A Clustering Approach for MANET Nodes Using Multiple Network Management Criteria

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A Clustering Approach for MANET Nodes Using
Multiple Network Management Criteria

• Boris Peltsverger Dean, School of CIS, Georgia
  Southwestern State University, USA
• Michael Bartolacci Associate Professor of IST,
  Penn State University Berks, USA
• Svetlana Peltsverger Assistant Professor of
  Computer Science, University of North Carolina
  Asheville, USA
• Vassiliki Cossiavelou Communication Secretary
  A, Greek Embassy, Beijing, China and Doctoral
  Candidate, Aegean University, Greece

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Clustering Network Nodes

• Utilized throughout the literature for both fixed
  line and mobile network nodes, mainly for ease of
  distributed routing of traffic
• Sivavakeesar and Pavlou (2005) Proposed a
  geographic region-based clustering of MANET nodes
  utilizing overlapping circular zones for routing
  purposes

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Clustering and Power Management

• Clustering Mobile Nodes can also be advantageous
  for power management purposes
• Cano and Manzoni (2001, 2002) utilized
  clustering for power management with a designated
  clusterhead node that facilitated power
  management within each cluster

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Clustering Based on a Single Goal

• Almost all of the approaches in the literature
  focus on a single goal with respect to the
  clustering of mobile nodes
• Only a few attempt to take into account more than
  one goal and those that do take only closely
  related secondary goals into account
• Such as hop minimization for routing and
  end-to-end average routing delays

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Proposed Approach for Clustering MANET Nodes

• Procedure allows for multiple network management
  criteria to be taken into account
• Uses Boolean operations on matrices to quickly
  and efficiently produce a clustering solution
  taking them into account
• Drawback is that priorities for criteria must be
  incorporated into the Boolean operations as
  opposed to traditional weighting schemes

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Clustering MANET Nodes
Each node of a MANET can be viewed as creating a
communication tree as its traffic is passed to
its neighboring nodes and then to other nodes
beyond those throughout the network. The trees
associated with all nodes in the network, when
overlaid, may show natural groupings or
clusterings of communicating nodes. This notion
of clusters can be expanded to include other
network parameters previously mentioned such as
power management.
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Example MANET

• Assume homogeneous nodes of varying levels of
  battery charge
• Channel assignments reduce interference between
  nodes at short distances
• 10 node network
• 2 clusters of nodes (parameter than can be tuned
  for larger networks)
• Full power transmission range of 70 meters for a
  given node (but is subject to noise at this
  distance and considered an unreliable signal)_

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Euclidean Distance Matrix (m)
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Battery Power Levels ( of full charge level)
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Network Conversion Procedure for Clustering

• Creates an adjacency matrix for each network
  management criterion chosen
• Adjacency matrices are then combined via logical
  operators into a single matrix, it is through the
  clever use of these operators that some
  rudimentary form of prioritization of criteria
  can be accomplished (such as using OR instead of
  AND before and after a given matrix in the string
  of matrices to be combined)

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Network Conversion Procedure for Clustering

• Traditional weighting schemes only add complexity
  to the clustering process, logical operators
  allow for ease of computation
• This final matrix is then utilized for
  identifying individual clusters of nodes via the
  algorithm developed by Peltsverger, et al (2004)

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First Network Management Criterion for Example MAN

• If nodal transmission reliability or a
  threshold/desirable S/N is considered
• If nodes are assumed to have a reliable
  transmission range or threshold/desirable S/N at
  a distance 30 meters or less
• Use this criterion to develop an adjacency matrix
  based on Euclidean distances

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Adjacency Matrix Based on Reliable Links
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Second Network Management Criterion for Example
MAN

• Battery power level
• Assumption that nodes with a battery power level
  of 30 of full charge or greater are reliable
  nodes
• Use this criterion to develop a second adjacency
  matrix assuming maximum power transmission range

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Adjacency Matrix Based on Battery Power Level
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Third Network Management Criterion for Example MAN

• Degree of a node (assuming links at the 30m
  reliable transmission range)
• Similar in nature to first criterion, but uses an
  arbitrary threshold of a degree quantity for a
  node to still be considered part of the network
  (in this example the threshold will be 3)
• Can ensure that geographic outlier nodes do not
  become integral parts of clusters (can be
  assigned to clusters after the fact or deemed
  clusters unto themselves)

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Adjacency Matrix Based on Reliable Nodal Link
Degree
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Logical Operators

• For this example MANET, we can approximate equal
  importance for all three criteria using only the
  logical operator AND when combining the matrices
  although in reality the sparsest of the matrices
  will impact the resulting matrix the most
• Matrix 1 AND Matrix 2 AND Matrix 3 yields a
  single adjacency matrix

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Combined Adjacency Matrix
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Identifying Clusters in the Combined Matrix

• The combined matrix forms a network that can be
  viewed as a graph
• The following different example illustrates the
  clustering algorithm developed by Peltsverger, et
  al (2004) that is performed on the graph
  depiction of the network for illustration purposes

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Some Definitions
Strong Component A strongly connected component
of a digraph is a maximal set of vertices in
which there is a path from any one vertex to any
other vertex in the set.
G1
G2
Condensed Graph Given a graph G, if two vertices
of G are identified and any loops or multiple
edges created by this identification removed, the
resulting graph is called the condensed graph.
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Some Definitions
Topological Order A topological ordering of a
digraph is a labeling of the vertices with
consecutive integers so that every arc is
directed from a smaller label to a larger label.
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1
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Isomorphic Two graphs are isomorphic if they are
the same graphs, drawn differently. Two graphs
are isomorphic if you can label both graphs with
the same labels so that every vertex has exactly
the same neighbors in both graphs. Here are two
isomorphic graphs
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Cluster Design
To illustrate the approach, we introduced a
network with 14 nodes. A final adjacency matrix
of reliable communications among the nodes is
represented on Fig.1. We made assumption that
we should have four clusters. The initial graph
G'' (Fig.1) and the optimal decomposition, graph
G (Fig.6), is represented below
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Generating Clusters Step 1
How to create subgroups?
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Step 1 of Clustering Algorithm

• Based on a final adjacency matrix W we can
  introduce a digraph G'' (V'', E''), where V''
  (v''1, v''2, , v''n) a set of vertices, E''
  (e''1, e''2, , e''q) a set of edges. We assume
  that all strong components of a graph G'' belong
  to one domain. Based on this assumption we can
  transform graph G'' to G' where vertices of G'
  are strong components of G''. G' contains no
  cycles and has low dimension (not greater) than
  graph G''.

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Generating Clusters Step 2
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Step 2 of Clustering Algorithm

• As a result of the transformation from G'' to G',
  a partial order has been introduced on the
  vertices of G'. The next step is to incorporate a
  linear order into an existing partial order. We
  can reach it by performing topological sorting.
  After this step we will get graph G with vertices
  that are in linear ordering and consequently the
  adjacency matrix of G is a lower (upper) triangle
  matrix. Below is a description of an algorithm
  for creating quasi decomposition of the graph G.

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Generating Clusters Step 3
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Step 3 of Clustering Algorithm

• Two graphs P and H are isomorphic if exists one
  to one correspondence, which saves adjacency. If
  A1 and A2 are adjacency matrices corresponding to
  different numeration of the same graph G then A1
  P-1 A2 P , where P pi,jn x n. pi,j 1 if
  a vertex i of graph G became vertex j of an
  rearranged isomorphic graph and pi,j 0
  otherwise .

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Step 4 of Clustering Algorithm

• The problem can also be formulated this way
  decompose a graph G to nonintersecting graphs G1,
  G2 Gm with a given number of vertices G1,
  G2, , Gm and a minimal number of edges among
  those graphs. Let us introduce squared
  submatrices (blocks) A1, A2 Am in adjacency
  matrix A of graph G with a given number of
  vertices G1, G2, , Gm respectively. This
  introduction identically defines a decomposition
  of graph G into nonintersecting graphs G1, G2
  Gm. Elements ai,j 1 of matrix A which do not
  belong to A1, A2 Am correspond to edges which
  connect subgraphs G1, G2 Gm.

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Generating Clusters Step 3
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Step 4 of Clustering Algorithm

• Changing the order of rows and columns in matrix
  A, we get different decompositions of graph G,
  because this rearrangement is equal to changing
  the numeration of the vertice in graph G.
  Resultant graph is defined by matrix P-1 A P,
  which will be isomorphic to graph G. In other
  words, to find an optimal decomposition of graph
  G we have to find the order ? vi1, vi2, , vin
  of vertices in which number of 1's out of
  diagonal blocks of P-1 A P will be minimal,
  where P is a matrix of permutations ?.

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Generating Clusters Step 4
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Step 5 of Clustering Algorithm

• To find the optimal decomposition, let us
  transform our initial matrix A into matrix A(?0)
  in with nonzero elements located as close as
  possible to the main diagonal. That is, we will
  find the vertices order ?0 of graph G which will
  have matrix A(?0) P-1 A P with minimal value of
  di max i - j for all ai,j ? 0 and j gt I for
  row i di is number of columns from column i till
  the last column j containing 1's (upper triangle
  matrix case).
• Building matrix A(?0) in this way gives a good
  possibility to get acceptable decomposition even
  under conditions of arbitrary forming of square
  submatrices Ai(?0), ( i 1, 2, , m ) of matrix
  A(?0), as in blocks Ai(?0) is combined the most
  tiered to each other vertices of graph G.

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Generating Clusters Step 5
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Step 6 of Clustering Algorithm

• Taking the current solution as initial and
  generating all cyclic permutations and
  corresponding transformation of matrix Ai(?0), (
  i 1, 2, , m ) can improve the given solution.

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Use of Resulting Clusters

• Since the model is quasi-static in nature,
  clusters define boundaries for paths for routing
  and other network management uses for a finite
  period of time
• As conditions change, clusters can be reformed
• Clusters can be layered

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Future Work

• More concrete examples of the advantages of the
  clustering approach
• Simulation testing of the approach on realistic
  networks

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Questions ?

• Michael Bartolacci
• mrb24_at_psu.edu