Instructor: Dr. Yinghsu Li Presented by: Chinh Vu

1. On Calculating Connected Dominating Set for Efficient Routing in Ad Hoc Wireless NetworksBy J. Wu and H. Li Instructor: Dr. Yinghsu Li Presented by: Chinh Vu

2. Algorithm • Marking Process • To find CDS • Prune redundant nodes from CDS • To reduce the size of CDS

3. 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 Example N(A) = {B,D}, N(B) = {A,C,D}, N(C) = {B, E}, N(D) = {A, B}, N(E) = {C}

4. Marking Process - Analysis Theorem: • 1) Given a G = (V,E) that is connected, but not completely connected, the vertex subset V’, derived from the marking process, forms a dominating set of G 2) The reduced graph G’ = G [V’] is a connected graph ◊ this marking process derives a CDS

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

6. Prune redundant nodes from CDS • Rule 1:Considers two vertices v and u in G’. If N[v] N[u], and id(v) < id(u), unmark v.

7. 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.

8. Update/Recalculate CDC Topological changes of an ad hoc wireless networks due to: • Mobile host’s switch on • Mobile host’s switch off • Mobile host’s movement

9. Mobile host’s switch on • When node v switches on, only its non-gateway neighbors need to update their status

10. Corresponding Marking Process • v broadcasts to its neighbors about its switch on • Each host w N[v] exchanges its open neighbor set N(w) with its neighbors • Mark v if there are 2 unconnected neighbors • Mark each non-gateway w N(v) if it has 2 unconnected neighbors • Apply Rule 1 and Rule 2

11. Mobile host’s switch off • Only gateway neighbors of the switched off host need to update their status

12. Corresponding Marking Process • v broadcasts its neighbors about its switching off • Each gateway neighbors that belongs to N(v) exchanges its open neighbors set • Unmark gateway if all neighbors are pairwise connected

13. Performance Evaluation • Can have trivial CDS • Time complexity: • Message complexity: • No guarantee to generate MCDS

14. Simulation result • Average number of gateway nodes relative to the number of nodes

15. Simulation result • Average number of gateway nodes relative to the radius r.