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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

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Outline
Outline

  • Assumptions

  • Objectives

  • Classifications

  • The proposed algorithm

  • Algorithm’s characteristics

  • Conclusion


Assumptions
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
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: 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
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
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
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
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
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
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
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
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)


Example
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
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
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
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
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 d1
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
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
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



Example1
Example

  • #nodes: 400

  • Trans. range: 300meter

  • #broadcasting nodes: 10


Conclusion
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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