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On Channel Assignment Of Graphs

On Channel Assignment Of Graphs. Author : Hsin-Ju Wu Adviser : Yung-Ling Lai Speaker : Shr-Jia Hung. Outline. Motivation and Definition Off-line Labeling On-line Labeling Conclusion and Future work. Outline. Motivation and Definition Off-line Labeling

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On Channel Assignment Of Graphs

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  1. On Channel Assignment Of Graphs Author : Hsin-Ju Wu Adviser : Yung-Ling Lai Speaker : Shr-Jia Hung

  2. Outline • Motivation and Definition • Off-line Labeling • On-line Labeling • Conclusion and Future work

  3. Outline • Motivation and Definition • Off-line Labeling • On-line Labeling • Conclusion and Future work

  4. Motivation • Channel assignment problem • the number of finite frequencies • Use a graph to model it.

  5. Motivation • Vertices transmitters • Edges Distances Adjacent very close Distance 2 Close B C A

  6. Definition • k-L(p,q) labeling f for a given graph G=(V,E), is a function f : V→{ 0,1,…,k } such that | f(x)-f(y) | p if d(x,y)=1 and | f(x)-f(y) | q if d(x,y)=2. • The L(p,q) labeling number of graph G is then defined as:

  7. Outline • Motivation and Definition • Off-line Labeling • On-line Labeling • Conclusion and Future work

  8. Off-line Labeling • L(d,1) labeling on • L(d,1) labeling on

  9. Outline • Motivation and Definition • Off-line Labeling • On-line Labeling • Conclusion and Future work

  10. Online base application

  11. Online base application

  12. Online base application

  13. Online base application

  14. Online base application

  15. Online base application

  16. Definition of online labeling • Given a graph G. • The vertices are given one-by-one arbitrarily. • Only the adjacency relation between the given vertices are known. • Satisfy the condition of L(2,1)-labeling. • Give a label right away which is not changeable later.

  17. Online L(2,1) labeling of path • Path algorithm Call Function Get_available_Number(N1,N2)

  18. Get_available_Number(N1,N2) Get_available_Number(N1,N2) N1=0 N1=1 N1=2 N2=0 N2=0 N2=1 N2=0 N2=1 N2=2

  19. N1=0 and N2=0 x

  20. N1=1 and N2=0 L1 x

  21. N1=1 and N2=1 vj L1 x L1 x

  22. L2 x L1 L2 L2 x x L1 L1 N1=2 and N2=0,1,2

  23. Time Complexity • Path algorithm 3.1 O(n) Call Function Get_available_Number(N1,N2)

  24. Time Complexity • Path algorithm Get_available_Number(N1,N2) O(n)

  25. Time Complexity • Path algorithm 3.1 O(n2) Call Function Get_available_Number(N1,N2)

  26. Online L(2,1) labeling of path Pattern A 26

  27. Online L(2,1) labeling of path 27

  28. Online L(2,1) labeling of cycle Pattern B 28

  29. Online L(2,1) labeling of cycle 29

  30. Star S9 7 9 8 6 0 2 7 3 5 1 9 0 2 4 4 6 5 3

  31. Online L(2,1) labeling of star n-1 1 n 0 1 2

  32. Online L(2,1) labeling of star 3 2 2 1 n 4 0 1

  33. Online---Other graph bound Double star: Full binary tree: 33

  34. Outline • Motivation and Definition • Off-line Labeling • On-line Labeling • Conclusion and Future work

  35. Conclusion • Off-line L(d,1) labeling - - • On-line L(2,1) labeling - Path - Cycle - Star - Double star - Full binary tree

  36. Future Work • On-line L(2,1) labeling • K2xPn , K2xCn • Wheel • Complete bipartite graph • relation with max degree • relation with radius , diamter • relation with density(size/order)

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