Download Problem Statement and Assumption

On the planning of Wireless Sensor Networks:
Energy-Efficient Joint Clustering and Routing
under Coverage Constraint
Ali Chamam, Student Member, IEEE,
Hichem Ayed Harhira, Student Member, IEEE
and Samuel Pierre, Senior Member, IEEE
Department of Electrical Engineering
Polytechnique, Montréal, Canada
Present by C.T. Lee
2007 / 10 / 2
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Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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I. Introduction (1/5)
 Minimizing energy dissipation and maximizing
network lifetime are among the central concerns
when designing sensor networks’ applications and
protocols.
 Authors address the global problem of maximizing
network lifetime under the joint clustering, routing and
coverage constraints.
 First, authors formulate this global problem as an
Integer Linear Programming model.
 Then, authors implement a greedy heuristic algorithm
to tackle the exponentially-increasing problem.
 Experimental results show that the proposed
centralized algorithm provides near-optimal network
lifetime values while performing low computation times,
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practically suitable for large-size sensor networks.
Introduction (2/5)
 Generally, energy conservation is dealt with
on five different levels
1. Efficient scheduling of sensor states to alternate
between sleep and active modes;
2. Efficient control of transmission power to ensure an
optimal tradeoff between energy consumption and
connectivity;
3. Energy-efficient routing, clustering and data
aggregation;
4. Data compression (source coding) to reduce the
amount of transmitted data;
5. Efficient channel access and packet retransmission
protocols on the Data Link Layer.
 The scope of this paper includes both the first and
the third levels.
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Introduction (3/5)
 Authors consider a sensor network that is deployed in a certain
area A to monitor some given events.
 The network is dense, sensing ranges of neighbor sensors
usually overlap.
 That means that when an event occurs at a point P of A, it
will be detected and reported by all the sensors that are
switched-on and whose sensing range encompasses P.
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Introduction (4/5)
 To save network energy and increase its lifetime, authors
propose to switch on only a subset of sensors that
covers A (above a given pre-defined coverage rate)
while all other sensors will be turned off. Figure 2 depicts
an example of full-covering sensor set.
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Introduction (5/5)
 However, in the best of authors' knowledge,
the optimal global planning of sensors’ states
maximizing network lifetime while considering
the joint clustering, coverage and routing
constraints within the same optimization
process has not been addressed.
 In authors' architecture, only CHs can route
data
 Because they have enough energy to do so.
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Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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II. Related Work
 Cluster formation is typically based on the energy reserve of
sensors and sensors proximity to the cluster head. For instance,
LEACH (Low-Energy Adaptive Clustering Hierarchy).
 It uses single-hop routing where each node can transmit
directly to the cluster-head and the sink. Therefore, it is not
applicable to networks deployed in large regions.
 PEGASIS (Power-Efficient GAthering in Sensor Information
Systems) is improvements of LEACH. Rather than forming
multiple clusters.
 PEGASIS forms chains of sensor nodes so that each node
transmits and receives from a neighbor and only one node is
selected from that chain to transmit to the PN.
 Excessive delay
 In [8], Yao and Giannakis propose an algorithm that finds
minimizes the dissipated energy of the whole network over the
period T. But no coverage constraint is considered.
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Outline
I. Introduction
II. Related Work
III. Problem Statement and Assumption
IV. Problem Modeling
V. Proposed Heuristic
VI. Simulation Results
VII. Conclusion
VIII. Comments
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III. Problem Statement and
Assumption (1/4)
 As shown in [5] for the case of WINS Rockwell seismic sensors,
a sensor can be in one of the following four activity modes,
characterized by their respective power consumptions: Transmit
(0.38 - 0.7 W), Receive (0.36 W), Idle (0.34 W) and Sleep (0.03
W).
 As depicted in Figure 3, authors will consider, without loss of
generality, that each sensor can be in one of three states: Sleep,
Active and Cluster Head (CH) having respectively power
consumptions ESleep, EActive and ECH per time unit, where ESleep
<< EActive < ECH.
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Problem Statement and Assumption
(2/4)
 Data received by CHs from sensors has to be routed
toward the PN. As shown on Figure 4, this makes the
overlay network formed by the CHs sufficient to route
data from any sensor toward the PN.
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Problem Statement and Assumption
(3/4)
 Definition 1: A set of sensors Sc is a covering set of
area A if and only if:  point PA;  i  Sc such as i
covers P.
 In this problem, the optimal network configuration must:
 contain a full-covering set of active sensors;
 contain a set of CHs so that connectivity of every sensor to a
CH is ensured;
 ensure that all CHs belong to a spanning tree over which
data will be routed toward the PN.
 Authors' objective is to find the optimal allocation of sensors’
states (Active, Sleep, CH) that meets these three conditions,
while minimizing the consumed energy of each node.
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Problem Statement and Assumption
(4/4)

Before modeling authors' problem, authors make the following assumptions:
1.
The ID and the position of each sensor are fixed and known to both the PN
and the sensor itself.
2.
Active sensors capture events occurring in their range and transmit data
associated with these events straightaway, without any buffering, because
sensors are usually not equipped with large (and costly) buffers.
3.
All sensors have the same sensing range Rc.
4.
Only CHs can perform data routing. Routing over the overlay network
composed of CHs can be performed using one of the energy-efficient routing
protocols for sensor networks proposed in the literature [14]. However, authors
do not address any specific routing mechanism.
5.
Each sensor has an initial energy E0. The Sink is assumed to have no energy
limitation. Authors assume that, when a sensor is Active, it dissipates the same
energy during a unit of time, no matter how the events’ distribution is.
6.
The network is dense enough so that when all the sensors are Active, the
monitored area is fully covered. Besides, authors assume that the sensor
network is connected with respect to the sensors’ transmission range.
7.
Network lifetime is defined as the time separating the instant the network starts
operating and the instant of the first node failure due to energy exhaustion.
8.
Authors assume ideal MAC layer conditions. That is, perfect transmission of
data on a node-to-node wireless link.
9.
Authors assume that sensors have idealized sensing capabilities. That is,
inside the sensor’s range, quality of sensing does not depend on the distance
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from the sensor.
Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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IV. Problem Modeling (1/10)
 Objective of the problem is to find the optimal
allocation of states to sensors that maximizes the
network lifetime.
 To maximize network lifetime
 minimizing total energy consumption and energy
consumption balancing among sensors
 Original ILP (exponentially-increasing number of subsets of S) 
Reformulation (non-linear term)
ILP (linearize, NPC) 
Greedy heuristic algorithm
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Problem Modeling (2/10)
 To model this optimization problem, authors first
define the following sets and constants:
 Then, authors define following binary decision
variables  i = 1..|S|;  j = 1..|S|:
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Problem Modeling (3/10)
 To balance energy consumption among
nodes, authors choose to minimize an
objective function that is a linear combination
of sensors scores. The score of a sensor i is
defined by:
 System favors the activation of sensors having
relatively higher residual energy.
Eri is the remaining energy of sensor i.
Edi≒5
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Problem Modeling (4/10)
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Problem Modeling (5/10)
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Problem Modeling (6/10)
 Objective function (1a) aims to balance the energy consumption
over the network.
 Constraint (1b) guarantees a full coverage of the monitored area,
such that every elementary cell is covered by at least one Active
sensor.
 Constraint (1d) ensures that there exist at least a CH located
one hop from the PN.
 Constraints (1e) to (1h) ensure that every Active and non-CH
sensor is connected to at least one CH within its range.
 Constraint (1i) gives an upper bound on the clusters size, such
that a CH serves at most Nmax Active sensors.
 Equations (1j) to (1n) describe the routing constraint ensuring
that the overlay network composed of CHs is connected and
hence, there exist a tree-like partial subgraph.
 1o are the integrality constraints.
 To ensure that a spanning tree connecting all the CHs exists in
any solution, constraints (1m) and (1n) require the enumeration
of all the subsets of S.
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Problem Modeling (7/10)
 Even though these constraints represent the
theoretical conditions to have a spanning tree in any
graph (no cycles and a connected graph), they
quickly result in a combinatorial explosion of the
number of constraints due the exponentiallyincreasing number of subsets of S. To circumvent this
problem, authors will proceed differently to force any
solution to have all its CHs connected to the same
spanning tree: authors represent the routing
constraint of authors' problem as a multi-flow
routing problem.
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Problem Modeling (8/10)
 To model this virtual flow routing problem, authors
define a binary variable representing the use of the
wireless link lk to convey a flow (i, j), where i, j, k and
l are CHs and i, j are respectively the source and
destination of the flow. Let:
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Problem Modeling (9/10)
 The following constraints ensure that the network
contains a spanning tree connecting all CHs:
Intermediate node
Source node
Destination node
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Problem Modeling (10/10)
 Equation (2a) is the flow constraint ensuring that a feasible path
exists between any pair of CHs to convey an elementary unit of
flow. Remaining constraints (2b) to (2e) limit the relevance of
this virtual flow problem to the overlay network. Constraint (2f) is
finally the integrality constraints.
 In (2a) is a non-linear term that needs to be linearized. For that,
authors define:
 To have a logical equivalence between Uij and Xi,Yj , authors
add the following constraints:
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Outline
I. Introduction
II. Related Work
III. Problem Statement and Assumption
IV. Problem Modeling
V. Proposed Heuristic
VI. Simulation Results
VII. Conclusion
VIII. Comments
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V. Proposed Heuristic (1/3)
 Authors propose a greedy heuristic algorithm that
finds acceptable solutions in reasonable computation
times. As shown on Algorithm 1.
 At each iteration, the node having the highest score
f as a CH. The score of a sensor i is given by:
 Where i is the number of its neighboring sensors that
are not already connected to any CH. The shape of
this score function is shown on Figure 6.
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Proposed Heuristic (3/3)
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Proposed Heuristic (2/3)
maximizing
maximizing
>=1
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Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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VI. Simulation Results (1/3)
A. Comparative performance evaluation:
GR-RCC vs. CPLEX

For instance, for a topology of 49 sensors, the gap
between GR-RCC and CPLEX is about 35/43 =
81.4% which is quite acceptable.
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Simulation Results (2/3)
B. Performance evaluation of GR-RCC:
Impact of the sensing range
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Simulation Results (3/3)
C. Performance evaluation: of GR-RCC:
Impact of the maximum cluster size
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Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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VII. Conclusion
 In this paper, authors proposed a novel centralized mechanism
for near-optimal state assignment to sensors in large-scale
cluster-based monitoring sensor networks.
 GR-RCC’s mechanism maximizes network lifetime while
ensuring the full coverage of the monitored area and the
network connectivity.
 Despite its centralized aspect, GR-RCC’s mechanism exhibits
low complexity and low computation times making its practical
implementation adaptable for large-scale networks.
 As future research directions,
 authors intend to develop a more sophisticated
heuristic algorithm to improve the network lifetime
 Furthermore, authors intend to consider distancedependent probabilistic event detection
 LR approach solves this problem
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Outline
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
Introduction
Related Work
Problem Statement and Assumption
Problem Modeling
Proposed Heuristic
Simulation Results
Conclusion
Comments
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VIII. Comments



Strengths
 Authors propose an optimal allocation of states to sensors
that maximizes the network lifetime, while ensuring
simultaneously full area coverage, connectivity of every
sensor to a CH and connectivity of the overlay network
composed of CHs
 References are sufficient and appropriate
Weaknesses
 In page 11 Fig. 5, authors do not make it clear
Recommended Changes


Page 5: For example, in [17], Yaoand Giannakis propose  [8]
 Page 12: (1n) |S|  S
 Page 12: Equations (1b) to (??)  Equations (1b) to (1o)
 Page 16: (5b) RHS  >=1
 Page 16: minimizing  maximizing
Recommendation
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 Authors should prepare a minor revision
Q&A
Thank You for Your Attention.
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