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# Broadcasting with Bounded Number of Redundant Transmissions - PowerPoint PPT Presentation

Broadcasting with Bounded Number of Redundant Transmissions. Majid Khabbazian. Outline. Assumptions Objectives Classifications The proposed algorithm Algorithm’s characteristics Conclusion. Assumptions. Single message broadcast Nodes are distributed in 2-D space

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Presentation Transcript

### Broadcasting with Bounded Number of Redundant Transmissions

Majid Khabbazian

• Assumptions

• Objectives

• Classifications

• The proposed algorithm

• Algorithm’s characteristics

• Conclusion

• Nodes are distributed in 2-D space

• The transmission range of each node is R

• We can use Unit Disk Graph (UDG) to model the network

• No Synchronization

• Perfect Medium Access Control (MAC)

• No errors or collisions

• Neighbors don’t transmit at the same time

• Nodes are static during the broadcast

• End-to-end delay is NOT a concern

• What do we care about?

• Full delivery

• Reducing the number of transmissions

• Each node has a local view of the network

• Flooding

• Every node transmits the first copy of received message

• Pros.

• A simple solution

• No need to have neighbor information

• Requires almost no computation

• Cons.

• All the nodes transmit the message

• It can cause a large number of redundant transmissions

• Can we minimize the total number of transmissions?

• This is related to fining a Minimum Connected Dominating Set (MCDS)

• Finding MCDS is NP-hard even for UDGs

• Good approximation algorithms?

• Case 1: The whole topology is known

• Case 2: Each node has a local view of the network

• Classifications

• Static (Proactive)

• Dynamic (Reactive)

• Static Approach

• A backbone is constructed first

• The backbone is a Connected Dominating Set

• Pros.

• Can be used for both broadcasting and unicasting

• Cons.

• May not be good where the network topology is dynamic

• The backbone is fixed in the static network

• Dynamic Approach

• There is no backbone

• Nodes decide “on-the-fly” based on their local view

• Pros.

• The backbone changes from one network-wide broadcast to another (even for the single source)

• More robust against failures than static approach

• Cons.

• Constructed backbone may not be stable

• Each node has the list of its 1-hop neighbors

• Exchanging “hello” messages

• Geographical information is available

• E.g., Using GPS

• Relative distance may suffice

• A small size backbone can be easily constructed

• Regionalizing the network

• Selecting a constant number of nodes in each region

• Example:

• Divide the network into square cells with diameter 1

• At most 20 nodes have to be selected in each cell

• Can we reduce the total number of transmissions in the worst case?

• Is constant approximation factor achievable?

• Our proposed algorithm is proven to achieve:

• Full delivery

• Constant approximation factor

• Each node decides on its own whether or not to transmit

• Before transmitting, the node removes the information attached to the message and adds the list of its 1-hop neighbors to the message

• The decision is made based on a self-pruning condition called the responsibility condition

• The closer, the more responsible

• A node u has to transmit the message if it has a neighbor v s.t.

• v has not received the message

AND

• There is no node w such that w has received the message and dist(wv )< dist(uv)

• A receives the message from H

• A knows that E, F and G have received the message and B, C and D have not

• Based on the responsibility condition A does not need to transmit the message

G

D

F

C

H

A

B

E

• It achieves full delivery

• The broadcast will eventually terminate

• Suppose there is a node that has not received the message

• Consider the set

• S={(u,v)| u and v are neighbors, u has received the message, v has not received the message}

• S is not empty

• S is not empty

There exists a pair (u’,v’) in S such that

Dist(u’,v’)<= dist(u,v)

for any pair (u,v) in S.

• u’ has the highest responsibility toward v’

• v’ has not receive the message

• Based on the responsibility condition

• u’ must have transmitted the message

• The proposed algorithm achieves a constant approximation factor

Sketch of proof

• There are at most a constant number of transmissions in each disk with radius ¼

• Transmission coverage of each node is a disk with radius 1

• Each node has a constant number of neighbors that transmit the message

• The number of transmission has to be within a constant factor of the optimum

• Transmitters: Blue nodes

• Blue nodes are neighbors

• All the nodes in the white disk will get the message after the first transmission

• Blue nodes are aware of this fact

• Every blue node is responsible for a unique red node

• The distance between a blue and a red node is at least ½

• The number of red nods must be constant

• Similar results can also be achieved when

• Nodes are distributed in 3-dimensional space

• Nodes can have different transmission ranges

• Nodes don’t have IDs

• Geographical information is not accurate

• Error must be less than ~0.1

• Geographical information can be represented using a constant number of bits

• Key Idea: Each node required to report its position to its neighbors

• We compared the performance of the proposed algorithm with

• Liu’s algorithm [Infocom 2006 ]

• A ratio-8 approximation algorithm [Infocom 2002 ]

• Used as a benchmark

• #nodes: 400

• Trans. range: 300meter