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Broadcasting with Bounded Number of Redundant Transmissions PowerPoint Presentation

Broadcasting with Bounded Number of Redundant Transmissions

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### 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
- 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

Objectives

- 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: A Simple Solution

- 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
- It can lead to significant performance degradation and network congestion

A Question

- 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
- Local Broadcast Algorithms

Local Broadcast Algorithms

- 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

Local Broadcast Algorithms (Con’d)

- 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

Further Assumptions

- 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

Static Approach

- 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

Dynamic Approach

- 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

Proposed Algorithm

- 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

Responsibility Condition

- 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)

- v has not received the message

Example

- 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

Full Delivery

- It achieves full delivery
- Proof by contradiction:
- 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

Full Delivery (Con’d)

- 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

Approximation Factor

- 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

Approximation Factor (Con’d)

- 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

Approximation Factor (Con’d)

- 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

Relaxing Some of the Assumptions

- 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

Simulation

- 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

Example

- #nodes: 400
- Trans. range: 300meter
- #broadcasting nodes: 10

Conclusion

- Reactive broadcast algorithms are in fact powerful
- Question: Can we do this without using geographical info. (or relative distances)?
- The answer is YES. This can be the subject of a future talk..

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