Lecture 7Peer-to-Peer

Interest Management

8 March 2010

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Point-to-Point Architecture

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Problem: Communication between

every pair of peers

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Idea (old): A peer p only needs to communicate with another peer q if p is relevant to q

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Recall: In C/S Architecture, the server has global information and decide who is relevant to who.

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Problem: No global information in P2P architecture.

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Naive Solution: Every peer keeps global information about all other peers and make individual decision.

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Maintaining global information is expensive (and that’s what we want to avoid in the first place!)

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Smarter solution: exchange position, then decide when should the next position exchange be.

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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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what if B moves?

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It still works if B also knows A position and computes the region that is irrelevant to A.

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Position exchanges occur once initially, and when a player moves outside of its irrelevant region wrt another player.

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Frontier Setscell-based, visibility-based IM

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Previously, we learnt how to compute cell-to-cell visibility.

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Frontier for cells X and Y consists of

two sets FXY and FYX

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No cell in FXY is visible from a cell in FYX, and vice versa.

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FXY and FYX are disjoint if X and Y are not mutually visible.

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FXY and FYX are empty if X and Y are mutually visible.

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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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A B C

D E F

G H I

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A B C

D E F

G H I

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A B C

D E F

G H I

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A B C

D E F

G H I

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A B C

D E F

G H I

NOT a frontier for A and I (D is visible from B).

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Position exchanges occur once initially, and when a player moves outside of its irrelevant region wrt another player.

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Initialize: Let player P be in cell XFor each player Q Let cell of Q be Y Compute FXY (or simply FQ)

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Move to new cell:Let X be new cellFor each player Q If X not in FQ

Send location to Q

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Receive Update: (location from Q)Send location to QRecompute FQ

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A B C

D E F

G H I

Update is triggered.

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A B C

D E F

G H I

New Frontier.

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A B C

D E F

G H I

Update triggered.

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A B C

D E F

G H I

New frontier (empty since E can see G)

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How to compute frontier?

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A good frontier is as large as possible, with two almost

equal-size sets.

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A B C

D E F

G H I

Build a visibility graph. Cells are vertices. Two cells areconnected by an edge if they are visible to each other

(EVEN if they don’t share a boundary)

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Let dist(X,Y) be the shortest distance between two cells X and Y on the visibility graph.

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A B C

D E F

G H I

0 1 2

212

2 3 3

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TheoremFXY = { i | dist(X,i) <= dist(Y,i) - 1}FYX = { j | dist(Y,j) < dist(X,j) - 1}

are valid frontiers.

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A B C

D E F

G H I

0 1 2

212

2 3 3 0

0

11

2 2

33 3

4

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A B C

D E F

G H I

0 1 2

212

2 3 3 0

0

11

2 2

33 3

4

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H

A B C

D E F

G I

0 1 2

212

2 3 3 0

0

11

2 2

33 3

4

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A B C

D E F

G H I

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TheoremFXY = { i | dist(X,i) <= dist(Y,i) - 1}FYX = { j | dist(Y,j) < dist(X,j) - 1}

are valid frontiers.

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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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FXY = { i |dist(X,i) <= dist(Y,i) - 1}FYX = { j |dist(Y,j) < dist(X,j) - 1}

dist(X,C) <= dist(Y,C) - 1dist(Y,D) < dist(X,D) - 1dist(C,D) = dist(D,C) = 1

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dist(X,C) <= dist(Y,C) - 1dist(Y,D) < dist(X,D) - 1dist(C,D) = dist(D,C) = 1

We also know thatdist(X,D) <= dist(X,C) + dist(C,D)dist(Y,C) <= dist(Y,D) + dist(D,C)

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1. dist(X,C) <= dist(Y,C) - 12. dist(Y,D) < dist(X,D) - 13. dist(C,D) = 14. 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 + 1From 5:dist(X,D) <= dist(Y,D) + 1

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1. dist(X,C) <= dist(Y,C) - 12. dist(Y,D) < dist(X,D) - 13. dist(C,D) = 14. 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) + 1Which contradict 2 dist(X,D) > dist(Y,D) + 1

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How good is the idea?

(How many messages can we save by using Frontier Sets?)

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q2dm3 q2dm4 q2dm8

Max dist()

Num of cells

4 5 8

666 1902 966

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Frontier Density: % of player-pairs with non-empty frontiers.

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q2dm3 q2dm4 q2dm8

Frontier Density 83.9 93.0 84.2

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Frontier Size: % of cells in the frontier on average

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q2dm3 q2dm4 q2dm8

Frontier Size 38.3% 67.3% 68.2%

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Compare with1. Naive P2P2. Perfect P2P

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Naive P2PAlways send update to 15 other players.

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Perfect P2PHypothetical protocol that sends messages only to visible players.

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q2dm3 q2dm4 q2dm8

NPP

PPP

Frontier

15 15.7 14.4

3.7 1.9 4.2

5.4 2.6 5.9

Number of messages per frame per player.

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Space ComplexityLet N be the number of cells. If we precompute Frontier for every pair of cells, we need

O(N3) space.

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If we store visibility graph and compute frontier as needed, we only need

O(N2) space.

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Frontier Setscell-based, visibility-based IM

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Limitations

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Works badly if there’s little occlusion in the

virtual world.

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Still need to exchange locations with every other

players occasionally.

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Frontier Setscell-based, visibility-based IM

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Voronoi Overlay Network: Aura-based Interest Management

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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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Keep a list of AOI-neighbors and exchange messages with AOI-neighbors.

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Q: How to initialize AOI-neighbors?

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Q: How to update AOI-neighbors?

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Problem: No global information in P2P architecture.

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Idea: Find closest node and ask for introductions

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Idea: New AOI-neighbors will likely be neighbors of my existing AOI-neighbors.

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Challenge: Need to discover new neighbors even if current node has no neighbor

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Question: How to find closest node?

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Every node is in charge of a region in the virtual world.

The region contains points closest to the node.

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Voronoi Diagram

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AOI Neighbors:Neighbors in AOI

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Enclosing Neighbors:Neighbors in adjacent region.

(may or may not be in AOI)

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Boundary Neighbors:Neighbors whose region intersect with AOI.

(may or may not be in AOI)

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Boundary andEnclosingNeighbor

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Regular AOI Neighbor:Non-boundaryand non-enclosingneighbor in AOI

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Unknown nodes (not neighbors!)

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Type in AOI? intersect? adjacent?

Regular yes no no

Enclosing maybe no yes

Boundary maybe yes no

Enclosing+Boundary

maybe yes yes

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A node always connect to its enclosing neigbours, regardless of whether they are in the AOI.

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A node connects to exchanges updates with all neighbors.

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A node maintains Voronoi of all neighbors(regardless of inside AOI or not)

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Suppose a player X wants to join. X sends its location to any node in the system.

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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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Forwarding is done greedily (at every step, forward to neighbor closest to X)

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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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True or false:

Enclosing neighbors of X are also enclosing neighbors of acceptor.

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When X moves, X learns about new neighbors from the boundary neighbors.

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Boundary neighbors’ enclosing neighbors may become new neighbors of X.

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When a node disconnects, Voronoi diagrams areupdated by the affected nodes. New boundary

neighbors may be discovered.

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Advantages of VON:

Number of connections depends on size of AOI, not size of virtual world

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We can bound number of connections by adjusting AOI radius (smaller AOI is crowded area).

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Advantages of VON:

Maintain a minimal number of enclosing neighbors when the world is sparse to ensure connectivity.

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Advantages of VON:

Boundary neighbors ensure that new neighbors are discovered.

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Problems with VON:

Inconsistency may occur (e.g. with fast moving nodes)

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No rigorous proof

Working on evaluation with realistic traces

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For now, simulation only

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World Size

Players

AOI

Connection Limit

Movement

Velocity

1200x1200

100 to 1000

100

20

Random Waypoint

Constant 5 units /step

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0

2

4

6

8

10

12

14

16

0 200 400 600 800 1000Number of Nodes

Size

(kb)

basicdAOIbasic (fixed density after 500 nodes)dAOI (fixed density after 500 nodes)

Average Transmission per Second

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Average Neighbor Size

0

5

10

15

20

25

30

35

40

45

50

0 200 400 600 800 1000Number of Nodes

Nei

ghbo

r Si

ze

connected neighbors (basic)AOI neighbors (basic)connected neighbors (dAOI)AOI neighbors (dAOI)

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Observed/Actual AOI Neighbors

99.90

99.91

99.92

99.93

99.94

99.95

99.96

99.97

99.98

99.99

100.00

100 200 300 400 500 600 700 800 900 1000Number of Nodes

Topo

logy

Con

sist

ency

(%

)

basicdAOI

106

actual - observed position (average over all nodes)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

100 200 300 400 500 600 700 800 900 1000Number of Nodes

Ave

rage

Drif

t Dis

tanc

e

basicdAOI

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Responsive

Consistent

Cheat-Free

Fair

Scalable

Efficient

Robust

Simple

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