Dynamic Automated Search of Shunting Routes within Mesoscopic Rail-Traffic Simulators

Table 5

Specifications of auxiliary sets and row vectors.

Symbols	Specifications
SV	The set of start vertices; (i) SV ⊂ V(G)
FV	The set of finish vertices; (i) FV ⊂ V(G)
XV	The set of forbidden vertices; (i) XV ⊂ V(G)
TV	The set of temporarily marked vertices; (i) TV ⊂ V(G)
UV	The set of ultimately marked finish vertices; (i) UV ⊂ V(G)
D	The row vector of distances; (i) D = ||||,  ∈ , z = 1, …, n\2, k = 1, 2; (ii) Each vertex  ∈ V(G) is tagged by a mark , which expresses the length of the currently detected shortest path from a vertex  ∈ SV to the vertex; (iii) If the above path to the vertex  ∈ V(G) does not exist, then  = d^∞ (d^∞ ∈ , and it is equal to the value that is greater than the length of the longest admissible path in the graph G); Note: symbol “\” denotes an integer division
P	The row vector of predecessors; (i) P = ||||,  ∈ V(G) ∪ {none}, z = 1, …, n\2, k = 1, 2; (ii) Each vertex  ∈ V(G) is tagged by a mark , which corresponds to a predecessor of the vertex on the currently detected shortest path from a vertex  ∈ SV to the vertex; (iii) If the above path to the vertex  ∈ V(G) does not exist, then  = none (the symbol none expresses the nonexistence of a relevant predecessor with regard to the vertex )
Seq	The linearly ordered set of the shortest path topology; (i) Seq = {[i, ] |i = 0, ..., q − 1,  ∈ V(G), z ∈〈1, …, n\2〉, k ∈ {1, 2}, q = |Seq|}; (ii) The element [0, ] represents a finish vertex ( ∈ FV) and the element [q − 1, ] a start vertex ( ∈ SV) of the shortest path