1. 1 Broadcast

2. 2

3. 3 Use a spanning tree Root

4. 4 synchronous It takes the same time at link to send a message It takes the same time at each node to process the incoming data

5. 5

6. 6

7. 7 Time complexity: levels nodes Message complexity:

8. 8 asynchronous Links and nodes may have different delays

9. 9

10. 10 slow link

11. 11 slow link

12. 12 Actual delivery

13. 13

14. 14 Time complexity: levels nodes Message complexity:

15. 15 Convergecast

16. 16 synchronous

17. 17

18. 18

19. 19

20. 20 Time complexity: levels nodes Message complexity:

21. 21 asynchronous

22. 22

23. 23

24. 24

25. 25

26. 26 Time complexity: levels nodes Message complexity:

27. 27 Building a BFS Spanning Tree

28. 28 Tree algorithm for node : Upon receipt of message from neighbor node : If not member of tree: accept invitation by sending message to ; (the father) If member of tree: decline invitation by sending message to ; Send invitations to all neighbors, except

29. 29 synchronous

30. 30 A node initiates the BFS process

31. 31 become members of tree

32. 32

33. 33

34. 34

35. 35

36. 36

37. 37

38. 38

39. 39

40. 40

41. 41 Alternative solution

42. 42

43. 43 reject

44. 44

45. 45

46. 46 Time complexity: diameter nodes Message complexity: edges

47. 47 asynchronous

48. 48

49. 49

50. 50

51. 51

52. 52 slow node

53. 53

54. 54

55. 55

56. 56

57. 57

58. 58 reject

59. 59

60. 60

61. 61 reject

62. 62

63. 63 Time complexity: diameter nodes Message complexity: edges

64. 64 The asynchronous algorithm may give deeper trees than the diameter Example: Clique graph Synchronous BFS Asynchronous BFS

65. 65 Building a DFS Spanning Tree

66. 66 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4

67. 67 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

68. 68 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

69. 69 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

70. 70 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

71. 71 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

72. 72 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

73. 73 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 reject

74. 74 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

75. 75 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

76. 76 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

77. 77 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

78. 78 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 reject

79. 79 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

80. 80 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 reject

81. 81 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

82. 82 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

83. 83 Time complexity: nodes Message complexity: edges 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1

84. 84 Building a DFS Spanning Tree with no specified root

85. 85 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1

86. 86 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 1

87. 87 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 18 1

88. 88 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 18 1

89. 89 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 88 1

90. 90 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 88 1

91. 91 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 88 1 reject

92. 92 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 1 8 88 1

93. 93 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1

94. 94 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1 8

95. 95 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1 8 8

96. 96 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1 8 8

97. 97 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 8 8 8 8 88 1 8 8

98. 98 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 8 8 8 8 88 1 8 8

99. 99 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1 8 8 root

100. 100 Time complexity: nodes Message complexity: edges 12 1 1 2 3 1 2 3 1 2 3 1 2 1 2 3 4 2 3 4 1 8 8 8 88 1 8 8 root