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

Dominating set -2- Csc8980 – Fall 2008 Algorithm  Marking Process o To find CDS  Prune redundant nodes from CDS o To reduce the size of CDS

Dominating set -3- Csc8980 – Fall 2008 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}

Dominating set -4- Csc8980 – Fall 2008 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

Dominating set -5- Csc8980 – Fall 2008 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

Dominating set -6- Csc8980 – Fall 2008 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.

Dominating set -7- Csc8980 – Fall 2008 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. Prune redundant nodes from CDS

Dominating set -8- Csc8980 – Fall 2008 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

Dominating set -9- Csc8980 – Fall 2008 Mobile host’s switch on When node v switches on, only its non-gateway neighbors need to update their status

Dominating set -10- Csc8980 – Fall 2008 Corresponding Marking Process 1.v broadcasts to its neighbors about its switch on 2.Each host w N[v] exchanges its open neighbor set N(w) with its neighbors 3.Mark v if there are 2 unconnected neighbors 4.Mark each non-gateway w N(v) if it has 2 unconnected neighbors 5.Apply Rule 1 and Rule 2

Dominating set -11- Csc8980 – Fall 2008 Mobile host’s switch off Only gateway neighbors of the switched off host need to update their status

Dominating set -12- Csc8980 – Fall 2008 Corresponding Marking Process 1.v broadcasts its neighbors about its switching off 2.Each gateway neighbors that belongs to N(v) exchanges its open neighbors set 3.Unmark gateway if all neighbors are pairwise connected

Dominating set -13- Csc8980 – Fall 2008 Performance Evaluation Can have trivial CDS Time complexity: Message complexity: No guarantee to generate MCDS

Dominating set -14- Csc8980 – Fall 2008 Simulation result Average number of gateway nodes relative to the number of nodes

Dominating set -15- Csc8980 – Fall 2008 Simulation result Average number of gateway nodes relative to the radius r.