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LOCI: Local Clustering Service for Large Scale Wireless Sensor Networks. Vineet Mittal. Committee Members: Dr. Anish Arora (advisor) Dr. Hakan Ferhatosmanoglu.

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loci local clustering service for large scale wireless sensor networks

LOCI: Local Clustering Service for Large Scale Wireless Sensor Networks

Vineet Mittal

Committee Members:

Dr. Anish Arora (advisor)

Dr. Hakan Ferhatosmanoglu

challenges in sensor networks
Challenges in Sensor Networks
  • Self-configuration
    • ad hoc node deployment
  • Self-healing
    • node failures, message loss and corruption
  • Scalability
    • large scale deployment and limited resources
hierarchical clustering
Hierarchical Clustering
  • Advantages
    • Network specific
      • facilitates distribution of control over the network
      • abstracts network state information: insulates changes and failures/joins in one part of the network from other parts
    • Application specific
      • energy efficient
challenges in clustering
Challenges in Clustering
  • Scalability
  • Local self-healing
  • Similar size clusters
  • Optimum number of overlaps between clusters
  • Minimum number of non-clustered nodes
  • Optimum number of clusters
  • Minimum communication overhead
problem statement
Problem Statement
  • Design a distributed, local, scalable, and self-stabilizing clustering program, LOCI, that given a cluster radius interval [R, mR],where R is the physical radius and m ≥ 2, constructs network partitions such that
    • a unique node is designated as a leader of the cluster
    • all nodes in the R-neighborhood of each leader belong to that cluster
    • maximum distance of a node from its leader is mR
    • each node belongs to the cluster of the closest clusterhead
outline
Outline
  • Model
  • LOCI Program
  • LOCI Correctness Proof
  • Theoretical Performance Analysis
  • Simulations based Performance Analysis
  • Conclusions
model
Model
  • Wireless sensor network
  • 2-D coordinate plane
  • Bi-directional links
  • Each node has a unique ID and unit transmission range
  • Distance estimation capability relative to other nodes
  • Density: nodes are distributed as per a homogeneous spatial Poisson process of intensity λ, such that at an average within a unit area circular region there are λ nodes
  • Fault model: nodes and links can fail-stop, new nodes and links can join the system, and state of a node can be arbitrarily corrupted.
outline1
Outline
  • Model
  • LOCI Program
  • LOCI Correctness Proof
  • Theoretical Performance Analysis
  • Simulations based Performance Analysis
  • Conclusions
loci program
LOCI Program

Grow the cluster iteratively

Wait for a random amount of time

Timeout and elect itself as a clusterhead

Legitimate Cluster

Valid cluster

Network partition constructed

R

mR

R

mR

mR

R

R

mR

loci program1
LOCI Program

Legitimate cluster constructed

Problem: Neighboring clusters overlap

Dynamic Priority : <Radius, - #Overlaps>

R

j

A

B

k

Radius: maximum distance d, such that all nodes ≤ d from the leader belong to the

same cluster as that of the leader

Overlaps: # of overlaps of a cluster with neighboring clusters of equal radius

loci abstract program
LOCI Abstract Program
  • timeout(can_lead(j)) →start_cluster(j)

[]

  • can_join(j, S) → join(j, S)

[]

(3) j and k are clusterheads Λ

overlapping_clusters(j, k) → resolve_overlap(j, k)

local healing using loci
Local Healing using LOCI
  • node join
    • may be subsumed by neighboring clusters if it is within mR distance

of a neighboring clusterhead

d = 1

(

(

)

(

)

)

(

)

cascading

)

(

)

(

)

(

)

(

R = [1, 1]

A

B

new node

(

)

(

)

(

)

(

)

R = [1, 2]

new node subsumed

local healing using loci1
Local Healing using LOCI
  • node join
    • may create a new cluster, affecting only neighboring clusters by subsuming nodes contained in them that are farther than R distance from their respective clusterheads

d = 2

(

(

)

(

)

)

(

)

)

(

(

)

(

(

)

)

(

)

R = [1, 2]

new cluster

local healing using loci2
Local Healing using LOCI
  • node fail-stops
    • new leader may be found in the original cluster, without affecting neighboring clusters, or
    • remaining nodes in the original cluster may affect neighboring clusters by joining them, or
    • may create new cluster(s), affecting only neighboring clusters by subsuming nodes contained in them
hierarchical clustering1
Hierarchical clustering

Legitimate cluster at level 1

Legitimate cluster at level 0

Clustering at Level 0

Represent clusters by a single

node, the clusterhead

R

1

R

0

Neighboring clusters at level 0 →

Corresponding clusterheads

are neighbors at level 1

Clustering at Level 1

i+1

i

(2mR)

- 1

]

[

)

(

mR

R

(2mR)

,

=

R

i

2mR – 1

outline2
Outline
  • Model
  • LOCI Program
  • LOCI Correctness Proof
  • Theoretical Performance Analysis
  • Simulations based Performance Analysis
  • Conclusions
loci correctness proof
LOCI correctness proof
  • Variables
    • d.j = distance of node j from the clusterhead
    • r.j = circular radius of the cluster
    • c.j = ID of the cluster to which j belongs
    • o.j = set of tuples that contains ID and radius of the overlapping

clusters

  • State predicates
    • Valid Cluster (VC.j) = circular radius of the cluster is r.j and all

the nodes in the cluster have correct values

    • Legitimate Cluster (LC.j) = circular radius of the cluster is R and

all the nodes in the cluster have correct values

loci correctness proof1
LOCI correctness proof
  • Theorem 1:I is an invariant of LOCI

I(Invariant)Ξif a node belongs to a cluster then that cluster is a valid cluster and the values of all the nodes in that cluster are correct

  • Theorem 2:F is a fixpoint of LOCI

F (Fixpoint) Ξall nodes belong to a legitimate cluster and there is a legitimate path from every node to its clusterhead

  • Theorem 3: Starting from an invariant state I, the system

eventually reaches a state in F

  • Theorem 4: Starting at an arbitrary state, every computation of the system reaches a state in I
outline3
Outline
  • Model
  • LOCI Program
  • LOCI Correctness Proof
  • Theoretical Performance Analysis
  • Simulations based Performance Analysis
  • Conclusions
performance analysis
Performance Analysis
  • Theorem 5: The convergence time of LOCI from invariant

state to fixpoint state is O(R4) rounds

  • Communication complexity
    • Cluster formation O(R3)
    • Individual node O(R3)
percentage of uncovered nodes
Percentage of uncovered nodes
  • For m≥2, LOCI constructs network partitions
  • For m<2, in the worst case the percentage of uncovered nodes using LOCI is
number of clusters constructed
Number of clusters constructed
  • Overhead in number of clusters constructed is 3

√3R

R

2R

(√2/3)R

Maximum number of clusters (LOCI) = 3n

Minimum number of clusters = n

outline4
Outline
  • Model
  • LOCI Program
  • LOCI Correctness Proof
  • Theoretical Performance Analysis
  • Simulations based Performance Analysis
  • Conclusions
simulation results
Simulation Results
  • Assumptions
    • Nodes are in a regular grid
    • Nodes are aware of their neighbor set

(unit transmission range)

simulation results1
Simulation Results

Overhead in the number of clusters (1-D network)

Overhead in the number of clusters (2-D network)

R: Radius of the cluster

N:Number of nodes

conclusions
Conclusions
  • A distributed, local, scalable, and self-stabilizing clustering scheme, LOCI, is presented that partitions the network into bounded radius clusters
  • Convergence time and self-healing in LOCI are scalable both in time and space
  • LOCI bounds the overhead in the number of clusters constructed by a constant
  • Clusters constructed by LOCI form a Voronoi tessellation
future work
Future Work
  • Convergence time of O(R2 log(R))
  • Integrating LOCI in the “Line in the Sand” tracking service to achieve scalability and fault tolerance
number of clusters constructed1
Number of clusters constructed
  • R (Radius) ≈ D (Diameter of the network)
    • Overhead in number of clusters constructed is 6

R

R

2R

R

R

R

cluster assignment
Cluster assignment
  • Assign clusterheads in surrounding region
  • Priority < n, id >
    • n: [0, 6]

R

2R+1

loci correctness proof2
LOCI correctness proof
  • Variables
    • d.j = distance of node j from the clusterhead
    • r.j = circular radius of the cluster
    • c.j = ID of the cluster to which j belongs
    • o.j = set of tuples that contains ID and radius of the overlapping

clusters

  • State predicates
    • VC.j = j is the clusterhead of a valid cluster
    • LC.j = j is the clusterhead of a legitimate cluster
    • H.j = variables stored at a node j have correct values
    • LP.j = legitimate path from a node j to its clusterhead