13th International Conference on Membrane Computing - MTA Sztaki

H. ElGindy, R. Nicolescu, H. Wu
4. Target cell (S 30 ): cf. Line 4.4
4.1.
1. S 30 g → min.min S 40 (g)↕
2. S 30 f j → min.min S 30 d ′ j (a)↓ j
3. S 30 → min S 40 | q
4. S 30 → min S 40 | p
5. All cells (S 40 , S 50 )
5.1. End of each search round
1. S 40 v k → max.max S 40 | s
2. S 40 v k → max.max S 40 | t
3. S 40 u j → max.max S 40
4. S 40 c l → max.max S 40
5. S 40 r j(X) → max.max S 40
6. S 40 r j(X) ′ → max.max S 40
7. S 40 a → max S 40
8. S 40 q → max S 40
9. S 40 p → max S 40
10. S 40 → min S 3
5.2. End of the algorithm
1. S 50 g → max S 50
2. S 50 n ′ j → max.min S 50
3. S 50 n ′′
k → max.min S 50
4. S 50 w k → max.min S 50
5. S 50 v k → max.min S 50
6. S 50 z k ′′ → max.min S 50
7. S 50 w → max S 50
8. S 50 v → max S 50
9. S 50 → min S 60
Cell σ i uses the following symbols to record its relationships with its neighbouring
cells, σ j and σ k : n ′ j indicates a structural parent; n′′
k
indicates a structural
child; d ′ j indicates an edge-disjoint path predecessor (dp-predecessor); d′′
k
indicates an edge-disjoint path successor (dp-successor); s ′ j indicates a current
sp-predecessor; s ′′
k
indicates a current sp-successor; z′′
k
indicates a st-successor;
r j (c m ) records σ j ’s reach-number, m (note that here j may indicate the current
cell, i, or one of its neighbours).
Additionally, cell σ i uses the following symbols to record its state: h(c m )
records its depth, m; n(c m ) is used to evaluate the minimum over its own depth
and the reach-numbers of its temporarily visited structural children; v indicates
that it is temporarily visited; w indicates that it is permanently visited; f indicates
that it is the frontier cell.
Cell σ i sends out messages consisting of the following symbols: f i is the
forward token; b i is the backtrack token; v i is the visited notification; w i is the
permanently visited notification; r i ′(cm ) is its updated reach-number, m; x is the
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