| (1) | function Shortest_Path(↓SV, ↓FV, ↓L, ↑Topol) |
| (2) | Topol ← ∅ |
| (3) | correct ← true |
| (4) | Start_Finish_Test(↓SV, ↓FV, ↓L, ↑↓correct) // admissibility of the start/finish vertices |
| (5) | if correct then |
| (6) | General_Init() // setting initial marks of all vertices |
| (7) | Start_Finish_Init(↓SV, ↓FV) // initialisation activities related to the start/finish vertices |
| (8) | Start_Mark(↓SV, ↓L) // remarking of transit successors of the start/finish vertices |
| (9) | repeat |
| (10) | if TV ≠ ∅ then |
| (11) | Vert_Select(↑) // selection of a new current vertex |
| (12) | if UV ≠ FVthen |
| (13) | Succ_Mark(↓, ↓L) // remarking successors of the current vertex |
| (14) | end |
| (15) | end |
| (16) | until (TV = ∅ or UV = FV) // algorithm termination testing |
| (17) | Get_Path(↑↓Topol) // getting a topology of the shortest path |
| (18) | end |
| (19) | end |
| (20) | function Start_Finish_Test(↓SV, ↓FV, ↓L, ↓↑okay) |
| (21) | if (SV = ∅ or FV = ∅) then |
| (22) | okay ← false |
| (23) | exit |
| (24) | end |
| (25) | for each ∈ SVdo |
| (26) | Get_Indexes(↓, ↑i, ↑x) |
| (27) | for each ∈ FVdo |
| (28) | Get_Indexes(↓, ↑j, ↑y) |
| (29) | if (x = y and i ≠ j) then |
| (30) | okay ← false // inadmissible combination of the start and finish vertices |
| (31) | exit |
| (32) | end |
| (33) | if (ω () < L or κ () < L) then |
| (34) | okay ← false // inadmissible weights/vacancies of the start/finish vertices |
| (35) | exit |
| (36) | end |
| (37) | end |
| (38) | end |
| (39) | end |
| (40) | function General_Init() |
| (41) | for z = 1 to n\2 do // symbol “\” denotes an integer division |
| (42) | for k = 1 to 2 do |
| (43) | ← d∞ // initialisation of the row vector of distance marks |
| (44) | ← none // initialisation of the row vector of marks-predecessors |
| (45) | end |
| (46) | end |
| (47) | TV ← ∅ |
| (48) | UV ← ∅ |
| (49) | end |
| (50) | function Start_Finish_Init(↓SV, ↓FV) |
| (51) | for each ∈ SVdo |
| (52) | Get_Indexes(↓, ↑i, ↑x) |
| (53) | for each ∈ FVdo |
| (54) | Get_Indexes(↓, ↑j, ↑y) |
| (55) | a ← (3 − i) |
| (56) | b ← (3 − j) |
| (57) | if SV = FVthen |
| (58) | XV ← {} // the forbidden vertex is a pair vertex to the start vertex |
| (59) | else |
| (60) | XV ← {, } // the forbidden vertex is a pair vertex to the finish vertex |
| (61) | ← 0 // initialisation of selected distance marks |
| (62) | end |
| (63) | end |
| (64) | end |
| (65) | end |
| (66) | function Start_Mark(↓SV, ↓L) |
| (67) | for each ∈ SVdo |
| (68) | for each ∈ () do |
| (69) | if ( ∉ XVand κ () ≥ L) then |
| (70) | TV ← TV ∪ {} // insertion of admissible transit successors into the set TV |
| (71) | ← 0 // initialisation of selected distance marks |
| (72) | ← // initialisation of selected marks-predecessors |
| (73) | end |
| (74) | end |
| (75) | end |
| (76) | end |
| (77) | function Vert_Select(↑) |
| (78) | if TV ≠ ∅ then |
| (79) | Min_Dist(↓TV, ↑) // selection of a vertex with the lowest distance mark |
| (80) | TV ← TV − {} |
| (81) | if ∈ FVthen |
| (82) | UV ← UV ∪ {} |
| (83) | end |
| (84) | end |
| (85) | end |
| (86) | function Try_Change_Mark(↓, ↓) |
| (87) | Get_Indexes(↓, ↑k, ↑z) |
| (88) | Get_Indexes(↓, ↑l, ↑s) |
| (89) | if > + ε ([, ]) then |
| (90) | ← + ε ([, ]) // remarking of the successor () of the vertex |
| (91) | ← |
| (92) | if ∉ TVthen |
| (93) | TV ← TV ∪ {} |
| (94) | end |
| (95) | end |
| (96) | end |
| (97) | function Succ_Mark(↓, ↓L) |
| (98) | for each ∈ ()do |
| (99) | if ( ∉ XVand κ () ≥ L and κ () = ω ()) then |
| (100) | Try_Change_Mark(↓, ↓) // potential remarking of the transit successor of |
| (101) | end |
| (102) | end |
| (103) | for each ∈ () do |
| (104) | if ( ∉ XVand κ () ≥ L) then |
| (105) | Try_Change_Mark(↓, ↓) // potential remarking of the reverse successor of |
| (106) | end |
| (107) | end |
| (108) | end |
| (109) | function Get_Path(↑↓Seq) |
| (110) | if UV ≠ ∅ then |
| (111) | Min_Dist(↓UV, ↑) |
| (112) | Get_Indexes(↓, ↑j, ↑y) |
| (113) | z ← y |
| (114) | k ← j |
| (115) | i ← 0 |
| (116) | while ( ≠ none or ∈ SV) do |
| (117) | Seq ← Seq ∪ {[i, ]} // successive reconstruction of the shortest path topology |
| (118) | if ∈ SVthen |
| (119) | exit |
| (120) | end |
| (121) | Predecessor(↓, ↑l, ↑t) // getting a predecessor of the vertex |
| (122) | z ← t |
| (123) | k ← l |
| (124) | i ← i + 1 |
| (125) | end |
| (126) | end |
| (127) | end |
