1. 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

2. Outline  Introduction  The MST-BASED Topology Control Algorithm Design Guideline The LMST Algorithm (Local Minimum Spanning Tree)  Properties of LMST  Performance evaluation  Conclusion

3. Introduction  Topology control and management Consuming minimum possible power Mitigate interference Optimize network spatial reuse Maintain network connectivity

4. 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 AB

5. The MST-BASED Topology Control Algorithm- Design Guideline  Network connectivity  The algorithm should be distributed  Bi-directional links  Small node degree

6. The MST-BASED Topology Control Algorithm- The LMST Algorithm  Information Exchange  Topology Construction  Construction of Topology with only Bi-directional Edges

7. The LMST Algorithm  Each node has the same maximum transmission range d max  G=(V,E) V is the set of nodes in the network  u v d max d(u,v) u v u v

8. Information Exchange  This is obtained by having each node broadcast a HELLO message using its maximal transmission power Node ID Position

9. Topology Construction  Each node u applies Prim’s Algorithm to obtain its Local Minimum Spanning Tree Power efficient minimum spanning tree T u =(V(T u ),E(T u ))

10. Topology Construction- unsymmetrical links

11. Construction of Topology with only Bi-directional Edges  Enforce all the uni-directional links in G 0 to become bi- directional  To delete all the uni-directional links in G 0

12. Properties of LMST  Properties of G 0 Degree bound Network connectivity  G 0 + and G 0 - preserve Properties of G 0

13. Properties of LMST- Degree bound u w v d(u,v) > d(u,w) d(u,v) > d(v,w)

14. Properties of LMST- Degree bound X

15. Properties of LMST- Network connectivity u1u1 v1v1 u2u2 v2v2 u k-1 v k-1 … ukuk vkvk … w

16. Properties of LMST- G 0 + and G 0 - preserve Properties of G 0  The degree of any node in G 0 + is bounded by 6  G 0 - preserves the connectivity of G 0

17. Properties of LMST- G 0 +

18. uv w uv w uv w uv w 60 0 - 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

19. Performance evaluation - Related works  CBTC- Cone Based Topology Control- CBTC(5л/6)  R&M- relay region,enclosure region

20. Performance evaluation d max =250m 100 nodes 1000m*1000m region

21. Performance evaluation

27. 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