Ad Hoc Networks

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25 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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Algorithms For Clustering In
Ad Hoc Networks

Presented For Your Enjoyment By Team 4


Jim Kile


Don Little


Samir Shah

2

What Is An Ad Hoc Network?


Wireless computer network


No central control


Computers talking to each other


Suitable for


Conference rooms


Classrooms


Battlefields


Wearable computing

3

What Is Clustering In Ad
-
hoc
Networks?


Partitioning wireless device nodes
into groups


Each group has clusterhead


Oversee channel allocation


Message routing within cluster


Message routing between clusters


Ordinary nodes within the
clusterhead's transmission range

4

What Are Benefits Of Clustering?


Controlling spatial reuse of shared
channel


Building/maintaining cluster
-
based virtual
network architectures

5

What Are Benefits Of Clustering?

Routing


Minimizing amount of data exchanged
for routing


Lower cost


fewer routes


Simplify routing tables/structure


Abstract network structure


Higher level structure unaffected by local
topology changes

6

What Are Goals Of Clustering?

1)
At least 1 neighboring clusterhead

Allows fast communications between nodes

2)
Nodes connected to “best" clusterhead

3)
Clusterheads well scattered throughout
the network

7

Why Is Clustering Important?

Infrastructure


Wired


Well defined infrastructure


Network structure is static


Link failure is infrequent


Wireless


Infrastructure
-
less


Rapid topology change


Frequent link failures


Routes calculated frequently

8

Why Is Clustering Important?

Range


Wired


Transmission range is large


Each node responsible for


Its own communications


Wireless


Transmission range is small relative to network size


Each node responsible for:


Its own communications


Forwarding communication from others (
multihop
)

9

Why Is Clustering Important?

Power


Wired


Virtually unlimited power


Wireless


Very limited power

10

Why Is Clustering Important?

Routing Algorithm


Wired


Pre
-
calculated routing algorithm


Designed for relatively stable networks


Wireless


New algorithm


Designed for


Mobile units


Topology continuously changing

11

How are Clusters Represented?


Graph G = (V E)


Vertices (V) represent individual nodes


Edge (E) connection between two vertices
within range

12

Abstracting Network Topology

BLUE = network structure

BLACK VERTICES = clusterheads

BLACK EDGES = virtual connections
between clusters

13

How Are Clusterheads Chosen?

Approximating Minimum Size Weakly
-
Connected Dominating Sets For Clustering
Mobil Ad Hoc Networks


Criterion: domination

in graphs



Distributed Clustering For Ad Hoc Networks


Criterion: generic weight

FIRST PAPER

Approximating Minimum Size
Weakly
-
Connected Dominating
Sets For Clustering Mobil Ad Hoc
Networks

Paper’s Main Contribution

“Finding a completely distributed
algorithm for identifying small weakly
connected dominating set’s”

16

Algorithms Presented


Presented 5 algorithms


Analyzed 2 algorithms


Their most important algorithm covered
here


Algorithm V Distributed Asynchronous
Approach

17

Dominating Set Of A Graph

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S
V
v
V
S

of
vertex
a

o
adjacent t
or

in
either

is

ex
every vert
such that

,
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vertex
a

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E)
(V,

G
graph

a

of
set

dominating
A



18

Black Vertices Form Dominating Set

19

Black Vertices Form Dominating Set


Vertices of dominating set =
clusterheads


Assign each vertex to cluster
corresponding to dominating vertex


Optimize smallest dominating set


Simplify the network structure


Finding a minimum size dominating set
in a general graph is np
-
complete

20

Connected Dominating Set (CDS)


Dominating set whose induced subgraph
is connected


Induced subgraph used for routing
messages between clusters


Connectivity requirement causes large
number of clusters


Finding minimum size connected
dominating set is NP
-
complete

21

Connected Dominating Set

BLUE = network structure

BLACK VERTICES = clusterheads

BLACK LINES = induced subgraph

22

Weakly
-
Connected Dominating Set
(WCDS)





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includes


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23

Weakly
-
Connected Dominating Set
(WCDS)


Remove edges


Resulting in a sparser structure


Can
y
ield fewer clusters than CDS

24

Desired Graph Properties


Goal is to find a small weakly
-
connected
dominating set in order to abstract the
network structure as much as possible


Smaller values are preferred


Improvement

number of pieces that
would be merged into a single cluster if
that piece

were clusterhead

25

Assumptions


We assume every node knows the role
and piece ID information of all its
neighbors


Each device has own internal decision
mechanism to determine its own (local)
best candidate


Multiple clusterheads are grown in
parallel

26

How Are Node Roles Shown?


Algorithms uses color to display role of
the vertex


White


not assigned to any cluster


Grey


assigned to a cluster but not
clusterhead


Black


clusterhead

27

Algorithm
-

Beginning


Each node starts out NOT
connected to any other node


Initially white
-
not connected to cluster


Change color as the algorithm progresses

28

Algorithm
-

Each Iteration


Gray and white node calculate cluster
size if they were the clusterhead


Node with largest improvement in its
closed neighborhood is new clusterhead


Chosen candidate node colored black


Neighboring white vertices


Colored gray
-

member of cluster


Merged into the cluster

29

Algorithm
-

Termination


Algorithm terminates when no piece
shows improvement


Black vertices constitute a Weakly
-
Connected Dominating Set

30

Prior To First Iteration

31

After First Iteration

32

Author’s Evaluation Methodology


Generate random graphs repeatedly


Ran this algorithm against test algorithm
from others


Compute dominating set size


Smallest dominating set is best

33

Author’s Evaluation Setup


Place vertices randomly in a rectangular area
in 2D
-
plane


Two levels of density


40 to 200 vertices


Assign each node a transmission range


According to a normal distribution


Centered at a predefined expected value


When two nodes are placed within range of
each other


An edge is added between the vertices


Simulates a reliable link between them

34

Author’s Evaluation Conclusion


For each randomly generated network


Measure the dominating set size resulting
from the algorithms


Authors believe demonstrated that their
algorithm generated smaller dominating
sets

35

Why They Are Wrong*


No reason to believe that algorithm
achieved optimum placement


Could be local optima


No reason to believe that algorithm they
tested against is ideal


Evaluated in 2D world


Does this generalize to 3D world?

*terminology per Dr Cha

SECOND PAPER

Distributed Clustering For Ad Hoc
Networks

37

Algorithm Presented


Presented 2 algorithms


Selected the Distributed Clustering
Algorithm (DCA)

38

Clustering Based Upon Weight


Each node has arbitrary weight assigned


Allow designer to choose nodes that are
better suited for clusterhead role


Hand carried devices would have a lower
weight than vehicle carried devices


Clusterhead has largest generic weight
in the neighborhood

39

Desired Graph Properties

1)
Every ordinary node has at least a
clusterhead as neighbor (dominance
property)

2)
Every ordinary node affiliates with the
neighboring clusterhead that has the
bigger weight

3)
No two clusterheads can be neighbors
(independence property)

40

Assumptions


Same as first paper


Author emphasis that sole knowledge of
the topology local to each node

41

Algorithm


At startup each node announces its
weight


Nodes with the highest weigh announce
that they are clusterheads


Nodes with lower weights join clusters


Node decides which role to assume only
when all its neighbors with bigger
weights have decided their own roles

42

Author’s Evaluation


Easy to implement


Time complexity


Changing topology of the ad hoc network


Rather than size of the network

43

Why They Are Wrong*


Weights would be difficult to assign a
priori


No reason to believe that algorithm
achieved optimum placement


Could be local optima


No demonstration that algorithm worked

*terminology per Dr Cha

44

Presenter’s Discussion

Same


Node decides its own role (clusterhead or
ordinary node)


Knowing its current one hop neighbors


As opposed to the knowledge of one and two hop
neighbors as required by previous algorithms


Both algorithms are executed at each node


Assumes nodes know identity of the one hop
neighbors


Organizes network with same clustering
structure

45

Presenter’s Discussion

Different


Paper 1


Metric is smallest number of clusters


Evaluation based upon creating clusters with
the largest possible number of nodes


Metric calculated by nodes


Paper 2


Uses arbitrary weight assigned to each node


Weight represents its ability to be a clusterhead