Efficient Backbone Construction Methods in MANETs Using Directional Antennas

1Shuhui Yang, 1Jie Wu, 2Fei Dai

1Department of Computer Science and Engineering Florida Atlantic University2Microsoft Corporation

< IEEE ICDCS 2007 >

Outline

• Introduction– Network Backbone ( DS、 CDS、 DCDS )

– Antenna Module

• Goal

• Backbone Construction Method– Node coverage condition (NCC)

– Edge coverage condition (ECC)

– Sector optimization (SO)

• Proof for Directional Connected Dominating Set

• Simulation Results

• Conclusions

Introduction - DS

• Broadcasting is the most frequently used operation for the dissemination of data and control messages in the preliminary stages of some other applications.

• The Dominating Set (DS) has been widely used in the selection of an efficient virtual network backbone.

nodes in the set

Introduction - CDS

• When a DS is connected, it is called a Connected Dominating Set (CDS).

• CDS as a connected virtual backbone has been widely used for efficient broadcasting in MANETs.

nodes in the set

Introduction - DCDS

• The use of directional antenna systems helps to – improve channel capacity as well as conserve energy since the sig

nal strength towards the direction of the receiver can be increased.

• Due to the constraint of the signal coverage area, interference can also be reduced.

a

b

nodes in the set

Introduction - Antenna Module

• A common directional antenna model involves dividing the transmission range of a node into K identical sectors.

• All nodes use a directional antenna for transmission and an omnidirectional antenna for reception.

a

d

c b

12

3

K

K-1a

bc

d

e

f

Introduction - Antenna Module

• Sectors in the antenna model are not necessary aligned.

• The antenna uses the steerable beam techniques.

Goal - minimum DCDS

• To find the minimum DCDS in directed network graph.– The problem of finding the smallest connected subgraph (CDS) in te

rms of number of edges in a given strongly connected graph (G) is NP-complete.

– Heuristic localized solutions to find the minimum DCDS in network graph (NP-complete).

• DCDS is a set of selected nodes and their associated selected edges.

nodes in the set

u v

Backbone Construction Method

• Each node has its unique ID.

• Each node sends out "Hello" messages K times to the K directions and accomplishes the directional neighborhood discovery.

• Dominating and Absorbant :

u’s dominating edgev’s absorbant edge

u’s absorbant neighborv’s dominating neighbor

Backbone Construction Method

• Authors propose an heuristic localized solutions to select forwarding nodes and edges for the DCDS.

• The status of each node depends on its h-hop topology only for a small constant h, and is usually determined after h rounds of "Hello" message exchange among neighbors.

• The given directed graph is strongly connected.– The graph is a directed graph with symmetric connectivity.

u v

Backbone Construction Method

• Using NCC (Node Coverage Conditions) and ECC (Edge Coverage Conditions) to unmark the nodes and directed edges.– unmarked nodes and directed edges : not in the DCDS.

– marked nodes and directed edges : in the DCDS.

• Some node properties can be used as node priority in NCC and ECC.– Energy Level

– Node Degree

– Node IDs (unique)

• Author assume that the priority of node u is p(u) based on the alphabetic order, such as p(u) > p(v) > p(w) > p(x).

Backbone Construction Method - NCC

• A node v is unmarked if, for any two dominating and absorbant neighbors, u and w, a directed replacement path exists connecting u to w such that– (1) each intermediate node on the replacement path has a higher pr

iority than v.

– (2) u has a higher priority than v if there is no intermediate node.

u

v

w

t

u

v

w

p(t) > p(v) p(u) > p(v)

a b c d e f g h i j k l m n o p q r s t u v w x y z26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01

Backbone Construction Method - ECC

• Edge Priority Assignment.– For each edge (v → w), the priority of this edge is p(v → w)

= (p(v), p(w)) = p(v) + p(w)

a b c d e f g h i j k l m n o p q r s t u v w x y z26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01

v w

p(v → w) = (p(v), p(w)) = p(v) + p(w) = 5 + 4 = 9

Backbone Construction Method - ECC

• Each marked node uses the edge coverage condition to determine the status of its dominating edges.– Edge (v → w) is unmarked if a directed replacement path exists

connecting v to w via several intermediate edges with higher priorities than (v → w).

v w

u

p(v → w) = 9

p(u → w) = 10p(v → u) = 11

p(v → u) > p(v → w) and p(u → w) > p(v →

w) a b c d e f g h i j k l m n o p q r s t u v w x y z26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 09 08 07 06 05 04 03 02 01

Backbone Construction Method - SO

• Sector Optimization (SO)– Align the edge of one sector to each selected forwarding edge, and

determine the one with the smallest number of switched-on sectors.

Proof for DCDS

• Before NCC and ECC : G ( V , E )

• After NCC and ECC : G’ ( V’ , E’ )

• Proof : Any two nodes s ∈ V’ and d ∈ V , there is a path SP with all intermediate nodes and edges only from V’ and E’, we prove that (V’, E’) is a DCDS.

• Prove by contradiction– SP connecting s to d has at least one unmarked edge

– SP connecting s to d has at least one unmarked node

s d

SP

Proof for DCDS

• SP connecting s to d has at least one unmarked edge.

• After ECC, (u → w) has higher priorities than other paths.

• If (u → w) is an unmarked edge, it must exists a replacement path RP that several intermediate edges in RP with higher priorities than (u → w).– Contradiction to ECC.

s d

SP

RP

u w

u’

Proof for DCDS

• SP connecting s to d has at least one unmarked node.

• If u' is unmarked node, it must exists a replacement path RP that

– 1. several intermediate nodes on the RP has a higher priority than u’.

– 2. no intermediate nodes on the RP, u has a higher priority than u’.

s

SP

RP

u w

u’’

du’

Proof for DCDS

• After NCC, u’ has higher priorities than other nodes.

• If u’ is unmarked node, it must exists a replacement path RP that several intermediate nodes on the RP has a higher priority than u’.– Contradiction to NCC step 1.

s

SP

RP

u w

u’’

du’

Proof for DCDS

• If u’ is unmarked node, it must exists a replacement path RP that no intermediate nodes on the RP, u has a higher priority than u’.– NCC step 2 already exclude this situation.

– Contradiction to NCC step 2.

s d

SP

RP

u wu’

Examples

• NCC– (10) ： (25) → (07) ， P(25)>P(10) ，

可取代 (25) → (10) → (07) ， (10) unmarked

– (07) ： (25) → (10) ， P(25)>P(07) 可取代 (25) → (07) → (10) ， (07) unmarked

– (04) ： (25) → (07) ， P(25)>P(04) ，可取代 (25) → (04) → (07) ， (04) unmarked

– (25) ：找不到 優先權更大的路徑可取代， (25) marked

– 不考慮 (10) 、 (07) 、 (04) 的 dominating edge

10 25

0407

10 25

0407

Examples

• ECC– (25)→(10) ， P(25)+P(10) =35 ，

(25)→(07)→(10) 優先權： 32<35 、 17<35(25)→(10) marked.

– (25)→(07) ， P(25)+P(07) =32 ，(25)→(04)→(07) 優先權： 29<32 、 11<32 (25)→(10)→(07) 優先權： 35 、 17<32 (25)→(07) marked.

– (25)→(04) ， P(25)+P(07) =29 ，(25)→(07)→(04) 優先權： 32 、 11<29(25)→(04) marked.

10 25

0407

Simulation Results

• Area : 100 x 100

• Communication Rang : 30

Simulation Results

• Area : 100 x 100

• Communication Rang : 40 (Larger)

Simulation Results

• Area : 100 x 100

• ECC with different h-hop local information.

Conclusions

• Using directional antennas, constructing a directional network backbone in MANETs further reduces total energy consumption as well as reducing interference in broadcasting applications.

• A heuristic localized algorithm for constructing a small DCDS is proposed.

• The sector optimization algorithm is developed for the second phase.

• Our future work includes some extensions of the ECC algorithm, such as applying ECC to topology control.

The End

THANK YOUTHANK YOU