On Reducing Broadcast Redundancy in Wireless Ad Hoc Network

1
On Reducing Broadcast Redundancy in Wireless Ad
Hoc Network

• Author
• Wei Lou, Student Member, IEEE, and Jie Wu, Senior
  Member, IEEE
• From IEEE transactions on mobile computing
  April-June 2002
• Presented By
• ????R92725034 Lin Ming Yuan

2
Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

3
Introduction

• Some characteristics of ad hoc network
• Without central infrastructure
• Temporary and changing topology
• In this paper, the author focused on the topic of
  broadcast problem and try to find the minimum
  number of forward nodes.

4
Introduction (cont.)

• Traditionally it used the concept of the flood
  tree to broadcast packets in ad hoc networks. The
  efficiency of the algorithm depends on the number
  of total forwarding nodes.
• The importance and application of broadcast
  service
• Route query process in several routing protocol
• Send an error message to erase invalid routes
• For reliable multicast

5
Introduction (cont.)

• The problem of finding minimum forwarding nodes
  can be reduce to a dominant set problem which is
  NP.
• Some previous algorithm
• Blinding flooding (broadcast storming problem)
• Dominating pruning (DP) algorithm

6
Introduction (cont.)

• The DP algorithm utilizes 2-hops neighborhood
  information to reduce redundancy transmissions
  and prolong the life of the network.
• The DP algorithm also can be considered as an
  approximation to the minimum flood tree problem.
• In this paper, the author proposed two extensive
  algorithm
• TDP (Total Dominant Pruning algorithm)
• PDP (Partial Dominant Pruning algorithm)

7
Outline

• Introduction
• Preliminaries
• The approximation of MCDS (AMCDS) algorithm
• The dominant pruning (DP) algorithm
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

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Preliminaries

• Lim and Kim prove that building a minimum
  flooding tree is the same as finding a minimum
  connected dominating set (MCDS) in a network,
  which is an NP-complete problem.
• Our approach is based on constructing a connected
  dominating set on-the-fly and it is suitable
  for dynamic networks with mobile hosts

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Preliminaries (redundancy problem)
U is the sender.
The transmissions between v and w are redundant.
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Outline

• Introduction
• Preliminaries
• The approximation of MCDS (AMCDS) algorithm
• The dominant pruning (DP) algorithm
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

11
Notation

• G (V ,E), where V represents a set of wireless
  mobile hosts (nodes) and E represents a set of
  edges. Such a graph forms an unit disk graph.
• N(u) represents the neighbor set of u (including
  u) and N(N(u)) represents the neighbor set of
  N(u) (i.e., the set of nodes that are within two
  hops from u).
• Clearly, and if
  , then
• .

12
Assumption

• 2-hop neighborhood information can be obtained by
  periodic Hello packets, each of which contains
  the senders identification and the list of its
  neighbor.
• In this paper, the author assumed that v (sender)
  and u (receiver) are neighbors.

13
Outline

• Introduction
• Preliminaries
• The approximation of MCDS (AMCDS) algorithm
• The dominant pruning (DP) algorithm
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

14
The approximation of MCDS (AMCDS) algorithm

• Step 1 At the start of the algorithm, all nodes
  are colored white and, then, the node with the
  maximum node degree is selected (put in set C)
  and colored black, and all of its neighbors are
  colored gray.
• Step 2 A recursive selection process runs until
  no white node exists Choose a gray node that has
  the maximum number of white neighbors. Color the
  selected node black and its white neighbors gray.

15
AMCDS algorithm (cont.)

• The drawback of this algorithm is that it needs
  to know the global network topology and,
  therefore, it is not suitable for ad hoc wireless
  networks.
• The result of the AMCDS algorithm can be used as
  the lower bound to compare with algorithm.

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Outline

• Introduction
• Preliminaries
• The approximation of MCDS (AMCDS) algorithm
• The dominant pruning (DP) algorithm
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

17
The dominant pruning (DP) algorithm(selection
process)

• 1. Let (empty list),
  (empty set) , and , where
  
• for .
• 2. Find set Si whose size is maximum in K. (In
  case of a tie, the one with the smallest
  identification I is selected.)
• 3. ,
  , and
  
• for all .
• If , exit otherwise, go to step
  2.

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The dominant pruning (DP) algorithm (cont.)

• F(u,v) is the forward bode list between sender v
  and receiver u.
• B(u,v)N(v)-N(u) to covers nodes in
  U(u,v)N(N(v))-N(v)-N(u).
• Z is a subset of U(u,v) and Si is the neighbor
  set of vi. K is the set of Si.
• Specifically, the greedy set cover algorithm is
  used for the selection of forward node.

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The dominant pruning (DP) algorithm (cont.)

• 1. Node v uses N(N(u)), N(u), and N(v) to obtain
  U(u, v) N(N(v)) - N(u) - N(v) and B(u, v)
  N(v) - N(u).
• 2. Node v then calls the selection process to
  determine F(u, v).

20
DP algorithm (graph.)
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Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• The total dominant pruning (TDP) algorithm
• The partial pruning dominant pruning (PDP)
  algorithm
• Termination criteria
• Performance evaluation
• Conclusions

22
The total dominant pruning (TDP) algorithm

• If node v can receive a packet piggybacked with
  N(N(u)) from node u, the 2-hop neighbor set that
  needs to be covered by vs forward node list F is
  reduced to U N(N(v)) N(N(u)).
• The total dominant pruning (TDP) algorithm uses
  the above method to reduce the size of U and,
  hence, to reduce the size of F.

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The total dominant pruning (TDP) algorithm (cont.)

• 1. Node v uses N(N(u)), N(u), and N(v) to obtain
  U(u, v) N(N(v)) N(N(u)) and B(u, v) N(v) -
  N(u).
• 2. Node v then calls the selection process to
  determine F.

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The total dominant pruning (TDP) algorithm
(theorem)

• Theorem 1. If a node w 2 N(N(v)) is also in
  N(N(u)), then w can be excluded from U.
• Proof consider all possible conditions of w
• w is 1-hop neighbor of the node u, then it has
  received broadcast packet during the transmission
  of u and v.
• w is 2-hop neighbor of the node u, then it will
  receive broadcast packets from the 1-hop neighbor
  of u like v.

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The total dominant pruning (TDP) algorithm
(theorem)

• Theorem 2. Let U N(N(v)) - N(N(u)) and
• B N(v) - N(u) then, U N(B).
• Proof by the concept of the complement set
• with x N(v) and Y N(U)

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The total dominant pruning (TDP) algorithm (graph)
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Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• The total dominant pruning (TDP) algorithm
• The partial pruning dominant pruning (PDP)
  algorithm
• Termination criteria
• Performance evaluation
• Conclusions

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The partial pruning dominant pruning (PDP)

• Besides excluding N(u) and N(v) from N(N(v)), as
  addressed in the DP algorithm, more nodes can be
  excluded from N(N(v)). These nodes are the
  neighbors of each node in .
  Such a node set is donated as
  .
• Therefore, the 2-hop neighbor set U in the PDP
  algorithm is
  .

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The partial pruning dominant pruning (PDP) (cont.)

• 1. Node v uses N(N(u)), N(u), and N(v) to obtain
  and
• U N(N(u)) - N(u) - N(v) P, and
• B N(v) N(u).
• 2. Node v then calls the selection process to
  determine F.

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The partial pruning dominant pruning (PDP)
(theorem)

• Theorem 3. Let
  
• U N(N(v)) - N(u) - N(v) P and B N(u)
  N(v), then .
• Proof by the concept of the set subtraction
• and
  with X N(u) and Y N(v). So,
  N(B) can cover U.

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The partial pruning dominant pruning (PDP) (graph)
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Example
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Result
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Result (cont.)
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Result (cont.)

• As the lower bound by using the AMCDS algorithm,
  the minimum connected dominating set is 2, 6, 7,
  11, so the number of forward nodes is 4.
• The number of the original DP is 8, TDPs is 5
  and PDPs is 6. (The more near global
  information, the better performance.)

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Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

37
Termination criteria

• The first one assigns a marked/unmarked status to
  each node.
• A node v is called marked if v has received a
  packet otherwise, v is called unmarked. We
  assume that, v knows the current marked/unmarked
  status of the nodes in N(v) at the time v decides
  its forward node list.
• When all nodes in N(v) are marked, v will stop
  rebroadcasting and discard the packet.

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Termination criteria (cont.)

• The second approach assigns a relayed/ unrelayed
  status to each node.
• A node v is called relayed when v has sent a
  packet otherwise, v is called unrelayed.
• Forward node v will stop rebroadcasting a packet
  only when v has sent that packet.

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Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

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Performance evaluation

• Static environment
• 400 randomly generated graph and parameters
• r the fixed transmitter range
• d the fixed average node degree (density)
• No contention in MAC layer

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Performance evaluation (No. of forward node)
Transmission range25/40 and use marked/unmarked
approach
15 improvement
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Performance evaluation (No. of forward node)
Transmission range55/70 and use marked/unmarked
approach
20 improvement
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Performance evaluation (No. of forward node)
Transmission range25/40 and use
relayed/unrelayed approach
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Performance evaluation (No. of forward node)
Average degree6/10 and use marked/unmarked
approach
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Performance evaluation (No. of forward node)
Average degree6/10 and use relayed/unrelayed
approach
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Performance evaluation (No. of received packets)
Transmission range25/40 and use marked/unmarked
approach
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Performance evaluation (No. of received packets)
Transmission range25/40 and use
relayed/unrelayed approach
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Performance evaluation (No. of received packets)
Average degree6/10 and use marked/unmarked
approach
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Performance evaluation (No. of received packets)
Average degree6/10 and use relayed/unrelayed
approach
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Performance evaluation (broadcast delivery rate)
Transmission range25/40 and No. of nodes100
X axis represents the speed of the nodes.
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Explanation of the result

• The larger transmission range the more covered
  neighborhood node information and can reduce more
  redundancy forward nodes.
• The higher degree the more redundancy
  transmission.
• Broadcast rate decreases as the speed of each
  node increases.

52
Explanation of the result (cont.)

• Performance AMCDSgtTDPgtPDPgtDP
• The marked/unmarked approach contains more
  neighbor information than relayed/ unrelayed
  approach and is better.

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Outline

• Introduction
• Preliminaries
• Enhanced dominant pruning algorithm
• Termination criteria
• Performance evaluation
• Conclusions

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Conclusions

• Original DP algorithm and improved TDP and PDP
  algorithm.
• Trade-off between broadcast redundancy (v.s the
  life of the ad hoc network) and broadcast
  delivery rate.
• Extend the proposed schema from 2-hops to k-hops.