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

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Algorithm

Marking Process

o To find CDS

Prune redundant nodes from CDS

o To reduce the size of CDS

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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}

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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

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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

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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.

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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

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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

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Mobile host’s switch on

When node v switches on, only its non-gateway neighbors need to update their status

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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

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Mobile host’s switch off

Only gateway neighbors of the switched off host need to update their status

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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

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Performance Evaluation

Can have trivial CDS

Time complexity:

Message complexity:

No guarantee to generate MCDS

)( 2

)( v

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Simulation result

Average number of gateway nodes relative to the number of nodes

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Simulation result

Average number of gateway nodes relative to the radius r.