SlideShare a Scribd company logo

Vine shortest example

Download as PPT, PDF
H
Hanyang University

The document describes an algorithm for generating multiple shortest paths in a network using the modified vine algorithm. It provides an example of applying the algorithm to a sample network. The algorithm works by first running the standard multi-path algorithm to find the optimal path, then branching at nodes to find additional paths within an upper cost boundary.

TechnologyBusiness
1 of 11
Download to read offline
1
2
3
4
5
6
7
8
9
10
11
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 ?

More Related Content

PDF
5year lahore board xi
Asad Shafat
 
PDF
hw2_prob2
Mark Yashar
 
PDF
aiboのAI：DeepLearning認識
Naoki Fujiwara
 
PDF
Debugging TV Frame 0x0F
Dmitry Vostokov
 
PDF
タイムインターメディア 会社紹介
Arai Ran
 
PDF
著作権法改正 新第47条の4 ver.β1
HiroM Ogawa
 
PPTX
Slides thumbs
Carlos Pereira Junior
 
PDF
16 cuerpos
FcoJavierMesa
 
5year lahore board xi
Asad Shafat
 
hw2_prob2
Mark Yashar
 
aiboのAI：DeepLearning認識
Naoki Fujiwara
 
Debugging TV Frame 0x0F
Dmitry Vostokov
 
タイムインターメディア 会社紹介
Arai Ran
 
著作権法改正 新第47条の4 ver.β1
HiroM Ogawa
 
Slides thumbs
Carlos Pereira Junior
 
16 cuerpos
FcoJavierMesa
 

What's hot (7)

PDF
IN HOUSE SYNERGIECAD_J750
Roger Cooke (Semicon Test Hardware Supplier)
 
PDF
Sesión de aprendizaje de Radicación Algebra pre u ccesa007
Demetrio Ccesa Rayme
 
PDF
AR勉強会第4回part2
NishoMatsusita
 
PPTX
Nois de la Torre. Tots els castells. 1975-2017
Josep Bargalló Valls
 
PDF
AR勉強会第4回part1
NishoMatsusita
 
PDF
Webセミナー「海外で対等に渡り合えるビジネス英語を習得するには？」
アシストマイクロ株式会社
 
PPTX
20121224 meeting standard cell routing via boolean satisfiability_mori ver
Hanson Chi
 
IN HOUSE SYNERGIECAD_J750
Roger Cooke (Semicon Test Hardware Supplier)
 
Sesión de aprendizaje de Radicación Algebra pre u ccesa007
Demetrio Ccesa Rayme
 
AR勉強会第4回part2
NishoMatsusita
 
Nois de la Torre. Tots els castells. 1975-2017
Josep Bargalló Valls
 
AR勉強会第4回part1
NishoMatsusita
 
Webセミナー「海外で対等に渡り合えるビジネス英語を習得するには？」
アシストマイクロ株式会社
 
20121224 meeting standard cell routing via boolean satisfiability_mori ver
Hanson Chi
 
Ad

Similar to Vine shortest example (20)

DOC
Branch and bound
Nv Thejaswini
 
PPTX
Branch and bounding : Data structures
Kàŕtheek Jåvvàjí
 
PPT
Tsp branch and bound
Dr.DHANALAKSHMI SENTHILKUMAR
 
PPT
dynamic programming Rod cutting class
giridaroori
 
DOCX
Tsp bn b
Musika Fredrick
 
PPTX
Data structures and algorithms
Kaviya452563
 
DOC
Unit 3 daa
Nv Thejaswini
 
PDF
Design and Analysis of Algorithms-DP,Backtracking,Graphs,B&B
Sreedhar Chowdam
 
PDF
travelingsalesmanproblem-170122053648.pdf
mounikanarra3
 
PPTX
Traveling salesman problem
Jayesh Chauhan
 
PPTX
Traveling salesman problem
Jayesh Chauhan
 
PPT
Unit-2 Branch & Bound Design of Algorithms.ppt
HarjotDhillon8
 
PPTX
A star
minhaz uddin
 
DOC
algorithm Unit 3
Monika Choudhery
 
PPT
8783733
P. Carmona
 
PPTX
Data structure and algorithm
vanmathy1
 
PPT
Chap07alg
Munhchimeg
 
PPT
Chap07alg
Munkhchimeg
 
PPTX
Travelling Salesman
Shuvojit Kar
 
PPTX
Dynamic Programming in design and analysis .pptx
dimpuk1
 
Branch and bound
Nv Thejaswini
 
Branch and bounding : Data structures
Kàŕtheek Jåvvàjí
 
Tsp branch and bound
Dr.DHANALAKSHMI SENTHILKUMAR
 
dynamic programming Rod cutting class
giridaroori
 
Tsp bn b
Musika Fredrick
 
Data structures and algorithms
Kaviya452563
 
Unit 3 daa
Nv Thejaswini
 
Design and Analysis of Algorithms-DP,Backtracking,Graphs,B&B
Sreedhar Chowdam
 
travelingsalesmanproblem-170122053648.pdf
mounikanarra3
 
Traveling salesman problem
Jayesh Chauhan
 
Traveling salesman problem
Jayesh Chauhan
 
Unit-2 Branch & Bound Design of Algorithms.ppt
HarjotDhillon8
 
A star
minhaz uddin
 
algorithm Unit 3
Monika Choudhery
 
8783733
P. Carmona
 
Data structure and algorithm
vanmathy1
 
Chap07alg
Munhchimeg
 
Chap07alg
Munkhchimeg
 
Travelling Salesman
Shuvojit Kar
 
Dynamic Programming in design and analysis .pptx
dimpuk1
 
Ad

Recently uploaded (20)

PDF
Transform Your ITIL® 4 & ITSM Strategy with AI in 2025.pdf
PDCA Consulting
 
PDF
Architecture types and enterprise applications.pdf
ChristopherTHyatt
 
PDF
DASA ADMISSION 2024_FirstRound_FirstRank_LastRank.pdf
rameswartudu05
 
PDF
Univ-Connecticut-ChatGPT-Presentaion.pdf
ry7r52mzb4
 
PPTX
Group 1 Presentation -Planning and Decision Making .pptx
MatthewLewis227954
 
PPTX
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
PDF
Hybrid model detection and classification of lung cancer
IAESIJAI
 
PDF
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
KodekX
 
PDF
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
PPTX
observCloud-Native Containerability and monitoring.pptx
anupsingh76937
 
PDF
Developing a website for English-speaking practice to English as a foreign la...
IAESIJAI
 
PDF
Video forgery: An extensive analysis of inter-and intra-frame manipulation al...
IAESIJAI
 
PDF
Zenith AI: Advanced Artificial Intelligence
Biz Preneurs
 
PPTX
Tartificialntelligence_presentation.pptx
ry7r52mzb4
 
PDF
Microsoft Solutions Partner Drive Digital Transformation with D365.pdf
Microsoft Dynamics
 
PPTX
O2C Customer Invoices to Receipt V15A.pptx
ssuserbfa915
 
PPTX
Final SEM Unit 1 for mit wpu at pune .pptx
anishtilekar08
 
PDF
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
PDF
Getting started with AI Agents and Multi-Agent Systems
Maxim Salnikov
 
PDF
NewMind AI Weekly Chronicles – August ’25 Week III
NewMind AI
 
Transform Your ITIL® 4 & ITSM Strategy with AI in 2025.pdf
PDCA Consulting
 
Architecture types and enterprise applications.pdf
ChristopherTHyatt
 
DASA ADMISSION 2024_FirstRound_FirstRank_LastRank.pdf
rameswartudu05
 
Univ-Connecticut-ChatGPT-Presentaion.pdf
ry7r52mzb4
 
Group 1 Presentation -Planning and Decision Making .pptx
MatthewLewis227954
 
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
Hybrid model detection and classification of lung cancer
IAESIJAI
 
From MVP to Full-Scale Product A Startup’s Software Journey.pdf
KodekX
 
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
observCloud-Native Containerability and monitoring.pptx
anupsingh76937
 
Developing a website for English-speaking practice to English as a foreign la...
IAESIJAI
 
Video forgery: An extensive analysis of inter-and intra-frame manipulation al...
IAESIJAI
 
Zenith AI: Advanced Artificial Intelligence
Biz Preneurs
 
Tartificialntelligence_presentation.pptx
ry7r52mzb4
 
Microsoft Solutions Partner Drive Digital Transformation with D365.pdf
Microsoft Dynamics
 
O2C Customer Invoices to Receipt V15A.pptx
ssuserbfa915
 
Final SEM Unit 1 for mit wpu at pune .pptx
anishtilekar08
 
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
Getting started with AI Agents and Multi-Agent Systems
Maxim Salnikov
 
NewMind AI Weekly Chronicles – August ’25 Week III
NewMind AI
 

Vine shortest example

  • 1. Modified Vine-Building Shortest Paths Algorithm Ikki Kim
  • 2. 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
  • 3. 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)
  • 4. 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,-,-)
  • 5. 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,-,-)
  • 6. 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)
  • 7. 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)
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. Thank you for your Attention ! Any Questions Or Comments ?