c c$
42:
end if
43:
end if
44:
end for
45:
end for
46:
end if
47:
end while