1. Lecture 7
Peer-to-Peer
Interest Management
8 March 2010
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2. Point-to-Point
Architecture
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3. Problem:
Communication between
every pair of peers
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4. Idea (old): A peer p only
needs to communicate
with another peer q
if p is relevant to q
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5. Recall: In C/S Architecture, the
server has global information
and decide who is relevant to
who.
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6. Problem: No global
information in P2P
architecture.
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7. Naive Solution: Every
peer keeps global information
about all other peers and
make individual decision.
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8. Maintaining global
information is expensive
(and that’s what we want
to avoid in the first place!)
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9. Smarter solution:
exchange position, then
decide when should the
next position exchange be.
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10. Idea: Assume B is static. If
A knows B’s position, A can
compute the region which is
irrelevant to B. Need not
update B if A moves within
that region.
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11. what if B moves?
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12. It still works if B also knows A
position and computes the
region that is irrelevant to A.
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13. Position exchanges occur once
initially, and when a player
moves outside of its irrelevant
region wrt another player.
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14. Frontier Sets
cell-based, visibility-based IM
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15. Previously, we learnt how to
compute cell-to-cell visibility.
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16. Frontier for cells X and Y
consists of
two sets FXY and FYX
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17. No cell in FXY is visible from
a cell in FYX, and vice versa.
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18. FXY and FYX are disjoint
if X and Y are not mutually visible.
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19. FXY and FYX are empty
if X and Y are mutually visible.
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20. Suppose X and Y are not
mutually visible, then
a simple frontier is
FXY = {X} FYX = {Y}
(many others are possible)
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21. A B C
D E F
G H I
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22. A B C
D E F
G H I
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23. A B C
D E F
G H I
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24. A B C
D E F
G H I
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25. NOT a frontier for A and I (D is visible from B).
A B C
D E F
G H I
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26. Position exchanges occur once
initially, and when a player
moves outside of its irrelevant
region wrt another player.
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27. Initialize:
Let player P be in cell X
For each player Q
Let cell of Q be Y
Compute FXY (or simply FQ)
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28. Move to new cell:
Let X be new cell
For each player Q
If X not in FQ
Send location to Q
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29. Receive Update:
(location from Q)
Send location to Q
Recompute FQ
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30. Update is triggered.
A B C
D E F
G H I
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31. New Frontier.
A B C
D E F
G H I
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32. Update triggered.
A B C
D E F
G H I
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33. New frontier (empty since E can see G)
A B C
D E F
G H I
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34. How to compute frontier?
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35. A good frontier is as large as
possible, with two almost
equal-size sets.
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36. Build a visibility graph. Cells are vertices. Two cells are
connected by an edge if they are visible to each other
(EVEN if they don’t share a boundary)
A B C
D E F
G H I
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37. Let dist(X,Y) be the shortest
distance between two cells X
and Y on the visibility graph.
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38. 0 1 2
A B C
2 1 2
D E F
2 3 3
G H I
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39. Theorem
FXY = { i | dist(X,i) <= dist(Y,i) - 1}
FYX = { j | dist(Y,j) < dist(X,j) - 1}
are valid frontiers.
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40. 0 3 1 3 2 3
A B C
2 2 1 2 2 4
D E F
2 1 3 1 3 0
G H I
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41. 0 3 1 3 2 3
A B C
2 2 1 2 2 4
D E F
2 1 3 1 3 0
G H I
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42. 0 3 1 3 2 3
A B C
2 2 1 2 2 4
D E F
2 1 3 1 3 0
G H I
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43. A B C
D E F
G H I
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44. Theorem
FXY = { i | dist(X,i) <= dist(Y,i) - 1}
FYX = { j | dist(Y,j) < dist(X,j) - 1}
are valid frontiers.
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45. FXY = { i |dist(X,i) <= dist(Y,i) - 1}
FYX = { j |dist(Y,j) < dist(X,j) - 1}
Proof (by contradiction)
Suppose there are two cells, C in
FXY and D in FYX, that can see each
other.
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46. FXY = { i |dist(X,i) <= dist(Y,i) - 1}
FYX = { j |dist(Y,j) < dist(X,j) - 1}
dist(X,C) <= dist(Y,C) - 1
dist(Y,D) < dist(X,D) - 1
dist(C,D) = dist(D,C) = 1
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47. dist(X,C) <= dist(Y,C) - 1
dist(Y,D) < dist(X,D) - 1
dist(C,D) = dist(D,C) = 1
We also know that
dist(X,D) <= dist(X,C) + dist(C,D)
dist(Y,C) <= dist(Y,D) + dist(D,C)
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48. 1. dist(X,C) <= dist(Y,C) - 1
2. dist(Y,D) < dist(X,D) - 1
3. dist(C,D) = 1
4. dist(X,D) <= dist(X,C) + dist(C,D)
5. dist(Y,C) <= dist(Y,D) + dist(D,C)
From 4, 1, and 3:
dist(X,D)
<= dist(Y,C) - 1 + 1
From 5:
dist(X,D) <= dist(Y,D) + 1
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49. 1. dist(X,C) <= dist(Y,C) - 1
2. dist(Y,D) < dist(X,D) - 1
3. dist(C,D) = 1
4. dist(X,D) <= dist(X,C) + dist(C,D)
5. dist(Y,C) <= dist(Y,D) + dist(D,C)
We have
dist(X,D) <= dist(Y,D) + 1
Which contradict 2
dist(X,D) > dist(Y,D) + 1
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50. How good is the idea?
(How many messages can we save
by using Frontier Sets?)
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51. q2dm3 q2dm4 q2dm8
Max dist() 4 5 8
Num of cells 666 1902 966
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52. Frontier Density:
% of player-pairs with
non-empty frontiers.
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53. q2dm3 q2dm4 q2dm8
Frontier
Density 83.9 93.0 84.2
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54. Frontier Size:
% of cells in the frontier
on average
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55. q2dm3 q2dm4 q2dm8
Frontier
Size 38.3% 67.3% 68.2%
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56. Compare with
1. Naive P2P
2. Perfect P2P
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57. Naive P2P
Always send update to
15 other players.
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58. Perfect P2P
Hypothetical protocol
that sends messages
only to visible players.
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59. Number of messages per frame per player.
q2dm3 q2dm4 q2dm8
NPP 15 15.7 14.4
PPP 3.7 1.9 4.2
Frontier 5.4 2.6 5.9
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60. Space Complexity
Let N be the number of cells. If
we precompute Frontier for
every pair of cells, we need
O(N 3)
space.
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61. If we store visibility graph and
compute frontier as needed,
we only need
O(N 2)
space.
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62. Frontier Sets
cell-based, visibility-based IM
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63. Limitations
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64. Works badly if there’s
little occlusion in the
virtual world.
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65. Still need to
exchange locations
with every other
players occasionally.
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66. Frontier Sets
cell-based, visibility-based IM
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67. Voronoi Overlay Network:
Aura-based Interest Management
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68. Diagrams and plots in the
sections are taken from
presentation slides by
Shun-yun Hu, available on
http://vast.sf.net
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69. Keep a list of AOI-neighbors and
exchange messages with AOI-neighbors.
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70. Q: How to initialize AOI-neighbors?
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71. Q: How to update AOI-neighbors?
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72. Problem: No global
information in P2P
architecture.
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73. Idea: Find closest node and
ask for introductions
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74. Idea: New AOI-neighbors will likely be
neighbors of my existing AOI-neighbors.
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75. Challenge: Need to discover new neighbors
even if current node has no neighbor
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76. Question: How to find
closest node?
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77. Every node is in charge of a
region in the virtual world.
The region contains points
closest to the node.
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78. Voronoi Diagram
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79. AOI Neighbors:
Neighbors in AOI
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80. Enclosing
Neighbors:
Neighbors in
adjacent region.
(may or may not
be in AOI)
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81. Boundary
Neighbors:
Neighbors whose
region intersect
with AOI.
(may or may not
be in AOI)
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82. Boundary and
Enclosing
Neighbor
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83. Regular AOI
Neighbor:
Non-boundary
and non-enclosing
neighbor in AOI
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84. Unknown nodes
(not neighbors!)
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85. Type in AOI? intersect? adjacent?
Regular yes no no
Enclosing maybe no yes
Boundary maybe yes no
Enclosing
maybe yes yes
+Boundary
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86. A node always
connect to its
enclosing neigbours,
regardless of whether
they are in the AOI.
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87. A node connects to
exchanges updates
with all neighbors.
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88. A node maintains
Voronoi of all
neighbors
(regardless of inside
AOI or not)
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89. Suppose a player X wants to
join. X sends its location to
any node in the system.
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90. X join request is forwarded to the node
in charge of the region (i.e., closest node
to X), called acceptor.
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91. Forwarding is done greedily
(at every step, forward to neighbor closest to X)
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92. Acceptor informs the joining node X of its neighbors.
Acceptor, X, and the neighbors update their Voronoi
diagram to include the new node.
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93. True or false:
Enclosing neighbors of X are
also enclosing neighbors of
acceptor.
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94. When X moves, X learns about new
neighbors from the boundary neighbors.
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95. Boundary neighbors’ enclosing neighbors
may become new neighbors of X.
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96. When a node disconnects,Voronoi diagrams are
updated by the affected nodes. New boundary
neighbors may be discovered.
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97. Advantages of VON:
Number of connections
depends on size of AOI, not
size of virtual world
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98. We can bound number of
connections by adjusting AOI
radius (smaller AOI is crowded
area).
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99. Advantages of VON:
Maintain a minimal number of
enclosing neighbors when the
world is sparse to ensure
connectivity.
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100. Advantages of VON:
Boundary neighbors ensure
that new neighbors are
discovered.
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101. Problems with VON:
Inconsistency may occur (e.g.
with fast moving nodes)
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102. No rigorous proof
Working on evaluation with
realistic traces
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103. For now, simulation only
World Size 1200x1200
Players 100 to 1000
AOI 100
Connection Limit 20
Movement Random Waypoint
Velocity Constant 5 units /step
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104. Average Transmission per Second
16
basic
14 dAOI
basic (fixed density after 500 nodes)
12 dAOI (fixed density after 500 nodes)
10
Size (kb)
8
6
4
2
0
0 200 400 600 800 1000
Number of Nodes
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105. Average Neighbor Size
50
connected neighbors (basic)
45 AOI neighbors (basic)
40 connected neighbors (dAOI)
AOI neighbors (dAOI)
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Neighbor Size
30
25
20
15
10
5
0
0 200 400 600 800 1000
Number of Nodes
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106. Observed/Actual AOI Neighbors
100.00
99.99
99.98
Topology Consistency (%)
99.97
99.96
99.95
99.94
99.93
99.92 basic
99.91 dAOI
99.90
100 200 300 400 500 600 700 800 900 1000
Number of Nodes
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107. actual - observed position (average over all nodes)
0.50
0.45
basic
0.40
Average Drift Distance
dAOI
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
100 200 300 400 500 600 700 800 900 1000
Number of Nodes
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108. Responsive
Consistent
Cheat-Free
Fair
Scalable
Efficient
Robust
Simple
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