Vine shortest example

Modified Vine-Building Shortest Paths Algorithm Ikki Kim

MVA and Multi-path Algorithm : Example Network 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 3 : turning penalty 3 : link cost

MVA Algorithm : Vine Searching Process 1 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 Label : node (cost, back node, back-back) 7(18,6,8) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 7(907,9,8) 1 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 Label : node (cost, back node, back-back) 7(18,6,8) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 7(907,9,8) 7(9,9,10)

MVA Algorithm : Backward Tracing Process 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-)

MVA Algorithm : The Final Result 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-)

Generating Multiple Paths (I) : Upper Rational Boundary 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 3(22,4,7) 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 3(22,4,7) 3(28,4,1)

Generating Multiple Paths (II) : Upper Rational Boundary 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) Label : node (cost, back node, back-back) 3(21,4,5) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4(22,5,10)

Generating Multiple Paths (III): Mark and save, then back-tracing repeatedly 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4 : Branching at-node 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4 : Branching at-node 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4 : Branching at-node 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4 : Branching at-node 9 3 2 4 5 1 S 6 7 8 R 10 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7 ) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) 4 : Branching at-node

Generating Multiple Paths : Final result in case of loose boundary S R S R S R S R S R S R Cost = 23 Cost = 24 Cost = 28 Cost = 30 Cost = 32 Cost = 33

Generating Multiple Paths : Final result in case of tight boundary 1 1 9 1 3 2 4 5 1 S 6 7 8 R 10 4 2 1 5 3 4 3 2 2 1 9 1 2 2 2 2 6 900 6 3 900 3 s(23,3,4) 3(21,4,5) 4(12,7,9) 4(24,1,2) 4(17,5,2) 1(13,4,7) 1(22,2,5) 2(14,1,4) 2(20,5,10) 5(16,2,1) 5(18,10,9) 7(18,6,8) 7(9,9,10) 10(6,9,8) 9(5,8,R) 9(7,10,9) 6(13,8,R) 8(3,R,-) R(0,-,-) Path Path Path Cost 23 24 28

Thank you for your Attention ! Any Questions Or Comments ?

Vine shortest example

Recomendados

Recomendados

Más contenido relacionado

La actualidad más candente

La actualidad más candente (7)

Similar a Vine shortest example

Similar a Vine shortest example (20)

Último

Último (20)

Vine shortest example