forwarded to the base station any longer. The cluster
head can also intentionally or due to software bugs
forward incorrect information. Depending on the
application case, the impact of such a failure can
vary from quality degradation of measurements to
alarm messages not being delivered to a back-end
system.
While forwarding messages, nodes can aggregate
data from multiple other nodes in order to reduce the
amount of data sent to the base station. One common
simple approach is to calculate the average of
correlated measured values such as temperature,
humidity and pressure, sending only one message to
the back-end. If a node generates incorrect data, the
data aggregation results can suffer deviations from
the real value. Also, if a node responsible for
generating the aggregated data is subject to a value
failure, the base station will receive incorrect
information of an entire region of the network.
2.2 Related Models
Fault tolerance has been recognized by some
authors. Yunxia Feng presents a fault Tolerant Data
Aggregation Scheduling with Local Information.
Authors divided a fault tolerant data aggregation
protocol into two parts: basic aggregation scheduling
and amendment strategies (Yunxia Feng, 2002). On
default, data is aggregated according to the basic
aggregation scheduling strategy. The amendment
strategy starts after a middle sensor node is out of
service. Nodes here are identified as Directly
Affected Node, Indirectly Affected Node and Non-
Affected Node. It emphasizes on how to amend the
tree according to various types of fault nodes.
XIAO Wei presents a Fault tolerant scheme for
data aggregation in event cluster. He used K-means
to aggregate data that can make approximated data
in a set and proposed a concept of creditability
whose value is calculated according to an average
value coming from the set (XIAO Wei, 2006). The
former described recovery of the aggregation tree
after the recognition of fault nodes, while the latter
devote to resolving faulty determination but does not
consider the isolated point. YANG Yan presented an
Ant Colony Algorithm MACCA which makes
different speed ant colony cluster with SACA
parallel to divide approximated set. But it also does
not present fault recognition and isolated point
(Yang Yan, 1984).
Ganeriwal S, Kumar R, Srivastava M B proposes
a fully distributed K-Means algorithm (Epidemic K-
Means) which does not require global
communication and is intrinsically fault tolerant.
The proposed distributed K-Means algorithm
provides a clustering solution which can
approximate the solution of an ideal centralized
algorithm over the aggregated data as closely as
desired(Ganeriwal S, Kumar R, Srivastava M B,
2003). But the algorithm assumes nodes
communicating peer to peer which doesn’t consider
the communication complex and energy
consumption.
3 A POLYNOMIAL ALGORITHM
FOR FAULT-TOLERANT
AGGREGATION
When detect abnormality, sensors must be clustered
into numbers of local sensor networks according to
the region they are located. Besides, each region of
sensors has their own autonomy. In other words, all
sensors, which are in the same region, can execute
the proposed protocol without the sink and other
unconcerned sensors. This can reduce the time for
collecting data and designing the final result. We
use LEACH to create clusters.
In classic WSN, if the detected value meets some
condition, then the initial value must be set to 1,
otherwise, 0. Take the fire control system for
instance, if the sensor detects the temperature is
higher than 50°C, then its initial value is 1,
otherwise, 0 as default (Dai Hui, Han R, 2004).
After clustering, the proposed protocol can let each
sensor reach an agreement and do the corresponding
action with the following assumptions.
➢ Let N be the set of all sensors in the local
autonomous WSN and| N |=n.
➢ The total number of faulty sensors and
transmission media in the local WSN is ہሺn-1)/4ۂ.
➢ Each sensor needs to collect messages through
ہ(n−1)/4ۂ+1 phases of message exchange and
each phase has two round.
➢ Each sensor has its own initial value Vi.
In the message exchange phase, each sensor collects
and exchanges messages from other sensors with
ہ(n−1)/4ۂ+1 phases of message exchange. As shown
in Fig. 1. In Fig 1, the algorithm contains f+1 phases,
each taking two rounds. Each node has a preferred
decision for each phase. At the first round of each
phase, all nodes in one cluster send their preferences
to each other. Let v
i
k
be the majority value in the set
of values received by node p
i
at the end of the first
round of phase k. If there is no majority, then a
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