1 Shuhui Yang, 1 Jie Wu, 2 Fei Dai
1 Department of Computer Science and Engineering Florida Atlantic University
2 Microsoft Corporation
< IEEE ICDCS 2007 >

• 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

• Broadcasting is the most frequently used operation for the dissemination of data and control messages in the preliminary stages of some other applications .
• The
D ominating S et (DS) has been widely used in the selection of an efficient virtual network backbone.
nodes in the set

• When a DS is connected, it is called a
C onnected D ominating
S et (CDS).
• CDS as a connected virtual backbone has been widely used for efficient broadcasting in MANETs.
nodes in the set

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

• 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 .
K
K -1
1
2
3 d c a b e d c a b f

• Sectors in the antenna model are not necessary aligned .
• The antenna uses the steerable beam techniques.

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

• 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 : v
’s dominating neighbor u u
’s dominating edge v ’s absorbant edge v u
’s absorbant neighbor

• 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

• 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 ).

• 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 priority than v .
– (2) u has a higher priority than v if there is no intermediate node.
t u w u w v v 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 z
26 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

• 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 ) v w p ( v
→ w ) = ( p ( v ), p ( w )) = p ( v ) + p ( w ) = 5 + 4 = 9 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 z
26 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

• 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 ) .
p ( v → u ) = 11 u p ( u
→ w ) = 10 v p ( v
→ w ) = 9 w 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 z
26 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

• 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.

• 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 S
P with all intermediate nodes and edges only from V’ and E’ , we prove that ( V’ , E’ ) is a DCDS.
s
S
P
• Prove by contradiction
– S
P
– S
P connecting s to d has at least one unmarked edge connecting s to d has at least one unmarked node d

• S
P connecting s to d has at least one unmarked edge.
R
P u’ s u w d
S
P
• After ECC, ( u
→ w ) has higher priorities than other paths .
• If ( u
→ w ) is an unmarked edge, it must exists a replacement path R
P that several intermediate edges in R priorities than ( u
→ w ).
P with higher
– Contradiction to ECC.

• S
P connecting s to d has at least one unmarked node.
R
P u’’ s u u’ w d
S
P
• If u' is unmarked node, it must exists a replacement path R
P that
– 1. several intermediate nodes on the R
P has a higher priority than
– 2. no intermediate nodes on the R
P
, u has a higher priority than u’ .
u’
.

s
u
R
P u’’ u’ w d
S
P
• After NCC, u’ has higher priorities than other nodes .
• If u’ is unmarked node, it must exists a replacement path R
P that several intermediate nodes on the R than u’
.
P has a higher priority
– Contradiction to NCC step 1.

s
R
P u u’ w d
S
P
• If u’ is unmarked node, it must exists a replacement path R
P that no intermediate nodes on the R
P than u’
.
, u has a higher priority
– NCC step 2 already exclude this situation.
– Contradiction to NCC step 2.

10
• 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
07
– (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
25
04
07 04

• 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
07
25
04

• Area : 100 x 100
• Communication Rang : 30

• Area : 100 x 100
• Communication Rang : 40 (Larger)

• Area : 100 x 100
• ECC with different h -hop local information.

• 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 .

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