Algorithm For Detecting Cuts In Wireless Sensor Networks

International Journal of Computer Trends and Technology (IJCTT) – volume 4 Issue10 – Oct 2013
ISSN: 2231-2803 http://www.ijcttjournal.org Page3418

Algorithm For Detecting Cuts In Wireless
Sensor Networks
M.Swathi, L.Thirupathi
Masters in Technology, Computer Science and Engineering,
Malla Reddy Institute of Engineering and Technology
Dhulapally, Hyderabad, India.

Abstract-- Wireless Sensor Networks (WSN) often suffers from
an interrupted connectivity caused by several aspects such as
unattended operation vulnerable to hostile tampering and
limited battery power of a node. The interference in
connectivity is often referred to as network cut, leads to data loss
improper routing decisions, and waste of energy. A wireless
sensor network can be divided into multiple connected
components due to the failure of some of its nodes that is called
a “cut”. In this article we would ponder the problem by
detecting cuts by the remaining nodes of a wireless sensor
network. We put forward an algorithm that allows (1) one or
more nodes (that are connected to the special node after the cut)
to detect the happening of the cut, and (2) every node to detect
when the connectivity to a specially designated node has been
lost. The algorithm is asynchronous and distributed: every node
needs to be communicated with only those nodes that are within
its communication range.

Keywords: network separation, sensor networks, network cut,
wireless networks.


I. INTRODUCTION

The Wireless sensor networks (WSN), comprises of
large numbers of low-power and low-cost wireless nodes,
have recently been engaged in many applications: (i) medical
care, (ii) military surveillance, and (iii) disaster response.
The characteristics of WSN are such as a battery powered
nodes, an unattended operation, and punitive environments
pose major challenges. Network disconnection, typically
referred to as a network cut could cause many a number of
problems. For example, inappropriate decisions to route data
to a node located in a disconnected segment of the network
might lead to wasted power consumption, data loss, and
congestion around the network cut. These failures can cause
a subset of nodes – that have not failed – to become
disconnected from the others, resulting in a “cut”. Any two
nodes are said to be disconnected if there is no path defined
between them.
We ponder the problemof detecting cuts by the nodes of
a wireless network. We assume that there is a specially
designated node in the network that we call as a source node.
The source node could be a base station that serves as an
interface between its users and the network since a cut may
or may not separate a node from the source node; we
differentiate between two distinctive outcomes of a cut for a
particular node. When a node ‘x’ is disconnected from the
source, we say that the DOS (Disconnected fromSource)
event has occurred for ‘x’. When a cut occurs in the network
that does not separate a node ‘x’ fromthe source node, we
say that the CCOS (Connected, but a Cut Occurred
Somewhere) event has occurred for ‘x’. By cut detection we
indicate that (a) detecting each node of a DOS event when it
occurs, and (b) detection of CCOS events by the nodes close
to a cut, and the approximate location of the cut. By
“approximate location” of a cut we mean the location of one
or more active nodes that lie at the border line of the cut and
that are connected to the source. The nodes that detect the
occurrence and approximate locations of the cuts can then
alert the source node or the base station.
In this article we suggest a distributed algorithmto
detect cuts, named as the Distributed Cut Detection (DCD)
algorithm. This algorithm allows every node to detect DOS
events and the subset of nodes to detect CCOS events. A key
component of the DCD algorithmis a distributed iterative
computational step through which the nodes calculate their
electrical potentials. The DOS detection part of the algorithm
is pertinent to arbitrary networks; a node only needs to
commune a scalar variable to its neighbors. The CCOS
detection part of the algorithm is restricted to networks that
are deployed in the 2D Euclidean spaces, and that the nodes
need to know their respective positions. The position
information need not be extremely precise.










II. DISTRIBUTED CUT DETECTION
International Journal of Computer Trends and Technology (IJCTT) – volume 4 Issue10 – Oct 2013
ISSN: 2231-2803 http://www.ijcttjournal.org Page3419


A. Problem Definitions and Formulation

Time is calculated with a distinct counter k =−1, . . . ,−1, 0, 1,
2, . . . . We replicate a sensor network as a time-varying graph
G(k) =(V(k), E(k)), where the node set V(k) represents the
sensor nodes active at time k and the edge set E(k) that
comprises of pairs of nodes (u, v) so that the nodes ‘u’ and ‘v’
can directly exchange messages between each other at ‘k’
time. By saying active node we mean that a node has not
failed permanently. Here the mentioned graphs are considered
undirected, i.e., (i, j) =(j, i). The neighbors of a node ‘i’ is the
set Ni of nodes connected to i, i.e. Ni ={j|(i, j) 2 E}. The
number of neighbors of ‘i’, |Ni(k)|, is called its degree, which
is denoted by di(k). The path from‘i’ to ‘j’ is a sequence of
edges connecting ‘i’ and ‘j’. The graph is called connected
when there is a path between each pair of nodes. A
component Gc of a graph ‘G’ is a maximal associated sub
graph of ‘G’ (i.e., no other connected sub-graph of ‘G’
contains Gc as its sub graph). In requisites of these
definitions, a cut event is formally defined as a raise in the
number of components of a graph due to the failure of a
subset of nodes (as replicated in Figure-I). The number of
cuts associated with a cut event is a rise in the number of
components after the event. . Each node keeps a scalar
variable that is called its state. The state of node ‘i’ at time ‘k’
is denoted by xi(k).

Figure-II shows the progression of the node states in a
network of 200 nodes when the states are computed using the
update law described above. The source node is located at the
center. The nodes shown as red squares in Figure II(b) fail at
k=100, and subsequently they do not participate in
communication or calculation. Figure II(c-d) show the time
evolution of the states of the two nodes ‘u’ and ‘v’, that are
marked by circles in Figure II(b). The state of node ‘u’ (that
is disengaged from the source due to the cut) decays to 0 after
attaining a positive value, whereas the state of the node ‘v’
(that is still connected after the cut) stays positive.


Fig I: examples of cuts and hole


Fig. II. (a)-(b): A sensor network with 200 nodes

(c)-(d): The states of two nodes ‘u’ and ‘v’ as
a function of iteration number

III. The Distributed Cut Detection (DCD) Algorithm

A. Detecting DOS event

Here the approach is to develop the fact that if the
state is close to 0 then the node is disconnected from the
source, or else not. To reduce sensitivity of the algorithmto
variations in network size and structure, we use a normalized
state. DOS detection part consists of steady-state detection,
normalized state computation, and separation/connection
detection. Every node ‘i’ maintains a binary variable
DOSi(k), that is set to 1 if the node believes it is disconnected
fromthe source and 0 otherwise. The variable, which is called
the DOS status, is initialized to 1 since there is no reason to
believe a node is connected to the source initially. The node
keeps track of the positive steady states seen in the past using
the following method. Every node ‘i’ computes the
normalized state difference ∂xi(k) as follows:

∂xi(k) =xi(k)-xi(k-1)/xi(k-1) if xi(k-1)>Єzero
∞ Otherwise

Where Єzero is a small positive number. The node ‘i’ keeps a
Boolean variable ‘Positive Steady State Reached’ (PSSR) and
updates PSSR(k)1 if |∂xi(k)| < ЄΔx for k =k −Tguard, k
−Tguard +1, . . . , k (i.e., for Tguard consecutive iterations),
where ЄΔx is a small positive number and Tguard is a small
integer. The initial value 0 of the state is not measured as a
steady state, so PSSR(k) =0 for k =0, 1, . . . , Tguard. Every
node keeps an estimate of the most recent “steady state”
observed, that is denoted by ˆx
i
ss (k). This approximate is
updated at every ‘k’ time according to the following rule: if
PSSR(k) =1, then ˆx
i
ss (k) xi(k), otherwise ˆx
i
ss (k)
ˆx
i
ss(k − 1). It is initialized as ˆx
i
ss (0) =1. Each node ‘i’ also
keeps a list of stable states seen in the past, one value for
every unpunctuated interval of time during which the state
was detected to be steady. This information is stored in a
International Journal of Computer Trends and Technology (IJCTT) – volume 4 Issue10 – Oct 2013
ISSN: 2231-2803 http://www.ijcttjournal.org Page3420

vector ˆX
i
ss(k), that is initialized to be empty and is
rationalized as follows. If PSSR(k) =1 but PSSR(k−1) =0,
then ˆxss(k) is appended to ˆX
i
ss(k) as a new entry. If steady
state was detected in both ‘k’ and k − 1 (i.e., PSSR(k) =
PSSR(k −1) =1), then the last entry of ˆX
i
ss(k) is updated to
ˆx
i
ss(k). Every node computes a normalized state x
i
norm(k)
as:

x
i
norm(k) := x
i
(k)/ˆx
i
ss(k) if ˆx
i
ss(k) >0
1 otherwise

Where ˆx
i
ss(k) is the last steady state seen by ‘i’ at ‘k’, i.e.,
the last entry of the vector ˆX
i
ss(k). If the normalized state of
‘i’ is less than ЄDOS, where ЄDOS is a small positive
number, then the node announces that a cut has taken place:
DOS
i
1. If the normalized state is 1, denoting that no steady
state was seen until ‘k’, then DOS
i
(k) is set to 0 if the state is
positive (i.e., xi(k) > Єzero) and otherwise its 1.

B. Detecting CCOS event:

The algorithmfor detecting CCOS events depends on
finding a shortest path round a hole, if it exists, and is
partially inspired by the jamming detection algorithmThe
method utilizes node states to assign the task of hole-
detection to the most suitable nodes. When a node notices a
large change in its local state as well as failure of one or more
of its neighbors, and both of these events occur within a pre-
planned small interval, the node initiates a PROBE message.
Each PROBE message ‘p’ contains the following
information: (1) a unique probe ID, (2) path traversed (3) the
angle traversed by the probe around the centroid, (4) probe
centroid Cp (in consecutive order), and (5) the destination
node. The probe is forwarded in a manner so that if the probe
is triggered by the creation of a small hole or cut (with
circumference less than max), the probe passes through a path
around the hole in a counter clockwise (CCW) direction and
reaches the node that initiated the probe. So in this case, the
net angle traversed by the probe is 3600. And on the other
hand, if the probe was initiated by the occurrence of a
boundary cut, even if the probe ultimately reaches its node of
initiation, the net angle traversed by the probe is 0. Nodes
forward a probe only if the distance traveled by the probe (the
number of hops) is smaller than a threshold value max.
Consequently if a probe is initiated due to a large internal
hole/cut, then it would be absorbed by a node (i.e., not
forwarded because it exceeded the distance threshold
constraint), and the absorbing node declares that a CCOS
event has taken place.

IV. Performance Evaluation

The performance of the DCD algorithmwas tested using
MATLAB simulations (lead in a synchronous manner) and
then on a real WSN system consisting of micaZ motes. Two
important metrics of performance for the DCD algorithmare
(i) detection delay, and (ii) detection accuracy. Detection
accuracy denotes to the ability to detect a cut when it occurs
and not declaring a cut when none has occurred. DOS
detection delay for a node ‘i’ that has undergone a DOS event
is the least number of iterations (after the node is
disconnected) it takes before the node switches its DOSi flag
from0 to 1. CCOS detection delay is the lowest number of
iterations it takes after the occurrence of a cut before a node is
detected.

A. Performance of DOS Detection

In replications with all the five networks, the node
failures occur at k=100. Performance of the DOS detection
part of the algorithmin relations to the error detection and
probability delays are summarized in Table (A). The error
probabilities shown are the ones that are empirically
computed at k=60 and k=160, i.e., 60 iterations after
deployment and after the node failures occurred, respectively.
The standard and mean deviation of DOS detection delay for
a network are computed by averaging over the nodes that
detected DOS events. We see from Table (A) that the
algorithmis able to successfully detect initial connectivity to
the source and then DOS events for all the five networks
without necessitating the parameters to be tuned for every
individual network.

B. Performance of CCOS Detection

We could evoke that the CCOS detection part of the
algorithm is not applicable to 3D networks. To site an
example, Figure (C) shows the path of the probes and their
originating nodes in the network of Figure 2. Two probes
were triggered by nodes close to the cut on the upper right
corner; both of themwere captivated when the length of their
path navigated exceeds the lmax hops that led to correctly
detecting CCOS events. Midst all the three probes that were
triggered by nodes near small holes in the network, one of
themnear the hole in the upper left corner failed to find a
path back to its patenting node, prominent to an erroneous
declaration of an CCOS event by the absorbing node. The
probability of a CCOS1/0 error in this case is therefore 0.33.

TABLE (A)
DOS detection performance for the networks shown in
Figure 4. The two values of the probability shown in
every cell that correspond to k=60 and k=160, respectively.

Network (a) (b) (c) (d) (e)
Prob(DOS0/1 error) 0/0 0/0 0/0 0/0 0/0
Prob(DOS0/1 error) 0/0 0/0 0/0 0/0 0/0
DOS Delay(mean) 2.0 17 21 36 31
DOS Delay(std dev.) 4.3 5.5 4.3 3.9 2
TABLE 3
International Journal of Computer Trends and Technology (IJCTT) – volume 4 Issue10 – Oct 2013
ISSN: 2231-2803 http://www.ijcttjournal.org Page3421

CCOS detection performance for four networks in
Figures 4(a)-(d). The error probabilities are at k=160.

Network (a) (b) (c) (d)
Prob(CCOS1/0 error) 0 0 0 0.33
Prob(CCOS0/1 error) 0 0 0 0
CCOS Delay 34 41 38 40




Fig. C. The path of the probe messages in the network .
Each probe path is marked with adistinct legend (circle,
triangle, square, etc.), and the node that initiated the
probe is shown as the one with thelarger legend.


Fig. 4. Partial view of the 24 node outdoor deployment.

V. CONCLUSIONS

The proposed DCD algorithmenables each node of a wireless
sensor network first to detect ‘Disconnected fromSource’
(DOS) events if they occur. Second, it enables a subset of
nodes that experience ‘Connected, but Cut Occurred
Somewhere’ (CCOS) events to detect themand estimate the
approximate position of the cut in the formof a list of active
nodes that reside in the boundary of the hole/cut. The DOS
and CCOS events are defined with respect to a specifically
designated source node. The algorithmis established on the
ideas fromparallel iterative solution of linear equations and
electrical network theory. Numerical simulations, as well as
experimental evaluation on a real WSN systemconsisting of
micaZ motes, shows that the algorithmworks effectively with
a large classes of graphs of varying size and structure,
without making any changes in the parameters. In certain
situations, the algorithm is assured to detect connection and
disconnection to the source node without any error. The key
to the strength of the DCD algorithm is the convergence rate
of the underlying iterative scheme is reasonably fast and
independent of the size and structure of the network that
makes detection using this algorithm pretty fast. The
application of the DCD algorithmto detect node separation
and re-joining to the source in mobile networks is a topic of
ongoing research.

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