![](bg2.png)
2 RELATED WORK
First algorithms proposed in the literature consider
that the cover sets are disjoint: a sensor node ap-
pears in exactly one of the generated cover sets. For
instance Slijepcevic and Potkonjak (Slijepcevic and
Potkonjak, 2001) propose an algorithm which allo-
cates sensor nodes in mutually independent sets to
monitor an area divided into several fields. Their al-
gorithm constructs a cover set by including in pri-
ority the sensor nodes which cover critical fields,
that is to say fields that are covered by the small-
est number of sensors. The time complexity of their
heuristic is O(n
2
) where n is the number of sen-
sors. (Cardei et al., 2002) present a graph color-
ing technique to achieve energy savings by organizing
the sensor nodes into a maximum number of disjoint
dominating sets which are activated successively. The
dominating sets do not guarantee the coverage of the
whole region of interest. In (Cardei and Du, 2005),
the authors propose a heuristic to compute the disjoint
set covers (DSC). In order to compute the maximum
number of covers, they first transform DSC into a
maximum-flow problem , which is then formulated as
a mixed integer programming problem (MIP). Based
on the solution of the MIP, they design a heuristic
to compute the final number of covers. The results
show a slight performance improvement in terms of
the number of produced DSC in comparison to (Sli-
jepcevic and Potkonjak, 2001) but it incurs higher ex-
ecution time due to the complexity of the mixed in-
teger programming resolution. Zorbas et al. (Zorbas
et al., 2007) present B{GOP}, a centralized coverage
algorithm introducing sensor candidate categorisation
depending on their coverage status and the notion of
critical target to call targets that are associated with
a small number of sensors. The total running time
of their heuristic is 0(mn
2
) where n is the number
of sensors, and m the number of targets. Compared
to algorithm’s results of Slijepcevic and Potkonjak
(Slijepcevic and Potkonjak, 2001), their heuristic pro-
duces more cover sets with a slight growth rate in ex-
ecution time.
In the case of non-disjoint algorithms (Chaudhary
and Pujari, 2011), sensors may participate in more
than one cover set. In some cases this may prolong
the lifetime of the network in comparison to the dis-
joint coverset algorithms but designing algorithms for
non-disjoint cover sets generally incurs a higher order
of complexity. Moreover in case of a sensor’s failure,
non-disjoint scheduling policies are less resilient and
less reliable because a sensor may be involved in more
than one coversets. For instance, Cardei et al. (Cardei
et al., 2005) present a linear programming (LP) solu-
tion and a greedy approach to extend the sensor net-
work lifetime by organizing the sensors into a max-
imal number of non-disjoint cover sets. Simulation
results show that by allowing sensors to participate
in multiple sets, the network lifetime increases com-
pared with related work (Cardei and Du, 2005).
3 ALGORITHMS DESCRIPTION
We try to produce an adaptive scheduling which al-
lows sensors to operate alternatively so as to prolong
the network lifetime. For convenience, the notations
and assumptions are described first.
3.1 Notations and Assumptions
• m : the number of targets
• n : the number of sensors
• K : maximal number of cover sets
• i : index of target (i = 1..m)
• j : index of sensor ( j = 1..n)
• k : index of cover set (k = 1..K)
• T
0
: initial set of targets
• S
0
: initial set of sensors
• T : set of targets which are not covered by at least one
cover set
• S : set of available sensors
• S
0
(i) : set of sensors which cover the target i
• T
0
( j) : set of targets covered by sensor j
• C
k
: cover set of index k
• T(C
k
) : set of targets covered by the cover set k
• NS(i) : set of available sensors which cover the target i
• NC(i) : set of cover sets which do not cover the target i
• |.| : cardinality of the set
We assume that the lifetimes of sensors are iden-
tical. Lifetime of a sensor is time duration when the
sensor is in the active state all the time. In order to
achieve lifetime extension, sensors must be divided
into a number of subsets, called cover sets, where
each cover set is capable of monitoring all the targets.
Sensors belonging to a scheduled cover set are in ac-
tive mode, while the others are in sleep mode. If the
cover sets are disjoint, then each sensor is allowed to
participate only in one cover set. The maximal num-
ber of possible disjoint cover sets is given by :
K
max
= min
i=1..m
|S
0
(i)| (1)
since each cover set must cover all targets and each
sensor can only be part of one cover set.
SENSORNETS2013-2ndInternationalConferenceonSensorNetworks
198