13th International Conference on Membrane Computing - MTA Sztaki

H. ElGindy, R. Nicolescu, H. Wu
8 r = r + 1
9 set σ s and (σ s, σ q) as visited
10 β = DFS(σ q, σ t, G r−1) // see Pseudocode 2
11 i f β = null then // failed round
12 G r = G r−1
13 endif
14 endwhile
15 i f β ≠ null then // successful round
16 α = σ s.β
17 P r = (P r−1 \ α −1 −1
) ∪ (α \ P r−1 )
18
−1
G r = (V, E r), where E r = (E \ P r) ∪ P r
19 reset all visited cells and arcs to unvisited
20 endif
21 until α = null
22 Output : P r, which is a maximum cardinality set of edge-disjoint paths
Pseudocode 2: Classical DFS, for residual digraph G r−1 = (V, E r−1 )
1 DFS(σ i, σ t, G r−1)
2 Input : the current cell, σ i ∈ V , the target cell, σ t ∈ V
3 and the residual digraph, G r−1
4 i f σ i = σ t then return σ t
5 i f σ i is visited then return null
6 set σ i as visited
7 foreach unvisited (σ i, σ k ) ∈ E r−1
8 set (σ i, σ k ) as visited
9 β = DFS(σ k , σ t, G r−1)
10 i f β ≠ null return σ i.β
11 endfor
12 return null
13 Output : a σ i-to-σ t path, if any; otherwise, null
Our new Algorithm C is described by Pseudocodes 3–6 and uses the same
variables as Algorithm A; additionally, this algorithm works in d successive
search rounds, defined by successive iterations of its for loop (line 3.8), where d
is the outdegree of σ s . Without loss of generality, we assume that σ s ’s children
are represented by the set {σ s1 , σ s2 , . . . , σ sd }.
Pseudocode 3: Algorithm C
1 Input : a digraph G = (V, E), a source cell, σ s ∈ V ,
2 and a target cell, σ t ∈ V
3 P 0 = ∅, G 0 = G
4 set σ s as permanently visited
5 foreach unvisited arc (σ j, σ s) ∈ E
6 set (σ j, σ s) as permanently visited
7 endfor
8 for r = 1 to d
9 i f σ sr is permanently visited then continue
10 set (σ s, σ sr) as permanently visited
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