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SURVEILLANCE SYSTEM
SUBMITTED BY:
Pranjal Kumar Srivastava (10103554)
Saksham Saxena (10103621)
SUBMITTED TO:
Dr. Manish Kumar Thakur
(Assistant Professor – JIIT)
INTRODUCTION
 In graph theory, a vertex cover of a graph is a set of vertices such that each
edge of the graph is incident to at least one vertex of the set. The problem of
finding a minimum vertex cover is a classical optimization
problem in computer science and is a typical example of an NP-
hard optimization problem that has an approximation algorithm.
 An algorithm that returns near-optimal solutions is called an approximation
algorithm. In computer science, the vertex cover problem or node cover
problem is one of Karp's 21 NP-complete problems. It is often used in
complexity theory to prove NP-hardness of more complicated problems.
 Any user who wants to install CCTV cameras in his/her building can upload
two files containing different positions of the building and their connections
on the website. The algorithm returns the best possible solution in the form of
table displaying the appropriate positions and the number of cameras required
at these positions along with the total approximate cost of installation. User
can also download all other possible solutions.
PROBLEM STATEMENT
To develop an application such that a user will input
the graph of a building or a locality to find minimum
number of CCTV cameras or security guards
required for the surveillance. Our application using
the optimum algorithm will return all the best
possible locations where the CCTVs can be installed
or security guards can be placed. It will also give
the number of cameras required and the total cost
of installation.
BENEFITS/NOVELITY OF THE
APPLICATION
 It helps remove the discrepancy in the result that occurs due to
human error. It selects the minimum number of nodes from which all
the edges can be accessed.
 This helps in placing cameras at minimum required places and helps in
reducing the human effort and cost that is put in selecting these
areas/places.
 This can also be used in placing minimum number of ATMs in the city
so as to reduce the overall cost.
 Our proposed algorithm ”Modified Alom” gives all possible sets of
minimum vertex cover, thus the user can opt for any one of them
according to his/her constraints.
ARCHITECTURE OF APPLICATION
 User uploads its Location file of the building which gives aus all the possible
locations to put the camera.
 User uploads its Connectivity file of the building which gives us the connectivity of
all possible locations with each other.
 The algorithm form the graph from the input in the form of adjacency matrix.
 It then calculates the minimum vertex cover using the proposed Modified Alom
algorithm keeping the constraints of costs and ranges in consideration and gives us
the output in the form of a table.
USE CASE DIAGRAM
ACTIVITY DIAGRAM
CONTROL FLOW DIAGRAM
TESTING REQUIRED
Type of Test
Will test be
performed?
Comments/ Explanations Software Component
Requirement Testing Yes
All the input requirements
need to be fulfilled
Graph.c, Connectivity.xls,
Locations.xls,
College_Graph.txt
Unit Yes
The application is mainly
divided into data input,
running of algorithm and
display
Input- College_Graph.txt
Algorithm-
Modified_Algorithm.c
Output-
College_Graph_Modified_Al
om.xls
Integration No
All three components of
application are independent
Performance Yes
Performance of the
algorithms to be tested
Analysis Table
Stress Yes
All the algorithms have been
tested on graphs with
approximately 1000 nodes.
Security No
At this point, security testing
is not required.
Load Yes Input is real time data
LIMITATION OF THE APPLICATION
 Algorithm is slow but accurate on large graphs.
 Application doesn’t consider the camera angle.
 It doesn’t give the direction in which the camera is to be
installed.
 Any extra installation cost is not considered in the final
cost displayed.
FINDINGS
 Approximation Algorithm: For minimum vertex cover problem, this algorithm randomly picks
up an edge from the graph and includes both of its vertices in the vertex cover set. It then
removes all the edges incident on those two vertices. It iteratively continues until no edges
are left.
 Greedy Algorithm: For minimum vertex cover problem, the greedy algorithm randomly picks
up an edge from the graph and includes its end vertex in the vertex cover set. It then removes
all the edges incident on that vertex from the graph. It iteratively continues until no edges are
left in the graph.
 Clever Greedy Algorithm: For minimum vertex cover problem, the clever greedy algorithm
finds the vertex with the maximum degree in the graph and includes it in the vertex cover set.
It then removes all the edges incident on that vertex from the graph. It iteratively continues
until no edges are left in the graph.
 Sorted List Left Algorithm: For minimum vertex cover problem, the Sorted List Left algorithm
selects the vertex belonging to the labelled graph that has at least one neighbor with a lower
degree or a right neighbor with the same degree. Then the vertex is included in the vertex
cover set.
 Alom Algorithm: For minimum vertex cover problem, the ‘Alom’ algorithm selects the vertex
which has maximum number of edges incident to it. All the edges are discarded incident to
that vertex. If more than one vertex have same maximum number of edges, this algorithm
select that vertex which have at least one edge that is not covered by other vertices, which
has maximum edge. This process is repeated until to cover all the vertices of the graph.
CONCLUSION
 Minimum Vertex Cover Algorithms are used in finding out the minimum
number of nodes or vertices that can traverse each path in the graph.
In this project, we have implemented five different algorithms for
finding out the minimum vertex cover of 20 different graphs. The aim
is to find the best possible algorithm that returns the minimum vertex
cover. The algorithm proposed by us is a slight modification in the
existing Alom Algorithm.
 The application is designed in such a way that it takes the input from
the user. The input will be an excel file containing the locations and
the connections of the locations. Algorithm is then run on this graph
and gives the best possible solution to the minimum vertex cover
problem. The most optimum solution is displayed in a table also
showing the required number of cameras at each location. Graph is
also displayed highlighting the positions where cameras are needed to
be installed. All other possible solutions can also be downloaded in
the form of excel sheet.
FUTURE WORK
 Angle of camera being installed can be
considered.
 Direction of camera must also be taken into
account.
 Other costs and charges should be added.
 Any other feature like giving information about
the various camera installation mechanics can be
given.
REFERENCES
 [1] C. E. Leiserson, C. Stein, R. L. Rivest, and T. H. Cormen ”Introduction to
Algorithms McGraw-Hill, New York, 2nd edition: Local 2-Approximation
Algorithm”,2001.
 [2] D.S. Johnson and M.R.Grarey, “Computers and Intractability-A guide to the
Theory of NP-Completeness, freeman: Greedy Algorithm for minimum vertex
cover”, 1978.
 [3] Durgesh Pant, Kamlesh Chandra Purohit, and Sushil Chandra Dimri, “Clever
Greedy Minimum Vertex Cover Algorithm”, 2010.
 [4] B. M. Monjurul Alom, Mohammad Abdur Rouf and Someresh Das, “Performance
Evaluation of Vertex Cover and Set Cover Problem using Optimal Algorithm”, 2011.
 [5] Christian Laforest, Eric Angel and Romain Campigotto, “Algorithms for the
Vertex Cover Problem on Large Graphs”, 2010.
 [6] Kaile Su, Qingliang Chen and Shaowie Cai, “ELWS-A new local search for
minimum vertex cover”, 2007.
 [7] Marija Milanovic, “Solving the generalized vertex cover algorithm by genetic
algorithm”, 2008.
 [8] Ge Xia, Iyad A.Kanj and Jianer Chen, “Improved Parameterized Upper Bounds
for Vertex Cover”, 2001.

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Surveillance System (Minimum Vertex Cover Problem)

  • 1. SURVEILLANCE SYSTEM SUBMITTED BY: Pranjal Kumar Srivastava (10103554) Saksham Saxena (10103621) SUBMITTED TO: Dr. Manish Kumar Thakur (Assistant Professor – JIIT)
  • 2. INTRODUCTION  In graph theory, a vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization problem in computer science and is a typical example of an NP- hard optimization problem that has an approximation algorithm.  An algorithm that returns near-optimal solutions is called an approximation algorithm. In computer science, the vertex cover problem or node cover problem is one of Karp's 21 NP-complete problems. It is often used in complexity theory to prove NP-hardness of more complicated problems.  Any user who wants to install CCTV cameras in his/her building can upload two files containing different positions of the building and their connections on the website. The algorithm returns the best possible solution in the form of table displaying the appropriate positions and the number of cameras required at these positions along with the total approximate cost of installation. User can also download all other possible solutions.
  • 3. PROBLEM STATEMENT To develop an application such that a user will input the graph of a building or a locality to find minimum number of CCTV cameras or security guards required for the surveillance. Our application using the optimum algorithm will return all the best possible locations where the CCTVs can be installed or security guards can be placed. It will also give the number of cameras required and the total cost of installation.
  • 4. BENEFITS/NOVELITY OF THE APPLICATION  It helps remove the discrepancy in the result that occurs due to human error. It selects the minimum number of nodes from which all the edges can be accessed.  This helps in placing cameras at minimum required places and helps in reducing the human effort and cost that is put in selecting these areas/places.  This can also be used in placing minimum number of ATMs in the city so as to reduce the overall cost.  Our proposed algorithm ”Modified Alom” gives all possible sets of minimum vertex cover, thus the user can opt for any one of them according to his/her constraints.
  • 5. ARCHITECTURE OF APPLICATION  User uploads its Location file of the building which gives aus all the possible locations to put the camera.  User uploads its Connectivity file of the building which gives us the connectivity of all possible locations with each other.  The algorithm form the graph from the input in the form of adjacency matrix.  It then calculates the minimum vertex cover using the proposed Modified Alom algorithm keeping the constraints of costs and ranges in consideration and gives us the output in the form of a table.
  • 9. TESTING REQUIRED Type of Test Will test be performed? Comments/ Explanations Software Component Requirement Testing Yes All the input requirements need to be fulfilled Graph.c, Connectivity.xls, Locations.xls, College_Graph.txt Unit Yes The application is mainly divided into data input, running of algorithm and display Input- College_Graph.txt Algorithm- Modified_Algorithm.c Output- College_Graph_Modified_Al om.xls Integration No All three components of application are independent Performance Yes Performance of the algorithms to be tested Analysis Table Stress Yes All the algorithms have been tested on graphs with approximately 1000 nodes. Security No At this point, security testing is not required. Load Yes Input is real time data
  • 10. LIMITATION OF THE APPLICATION  Algorithm is slow but accurate on large graphs.  Application doesn’t consider the camera angle.  It doesn’t give the direction in which the camera is to be installed.  Any extra installation cost is not considered in the final cost displayed.
  • 11. FINDINGS  Approximation Algorithm: For minimum vertex cover problem, this algorithm randomly picks up an edge from the graph and includes both of its vertices in the vertex cover set. It then removes all the edges incident on those two vertices. It iteratively continues until no edges are left.  Greedy Algorithm: For minimum vertex cover problem, the greedy algorithm randomly picks up an edge from the graph and includes its end vertex in the vertex cover set. It then removes all the edges incident on that vertex from the graph. It iteratively continues until no edges are left in the graph.  Clever Greedy Algorithm: For minimum vertex cover problem, the clever greedy algorithm finds the vertex with the maximum degree in the graph and includes it in the vertex cover set. It then removes all the edges incident on that vertex from the graph. It iteratively continues until no edges are left in the graph.  Sorted List Left Algorithm: For minimum vertex cover problem, the Sorted List Left algorithm selects the vertex belonging to the labelled graph that has at least one neighbor with a lower degree or a right neighbor with the same degree. Then the vertex is included in the vertex cover set.  Alom Algorithm: For minimum vertex cover problem, the ‘Alom’ algorithm selects the vertex which has maximum number of edges incident to it. All the edges are discarded incident to that vertex. If more than one vertex have same maximum number of edges, this algorithm select that vertex which have at least one edge that is not covered by other vertices, which has maximum edge. This process is repeated until to cover all the vertices of the graph.
  • 12. CONCLUSION  Minimum Vertex Cover Algorithms are used in finding out the minimum number of nodes or vertices that can traverse each path in the graph. In this project, we have implemented five different algorithms for finding out the minimum vertex cover of 20 different graphs. The aim is to find the best possible algorithm that returns the minimum vertex cover. The algorithm proposed by us is a slight modification in the existing Alom Algorithm.  The application is designed in such a way that it takes the input from the user. The input will be an excel file containing the locations and the connections of the locations. Algorithm is then run on this graph and gives the best possible solution to the minimum vertex cover problem. The most optimum solution is displayed in a table also showing the required number of cameras at each location. Graph is also displayed highlighting the positions where cameras are needed to be installed. All other possible solutions can also be downloaded in the form of excel sheet.
  • 13. FUTURE WORK  Angle of camera being installed can be considered.  Direction of camera must also be taken into account.  Other costs and charges should be added.  Any other feature like giving information about the various camera installation mechanics can be given.
  • 14. REFERENCES  [1] C. E. Leiserson, C. Stein, R. L. Rivest, and T. H. Cormen ”Introduction to Algorithms McGraw-Hill, New York, 2nd edition: Local 2-Approximation Algorithm”,2001.  [2] D.S. Johnson and M.R.Grarey, “Computers and Intractability-A guide to the Theory of NP-Completeness, freeman: Greedy Algorithm for minimum vertex cover”, 1978.  [3] Durgesh Pant, Kamlesh Chandra Purohit, and Sushil Chandra Dimri, “Clever Greedy Minimum Vertex Cover Algorithm”, 2010.  [4] B. M. Monjurul Alom, Mohammad Abdur Rouf and Someresh Das, “Performance Evaluation of Vertex Cover and Set Cover Problem using Optimal Algorithm”, 2011.  [5] Christian Laforest, Eric Angel and Romain Campigotto, “Algorithms for the Vertex Cover Problem on Large Graphs”, 2010.  [6] Kaile Su, Qingliang Chen and Shaowie Cai, “ELWS-A new local search for minimum vertex cover”, 2007.  [7] Marija Milanovic, “Solving the generalized vertex cover algorithm by genetic algorithm”, 2008.  [8] Ge Xia, Iyad A.Kanj and Jianer Chen, “Improved Parameterized Upper Bounds for Vertex Cover”, 2001.