On Reducing Broadcast Redundancy in Wireless Ad Hoc Network

Author: Wei Lou, Student Member, IEEE, and Jie Wu, Senior Member, IEEEFrom IEEE transactions on mobile computing April-June 2002 Presented By資管研一 R92725034 Lin Ming Yuan

Outline

Introduction Preliminaries Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

Introduction

Some characteristics of ad hoc networkWithout central infrastructureTemporary 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.

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

Introduction (cont.)

The problem of finding minimum forwarding nodes can be reduce to a dominant set problem which is NP.

Some previous algorithmBlinding flooding (broadcast storming problem)Dominating pruning (DP) algorithm

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)

Outline

Introduction Preliminaries

The approximation of MCDS (AMCDS) algorithm The dominant pruning (DP) algorithm

Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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

Preliminaries (redundancy problem)U is the sender.

The transmissions between v and w are redundant.

Outline

Introduction Preliminaries

The approximation of MCDS (AMCDS) algorithm The dominant pruning (DP) algorithm

Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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 .

))(()(}{ uNNuNu )(vNu

))(()( uNNuN

Assumption

2-hop neighborhood information can be obtained by periodic “Hello” packets, each of which contains the sender’s identification and the list of its neighbor.

In this paper, the author assumed that v (sender) and u (receiver) are neighbors.

Outline

Introduction Preliminaries

The approximation of MCDS (AMCDS) algorithm The dominant pruning (DP) algorithm

Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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.

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.

Outline

Introduction Preliminaries

The approximation of MCDS (AMCDS) algorithm The dominant pruning (DP) algorithm

Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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.

ZSK []),( vuF

),()( vuUvNS ii ),( vuBvi

kvvuFvuF ||),(),( iSZZ iSKK ijj SSS KS j ),( vuUZ

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.

)()(),( uNvNvuB

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).

DP algorithm (graph.)

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

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 v’s 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.

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.

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.

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 setwith x= N(v) and Y = N(U)

( ) ( ) ( )N X N Y N X Y

The total dominant pruning (TDP) algorithm (graph)

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

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 .

)()( vNuN ))()((),( uNuNNvuP

PvNuNuNNU )()())((

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.

))()((),( uNuNNvuP

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.

))()((),( uNuNNvuP

)(BNU

( ( )) ( ) ( ) ( ( ) ( )) ( ( )) ( ( ) ( ))N N v N v N u N N u N v N N v N N u N v

( ) ( ) ( ( )) ( )N X N X Y N X X Y N X Y

The partial pruning dominant pruning (PDP) (graph)

Example

Result

Result (cont.)

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, TDP’s is 5 and PDP’s is 6. (The more near global information, the better performance.)

Outline

Introduction Preliminaries Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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.

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.

Outline

Introduction Preliminaries Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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

Performance evaluation (No. of forward node)

Transmission range=25/40 and use marked/unmarked approach15% improvement

Performance evaluation (No. of forward node)

Transmission range=55/70 and use marked/unmarked approach20% improvement

Performance evaluation (No. of forward node)

Transmission range=25/40 and use relayed/unrelayed approach

Performance evaluation (No. of forward node)

Average degree=6/10 and use marked/unmarked approach

Performance evaluation (No. of forward node)

Average degree=6/10 and use relayed/unrelayed approach

Performance evaluation (No. of received packets)

Transmission range=25/40 and use marked/unmarked approach

Performance evaluation (No. of received packets)

Transmission range=25/40 and use relayed/unrelayed approach

Performance evaluation (No. of received packets)

Average degree=6/10 and use marked/unmarked approach

Performance evaluation (No. of received packets)

Average degree=6/10 and use relayed/unrelayed approach

Performance evaluation (broadcast delivery rate)

Transmission range=25/40 and No. of nodes=100

X axis represents the speed of the nodes.

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.

Explanation of the result (cont.)

Performance : AMCDS>TDP>PDP>DP

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

Outline

Introduction Preliminaries Enhanced dominant pruning algorithm Termination criteria Performance evaluation Conclusions

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.