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
S
S
V
v
V
S
of
vertex
a
o
adjacent t
or
in
either
is
ex
every vert
such that
,
subset
vertex
a
is
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)
set
vertex
the
as
neighbors
their
of
all
and
S
in
vertices
the
includes
.
))
(
,
(
graph
the
is
)
(
by
induced
eakly
Subgraph w
w
w
S
xS
S
N
E
S
N
S
V
S
S
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
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