C ONSTRUCTING A L OAD -B ALANCED V IRTUAL B ACKBONE IN W IRELESS S - - PowerPoint PPT Presentation

CONSTRUCTING A LOAD-BALANCED VIRTUAL BACKBONE IN WIRELESS SENSOR NETWORKS

Jing He*, Shouling Ji*, Pingzhi Fan**, Yi Pan*, Yingshu Li*

*Georgia State University **Southwest Jiaotong University

Presenter: Dr. Kai Xiang

OUTLINE

Background & Motivation Load-Balanced Virtual Backbones (LBVB)

Construction Problem

 Load-Balancedly Allocate Dominatees (LBAD)

Problem

Simulation Results Conclusions

2

WHAT IS DS?

A Dominating Set (DS) is a subset of all

the nodes such that each node is either in the DS or adjacent to some node in the DS.

3

Background & Motivation

WHAT IS CDS?

A Connected Dominating Set (CDS) is a

subset of the nodes such that it forms a DS and all the nodes in the DS are connected.

4

Background & Motivation

APPLICATION OF CDS: VIRTUAL BACKBONE

5

Virtual Backbone Flooding Reduction of communication

• verhead

Redundancy Contention Collision Reliability Unreliability

CDS is used as a virtual backbone in wireless networks.

Background & Motivation

RELATED WORK

 Constructing Minimum-sized CDS

(MCDS) --- NP-hard

 Subtraction-based: begin with the set of all

nodes in the network, then systematically remove nodes by some rules to obtain the CDS.

 Addition-based: start from a subset of

nodes, then include additional nodes to form the CDS.

6

Background & Motivation

VARIETY OF CDS

• k-connected m-dominating Set --- fault tolerance
• k-connectivity: between any pair of backbone nodes there exists

at least k independent paths

• m-domination: every dominatee has at least m adjacent

dominator neighbors

• Minimum Routing Cost CDS --- delivery delay
• It can guarantee that each routing path between any pair of nodes

is also the shortest path in the network.

• D-Hop Dominating Sets
• Minimum CDS with bounded Diameters

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Background & Motivation

OUR INTERESTS

 Load-Balanced Virtual Backbone (LBVB)

8

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8  MCDS LBVB Background & Motivation

OUR INTERESTS

 Load-Balancedly Allocate Dominatees (LBAD)

9

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8  Background & Motivation Unbalanced Allocation LBAD

MEASURE LOAD BALANCE OF A VIRTUAL BACKBONE

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LBVB

VB p-norm:

degree. mean the is dominator; each

• f

degree the is where ) | | ( | |

_ 1 1 _

d d d d D

i p M i p i p





 

1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 ) 3 3 ( ) 3 6 ( | |

2 2

    

p

D

2 ) 3 3 ( ) 3 4 ( ) 3 4 ( | |

2 2 2

      

p

D

10

PROBLEM DEFINITION

Load-balanced VB (LBVB) Problem:

For a WSN represented by graph G = (V, E), the LBVB problem is to find a node set , D = {s1, s2, ..., sM}, such that: 1) The induced graph is connected, Where . 2) and , such that . 3) .

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LBVB

11

V D  ) , ( ] [

'

E D D G  } ) , ( , , ), , ( | {

'

E v u D v D u v u e e E      V u  D u D v  E v u  ) , (

2 1 1 2 _

) | | ( | | min

 

 

M i i p

d d D

GREEDY ALGORITHM

12

2 2 4 6 2 4 3 1 2 2 4 6 2 4 3 1 2 2 4 6 2 4 3 1

3 



d

Greedy criterion:

| | min



 d di

LBVB

LOAD-BALANCEDLY ALLOCATE DOMINATEES

LBAD

 Allocated Dominatee Set: A(si)  Valid Degree: di’  Allocation p-norm: 13

1 1 3 1 1 1 1 1 1 1 2 1 1 2 1 1

3 5 3 3 8

_

   p

2.67 ) 3 5 1 ( ) 3 5 1 ( ) 3 5 3 ( | |

2 2 2

      

p

D 67 . ) 3 5 1 ( ) 3 5 2 ( ) 3 5 2 ( | |

2 2 2

      

p

D

. M M

• N

where , ) | | ( | |

_ 1 1 _ '

   



p p d D

M i p p i p

PROBLEM DEFINITION

Load-balancedly Allocate Dominatees (LBAD) Problem:

For a WSN represented by graph G = (V, E), and a VB D = {s1, s2, ..., sM}, the LBAD problem is to find M disjoint node sets on V, , such that: 1) Each set contains exactly one dominator si . 2) . 3) and , such that . 4) .

14 14

) ( ),......, ( ), ( ., .

1 1 M

s A s A s A e i ) 1 ( ) ( M i s A

i

  M) j i (1 ) ( ) ( , ) (

1

     

 j i i M i

s A s A V s A 



2 1 1 2 _

) | | ) ( || ( | | min

 

 

M i i p

p s A D

LBAD

M) i (1 A(s u

i

    )

i

s u  E s u

i 

) , (

CENTRALIZED ALGORITHM

 Expected Allocation Probability (pij): for each dominatee and

dominator pair, there is an pij, which represents the expected probability that the dominatee is allocated to the dominator.

 Constrained non-linear programming

15

LBAD

. dominatee the

• f

dominators neighoring

• f

number the is | ) ( | 1, , where , 1 , dominatee : Subject to , ) | (| ( | | : Minimize

_ | ) ( | 1 1 1 | ) ( | 1 _ i i ij s N j ij i M j p s A i p ij p

s s N p M M N p p s p p D

i j

       

  

  

15

DISTRIBUTED ALGORITHM

16

LBAD

16

1 1 1 5 1 2 2 1 1 1 3 3 1 2 2 1 2/7 5/7 3/8 3/8 1/4

' | ) ( | | ) ( | ' 2 2 ' 1 1

......

i i

s N s N i i i

d p d p d p   

 The distributed LBAD problem can be transformed to

calculate the pij value of each dominatee locally

SIMULATION SET UP

 N nodes are randomly deployed in a fixed area of 100m *100m.

All nodes have the same transmission range 10m.

 VB-based broadcasting used as the communication mode  Four different schemes are implemented  LBCDS with LBAD, noted by LB-A  LBCDS with the smallest ID dominator selection, noted by LB-ID  MIS-based CDS with LBAD, noted by MIS-A  MIS-based CDS with the smallest ID dominator selection, noted by

MIS-ID

Simulation

17

SIMULATION RESULTS

18

Simulation

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CONCLUSIONS

 For the LBVB problem, we design a greedy algorithm.  For the LBAD problem, we introduce a new term Expected

Allocation Probability. Based on the probability, we formulate the LBAD problem into a constrained non-linear programming optimization problem.

 For the LBAD problem, we also propose a probability-based

distributed algorithm.

 We conduct simulations to validate our proposed algorithms.

19

20

Q & A