1. CLUSTERING SCHEMES FOR MOBILE AD HOC NETWORK Speaker ： Fu-Yuan Chuang Advisor ： Ho-Ting Wu Date ： 2006.04.25

2. Outline Introduction Clustering Scheme Overview Classifying Clustering Schemes DS-based clustering  Wu’s CDS Algorithm  Chen’s WCDS Algorithm Summary of DS-based Clustering

3. Introduction Dynamic routing is the most important issue in MANETs A flat structure encounters scalability problem Proactive routing protocols is O(n^2) Reactive routing sheme:  RREQ flooding over the whole network  Route setup delay A hierarchical architecture

4. Clustering Scheme Overview Virtual group Clusterhead  a local coordinator, performing intra-cluster transmission arrangement, data forwarding Clustergateway  non-clusterhead node with inter-cluster links access neighboring clusters, forward information between clusters Clustermember  ordinary node, non-clusterhead node without any inter- cluster links

6. Three Benefits spatial reuse of resources to increase the system capacity  the same frequency or code set routing  The generation and spreading of routing information can be restricted in the set of clusterheads and clustergateways an ad hoc network appear smaller and more stable in the view of each mobile terminal  when a mobile node changes its attaching cluster, only nodes residing in the corresponding clusters need to update the information

7. The cost of clustering (1/3) Explicit control message for clustering  Clustering requires explicit clustering-related information exchanged between node pairs Ripple effect of re-clustering  The re-election of a single clusterhead may affect the cluster structure of many other clusters and completely alter the cluster topology over the whole network

8. The cost of clustering (2/3) Stationary assumption for cluster formation  Assume that mobile nodes keep static when cluster formation is in progress Constant Computation round  Computation round is the number of rounds that a cluster formation procedure

9. The cost of clustering (3/3) Communication complexity  The total amount of clustering-related message exchanged for the cluster formation

10. Classifying Clustering Schemes(1/3) DS-based clustering  Finding a (weakly) connected dominating set to reduce the number of nodes participating in route search or routing table maintenance Low-maintenance clustering  Providing a cluster infrastructure for upper layer applications with minimized clustering-related maintenance cost

11. Classifying Clustering Schemes(2/3) Mobility-aware clustering  Utilizing mobile nodes’ mobility behavior for cluster construction and maintenance and assigning mobile nodes with low relative speed to the same cluster to tighten the connection in such a cluster Energy-efficient clustering  Avoiding unnecessary energy consumption or balancing energy consumption for mobile nodes in order to prolong the lifetime of mobile terminals and a network

12. Classifying Clustering Schemes(3/3) Load-balancing clustering  Distributing the workload of a network more evenly into clusters by limiting the number of mobile nodes in each cluster in a defined range Combined-metrics-based clustering  Considering multiple metrics in cluster configuration, including node degree, mobility, battery energy, cluster size

13. DS-based clustering A dominating set of a graph G= (V, E) is a vertex subset S ⊆ V, such that every vertex v ∈ V is either in S or adjacent to a vertex of S A connected dominating set (CDS) of a graph G is a dominating set whose induced graph is connected

15. DS-based clustering(cont.) Table-driven routing  Only codes in the CDS are required to construct and maintain the routing tables On-demand routing  The route search space is limited to the CDS To keep a DS connected and with approximately minimum size is not a trivial task

16. DS-based clustering Algorithm Wu’s CDS Algorithm Marking Process  To find CDS Prune redundant nodes from CDS  To reduce the size of CDS

17. Marking Process Define a network as a graph G = (V,E) Initially, all nodes are unmarked Every v exchanges its N(v) with all its neighbors Mark v if there exists 2 unconnected neighbors

18. Example A B C E D Open neighbors set of all nodes: N(A) = {B,D} N(B) = {A,C,D} N(C) = {B, E} N(D) = {A, B} N(E) = {C} After step 2: A: N(B), N(D) B: N(A), N(C), N(D) C: N(B), N(E) D: N(A), N(B) E: N(C)

19. Prune redundant nodes from CDS Assign a distinct id, id(v) to each vertex v in G Define N[v] as a closed neighbor set of v

20. Prune redundant nodes from CDS Rule 1: Considers two vertices v and u in G ’. If N[v] N[u] in G, and id(v) < id(u), change the marker of v to F if node v is marded

21. Prune redundant nodes from CDS Rule 2: Assume u and w are two marked neighbors of marked vertex v in G ’. If N(v) N(u) U N(w) in G and id(v) = min{id(v), id(u), id(w)}, then unmark v.

22. DS-based clustering Algorithm Chen’s WCDS Algorithm Reduce the number of clusters by relaxing the connectivity requirement The subgraph weakly induced by S(S ⊆ V) is the graph w=(N [S], E ∩ (N [S]×S)). w includes the vertices in S and all of their neighbors as vertex set The edges of w are all edges of G which have at least one end point in S

23. Weakly induced subgraph (example) Vertex set: black vertices Edge set: black lines

24. Weakly-connected dominating set A vertex subset S is a weakly-connected dominating set (WCDS), if S is a dominating set and w is connected

25. Algorithms for finding small WCDS Algorithm I and II: Two centralized algorithms Algorithm III and IV: Distributed Implementations of Algorithm I and II Algorithm V: Distributed Asynchronous Approach

26. Chen’s WCDS Algo I (overview) Given a graph G=(V,E), each vertex is associated with a color (white, gray, or black) All vertices are initially colored white In each iteration, the algorithm color a white or gray vertex black and all its neighboring white vertices gray At the end, the black vertices form a weakly- connected dominating set

27. Term: piece Piece refers to a particular substructure of the graph A white piece is simply a white vertex A black piece contains a maximal set of black vertices whose weakly induced subgraph is connected plus any adjacent gray vertices The pieces are indicated by dotted regions

28. Term: improvement The improvement of a (non-black) vertex u is the number of pieces that would be merged into a single black piece if u were to be dyed black In last example, dying vertex 5 black would merge 4 piece, while dying vertex 4 would merge 3 pieces

29. Chen’s WCDS Algo I(detail) In each iteration, the algorithm choose a single white or gray vertex to dye black The vertex is chosen greedily: a vertex with maximum improvement is chosen Until there is only one piece left

30. Initially, all nodes are white 7 7 4 5 3 3 3 5 5 4 3 5 5 4 4 4 7 3 5 6

31. First Iteration 7 7 4 5 3 3 3 5 5 4 3 5 4 4 4 7 3 5 5 6

32. 2 3 3 3 5 5 4 3 5 4 4 4 3 3 5 2

33. Second Iteration 2 3 3 5 5 4 3 5 4 4 4 3 3 5 2

34. 2 3 3 3 2 5 4 4 4 3 3 5 2

35. Third Iteration 2 3 3 3 2 5 4 4 4 3 3 5 2

36. 2 3 3 3 4 3 3

37. Fourth Iteration 2 3 3 3 4 3 3

38. 2 3 3 2

39. Last Iteration

40. Summary of DS-based Clustering

42. References J. Y. YU and P. H. J. CHONG, "A Survey of Clustering Schemes for Mobile Ad Hoc Networks," IEEE Communications Surveys and Tutorials, First Quarter 2005, Vol. 7, No. 1, pp. 32--48. J. Wu and H. L. Li, “On Calculating Connected Dominating Set for Efficient Routing in Ad Hoc Wireless Networks,” Proc. 3rd Int’l. Wksp. Discrete Algorithms and Methods for Mobile Comp. and Commun., 1999, pp. 7–14 Y.-Z. P. Chen and A. L. Liestman, “Approximating Minimum Size Weakly-Connected Dominating Sets for Clustering Mobile Ad Hoc Networks,” in Proc. 3rd ACM Int’l. Symp. Mobile Ad Hoc Net. & Comp., June 2002, pp. 165–72.