\today
\end{flushright}%
-\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS
+\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6174 CNRS
\hspace{-2cm}University Bourgogne Franche-Comt\'e
``Perimeter-based Coverage Optimization \\
to Improve Lifetime in Wireless Sensor Networks''\\
-by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raph\"ael Couturier
+by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon and Raph\"ael Couturier
\medskip
application of these methods for the coverage scheduling problem.\\
\textcolor{blue}{\textbf{\textsc{Answer:} To the best of our knowledge, no
- integer linear programming based on perimeter coverage has been already
+ integer linear programming based on perimeter coverage has ever been
proposed in the literature. As specified in the paper, in Section 4, it is
inspired from a model developed for brachytherapy treatment planning for
optimizing dose distribution. In this model the deviation between an actual
assumption made on the selection criteria for the leader seems too vague. \\
\textcolor{blue}{\textbf{\textsc{Answer:} The selection criteria for the leader
- inside each subregion is explained in page~9, at the end of Section~3.3
- After information exchange among the sensor nodes in the subregion, each
- node will have all the information needed to decide if it will the leader or
+ inside each subregion is explained page~9, at the end of Section~3.3. After
+ the information exchange among the sensor nodes in the subregion, each node
+ will have all the information needed to decide if it will be the leader or
not. The decision is based on selecting the sensor node that has the larger
number of one-hop neighbors. If this value is the same for many sensors, the
node that has the largest remaining energy will be selected as a leader. If
\textcolor{blue}{\textbf{\textsc{Answer:} The communication and information
sharing required to cooperate and make these decisions is discussed at the
- end of page 8. Position coordinates, remaining energy, sensor node ID and
+ end of page 8. Position coordinates, remaining energy, sensor node ID, and
number of one-hop neighbors are exchanged.}}\\
\noindent {\bf 4.} The definitions of the undercoverage and overcoverage
coverage interval $i$. If the sensor $j$ is undercovered, there exists at
least one of its CI (say $i$) for which the number of active sensors
(denoted by $l^{i}$) covering this part of the perimeter is less than $l$
- and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if
+ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. On the contrary, if
the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
for which the number of active sensors (denoted by $l^{i}$) covering this
part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$,
for alpha and beta. Table 4 presents the results obtained for a WSN of
200~sensor nodes. It explains the value chosen for the simulation settings
in Table~2. \\ \indent The choice of alpha and beta should be made according
- to the needs of the application. Alpha should be enough large to prevent
- undercoverage and so to reach the highest possible coverage ratio. Beta
- should be enough large to prevent overcoverage and so to activate a minimum
- number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all
- coverage intervals $i$ of one sensor $j$ in order to express that the
- perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$
- values can be differentiated between sensors to force some regions to be
- better covered than others. The choice of $\beta \gg \alpha$ prevents the
- overcoverage, and so limit the activation of a large number of sensors, but
- as $\alpha$ is low, some areas may be poorly covered. This explains the
- results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a large number
- of periods with low coverage ratio. With $\alpha \gg \beta$, we favor the
- coverage even if some areas may be overcovered, so high coverage ratio is
- reached, but a large number of sensors are activated to achieve this goal.
- Therefore network lifetime is reduced. The choice $\alpha=0.6$ and
- $\beta=0.4$ seems to achieve the best compromise between lifetime and
- coverage ratio.}}\\
+ to the needs of the application. Alpha should be large enough to prevent
+ undercoverage and thus to reach the highest possible coverage ratio. Beta
+ should be large enough to prevent overcoverage and thus to activate a
+ minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical
+ for all coverage intervals $i$ of one sensor $j$ in order to express that
+ the perimeter of each sensor should be uniformly covered, but
+ $\alpha_{i}^{j}$ values can be differentiated between sensors to force some
+ regions to be better covered than others. The choice of $\beta \gg \alpha$
+ prevents the overcoverage, and so limit the activation of a large number of
+ sensors, but as $\alpha$ is low, some areas may be poorly covered. This
+ explains the results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a
+ large number of periods with low coverage ratio. With $\alpha \gg \beta$,
+ we favor the coverage even if some areas may be overcovered, so a high
+ coverage ratio is reached, but a large number of sensors are activated to
+ achieve this goal. Therefore the network lifetime is reduced. The choice
+ $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between
+ lifetime and coverage ratio.}}\\
\noindent {\bf 6.} The authors have performed a thorough review of existing
coverage methodologies. However, the clarity in the literature review is a
\textcolor{blue}{\textbf{\textsc{Answer:} References have been carefully checked
and seem to be consistent with the journal template. In Section~2, ``Related
literature'', we refer to papers dealing with coverage and lifetime in
- WSN. Each paragraph of this Section discusses the literature related to a
+ WSN. Each paragraph of this section discusses the literature related to a
particular aspect of the problem : 1. types of coverage, 2. types of scheme,
3. centralized versus distributed protocols, 4. optimization method. At the
- end of each paragraph we position our approach.}}\\
+ end of each paragraph we position our approach. We have also added a last
+ paragraph about our previous work on DiLCO protocol to explain the
+ difference with PeCO. }}\\
\noindent {\bf 7.} The methodology is implemented in OMNeT++ (network simulator)
and tested against 2 existing algorithms and a previously developed method by
may be an issue if this approach is used in an application that requires high
coverage ratio. \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Your remark is interesting. Indeed,
- Figures 8(a) and (b) highlight this result. PeCO protocol allows to achieve
+\textcolor{blue}{\textbf{\textsc{Answer:} Your remark is very interesting. Indeed,
+ Figures 8(a) and (b) highlight this result. The PeCO protocol allows to achieve
a coverage ratio greater than $50\%$ for far more periods than the others
three methods, but for applications requiring a high level of coverage
- (greater than $95\%$), DiLCO method is more efficient. It is explained at
+ (greater than $95\%$), the DiLCO method is more efficient. It is explained at
the end of Section 5.2.4.}}\\
%%%%%%%%%%%%%%%%%%%%%% ENGLISH and GRAMMAR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
every Section is indented in the new version. }}\\
\noindent {\ding{90} You seem to be writing in the first person. I suggest
- rewriting sentences that include “we” “our” or “I” in the third person. (There
+ rewriting sentences that include ``we'' ``our'' or ``I'' in the third person. (There
are too many instances to list them all. They are easily found using the find
tool.) } \\
\textcolor{blue}{\textbf{\textsc{Answer:} It is very common to find sentences
- with "we" and "our" in scientific papers to explain the work made by the
+ with ``we'' and ``our'' in scientific papers to explain the work made by the
authors. Nevertheless we agree with the reviewer and we reformulated some
sentences in the paper to avoid too many uses of the first person. }}\\
\noindent {\ding{90} Add an “and” after the comma on page 3 line 34.} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} “model as” instead of “Than” on page 10 line 12.} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} “no longer” instead of “no more” on page 10 line 31.} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} “in the active state” add the on page 10 line 34. } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent { \ding{90} Lots of English and grammar mistakes. I recommend
rereading the paper line by line and adjusting the sentences that do not make
between any pairs of sensors inside a subregion is less than or equal
to~3. Concerning the choice of the sensing period duration, it is correlated
with the types of applications, with the amount of initial energy in sensors
- batteries and also with the duration of the exchange phase. All applications
- do not have the same Quality of Service requirements. In our case
- information exchange is executed every hour, but the length of the sensing
- period could be reduced and adapted dynamically. On the one hand a small
- sensing period would allow to be more reliable but would have higher
- communication costs. On the other hand the choice of a long duration may
- cause problems in case of nodes failure during the sensing period.
- Several explanations on these points are given throughout the paper. In
- particular, we discuss the number of subregions in Section 5.2 and the
- sensing duration in the second paragraph of Section 5.1.}}\\
+ batteries, and also with the duration of the exchange phase. All
+ applications do not have the same Quality of Service requirements. In our
+ case, information exchange is executed every hour, but the length of the
+ sensing period could be reduced and adapted dynamically. On the one hand, a
+ small sensing period would allow the network to be more reliable but would
+ have higher communication costs. On the other hand, the choice of a long
+ duration may cause problems in case of nodes failure during the sensing
+ period. Several explanations on these points are given throughout the
+ paper. In particular, we discuss the number of subregions in Section 5.2 and
+ the sensing duration in the second paragraph of Section 5.1.}}\\
\noindent {\bf 2.}Page 9, Section 4, is the Perimeter-based coverage problem
NP-hard? This question is important for justifying the use of a Mixed Integer
\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter scheduling coverage
problem is NP-hard in general, it has been proved in the paper entitled
- "Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors
- with a Single Continuous Cover Range" from Ka-Shun Hung and King-Shan Lui
+ ``Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors
+ with a Single Continuous Cover Range'' from Ka-Shun Hung and King-Shan Lui
(EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075
doi:10.1155/2010/926075). In this paper, authors study the coverage of the
perimeter of a large object requiring to be monitored. In our study, the
large object to be monitored is the sensor itself (or more precisely its
- sensing area). This point has been highlighted at the beginning of
+ sensing area). This point has been highlighted at the beginning of
Section~4.}}\\
\noindent {\bf 3.} Page 9, the major problem with the present paper is, in my
should mention at the beginning of the paper what are the aims of the protocol,
and explain how the protocol is built to optimize these objectives. \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right. The mixed Integer Linear
+\textcolor{blue}{\textbf{\textsc{Answer:} Right. The Mixed Integer Linear
Program adresses a multiobjective problem, where the goal is to minimize
- overcoverage and undercoverage for each coverage interval of a sensor. As
- far as we know, representing the objective function as a weighted sum of
- criteria to be minimized in case of multicriteria optimization is a
+ overcoverage and undercoverage for each coverage interval of a sensor. To
+ the best of our knowledge, representing the objective function as a weighted
+ sum of criteria to be minimized in case of multicriteria optimization is a
classical method. In Section 5, the comparison of protocols with a large
variety of performance metrics allows to select the most appropriate method
according to the QoS requirement of the application.}}\\
Total number & S & I & GLPK IP & GLPK LP & nodes&CPLEX\\
of nodes &&&&relaxation &B\&B tree &\\
\hline
-100 & 6.25& 5&0.2 MB & 0.2 Mb &1 & 64 kB\\
+100 & 6.25& 5&0.2 MB & 0.2 MB &1 & 64 KB\\
\hline
-200 & 12.5& 11&1.7 MB & 1.6 Mb &1 & 281 kB\\
+200 & 12.5& 11&1.7 MB & 1.6 MB &1 & 281 KB\\
\hline
-300 &18.5 & 17&3.6 MB & 3.5 Mb & 3 &644 kB\\
+300 &18.5 & 17&3.6 MB & 3.5 MB & 3 &644 KB\\
\hline
\end{tabular}
-\medskip \\
-It is noteworthy that the difference of memory used with GLPK between the
-resolution of the IP and its LP-relaxation is very weak (not more than 0.1
-MB). The size of the branch and bound tree dos not exceed 3 nodes. This result
-leads one to believe that the memory use with CPLEX\textregistered for solving
-the IP would be very close to that for the LP-relaxation, that is to say around
-100 Kb for a subregion containing $S=10$ sensors. Moreover the IP seems to have
-some specifities that encourage us to develop our own solver (coefficents matrix
-is very sparse) or to use an existing heuristic to find good approximate
-solutions (Reference : ``A feasibility pump heuristic for general mixed-integer
-problems", Livio Bertacco and Matteo Fischetti and Andrea Lodi, Discrete
-Optimization, issn 1572-5286).
+\medskip \\ It is noteworthy that the difference of memory used with GLPK
+between the resolution of the IP and its LP-relaxation is very weak (not more
+than 0.1 MB). The size of the branch and bound tree does not exceed 3
+nodes. This result leads one to believe that the memory use with
+CPLEX\textregistered for solving the IP would be very close to that for the
+LP-relaxation, that is to say less than 300 KB for a subregion containing $S=12$
+sensors. Moreover the IP seems to have some specifities that encourage us to
+develop our own solver (coefficents matrix is very sparse) or to use an existing
+heuristic to find good approximate solutions (Reference : ``A feasibility pump
+heuristic for general mixed-integer problems", Livio Bertacco and Matteo
+Fischetti and Andrea Lodi, Discrete Optimization, issn 1572-5286).
\item the subdivision of the region of interest. To make the resolution of
integer programming tractable by a leader sensor, we need to limit the number
of nodes in each subregion (the number of variables and constraints of the
- integer programming is directly depending on the number of nodes and
+ integer programming directly depends on the number of nodes and
neigbors). It is therefore necessary to adapt the subdvision according to the
number of sensors deployed in the area and their sensing range (impact on the
number of coverage intervals).
\noindent {\ding{90} Page 5, lines 34 and 37, replace [0, $2\pi$] with [0,
$2\pi$) } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 5, line 36 and 43, replace ``figure 2" with ``Figure 2"
} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 5, line 50, replace ``section 4" with ``Section 4" } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 5, line 51, replace ``figure 3" with ``Figure 3"} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 7, line 20 ``regular homogeneous subregions" is too vague. } \\
\textcolor{blue}{\textbf{\textsc{Answer:} As mentioned in the previous remark,
the spatial subdivision was not clearly explained in the paper. We added a
discussion about this question in the article. Thank you for highlighting
- it. }}.\\
+ it. }}\\
\noindent {\ding{90} Page 7, line 24, replace ``figure 4" with ``Figure 4"} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 7, line 47, replace ``Five status" with ``Five statuses" } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 9, the constraints of the Mixed Integer Linear Program
(2) are not numbered. There are two inequalities for overcoverage and
\textcolor{blue}{\textbf{\textsc{Answer:} For minimizing the objective function,
$M_{i}^{j}$ and $V_{i}^{j}$ should be set to the smallest possible value
- such that the inequalities are satisfied. It is explained in the answer 4
- for the reviewer 1. But, at optimality, constraints are not necessary
+ such that the inequalities are satisfied. It is explained in answer 4
+ for reviewer 1. But, at optimality, constraints are not necessary
satisfied with equality. For instance, if a sensor $j$ is overcovered, there
exists at least one of its coverage interval (say $i$) for which the number
of active sensors (denoted by $l^{i}$) covering this part of the perimeter
connected". In order to assess this, the communication range should be known,
but it is not given in Table 2. } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed}}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 10, line 53, the ``Coverage ratio" definition is
provided for a given period p? Then in the formula on top of page 11, N is set
\noindent {\ding{90} Page 11, line 17 in the formula of ASR, |S| should be
replaced with J (where J is defined page 4 line 16). } \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
\noindent {\ding{90} Page 13, line 41 and 43, replace ``figure 8" with ``Figure 8"
} \\
-\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed.}}\\
We are very grateful to the reviewers who, by their recommendations, allowed us
to improve the quality of our article.
