Design and Analysis of an MST-Based Topology

Control Algorithm

Ning Li, Jennifer C. Hou, and Lui Sha

Department of Computer Science

University of Illinois

IEEE Infocom 2003

Outline Introduction The MST-BASED Topology Control Algorithm

Design Guideline The LMST Algorithm (Local Minimum Spanning Tree)

Properties of LMST Performance evaluation Conclusion

Introduction Topology control and management

Consuming minimum possible power Mitigate interference Optimize network spatial reuse Maintain network connectivity

Introduction The contributions of this paper

LMST preserves the network connectivity The degree of any node in the resulting topology is

bounded by 6 The resulting topology can be converted into one with only

bi-directional links

A B

The MST-BASED Topology Control Algorithm- Design Guideline

Network connectivity The algorithm should be distributed Bi-directional links Small node degree

The MST-BASED Topology Control Algorithm- The LMST Algorithm

Information Exchange Topology Construction Construction of Topology with only Bi-directional

Edges

The LMST Algorithm Each node has the same maximum transmission range dmax

G=(V,E) V is the set of nodes in the network

VvudvudvuE ,,,:, max

u v

dmax

d(u,v)

vu vu

vwwuvu n ...: 1

vwwuvu n ...: 1

u v u v

Information Exchange This is obtained by having each node broadcast a

HELLO message using its maximal transmission power Node ID Position

Topology Construction Each node u applies Prim’s Algorithm to obtain its Local

Minimum Spanning Tree Power efficient minimum spanning tree Tu=(V(Tu),E(Tu))

2,* rdcPower r

Topology Construction- unsymmetrical links

Construction of Topology with only Bi-directional Edges Enforce all the uni-directional links in G0 to become bi-

directional

To delete all the uni-directional links in G0

)(,)(,:, 000 GEuvandGEvuvuE

)(,)(,:, 000 GEuvorGEvuvuE

000 , EVG

00 VV

000 , EVG

00 VV

Properties of LMST Properties of G0

Degree bound Network connectivity

G0+ and G0

- preserve Properties of G0

Properties of LMST- Degree bound

u

w

v

d(u,v) > d(u,w)d(u,v) > d(v,w)

vu

Properties of LMST- Degree bound

121 uwwxuw uwwuxw 121

X),(),( 11 xwduwd

),(),( 1 xuduwd

Properties of LMST- Network connectivity

V, u,vu,vir For any pa

v then udu,vIf d max vwwu n ...1

u1 v1 u2 v2

uk-1 vk-1

…

uk vk…

w

pairs ere are k suppose th

Properties of LMST- G0

+ and G0- preserve Properties of G0

The degree of any node in G0

+ is bounded by 6

G0

- preserves the connectivity of G0

000 , EVG

000 , EVG

Properties of LMST- G0+

Properties of LMST- G0+

uv

w

uv

w

uv

w

uv

w

600- 600-

600- 600-

d(u,w)>d(u,v)

d(w,v)>d(u,w)

d(w,v) is the longest

d(w,v)>d(u,w)d(w,v)>d(u,v)

d(w,v) is the longest

Performance evaluation- Related works

CBTC- Cone Based Topology Control- CBTC(5л/6)

R&M- relay region ,enclosure region

Performance evaluation dmax=250m

100 nodes

1000m*1000m region

Performance evaluation

Performance evaluation

Performance evaluation

Performance evaluation

Performance evaluation

Performance evaluation

Conclusion A decentralized MST-based topology control

algorithm is proposed The topology derived preserves the network

connectivity The degree of any node in the topology is bounded by

6