This document describes a surveillance system application that finds the minimum number of CCTV cameras needed to monitor a building or area. The application takes input of a building's layout and connectivity between locations. It uses a modified Alom algorithm to find the minimum vertex cover of this graph, representing the optimal camera placements. The output is a table showing camera locations and numbers, along with the total installation cost. The application aims to accurately and cost-effectively determine surveillance needs compared to human estimates.

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.

6. USE CASE DIAGRAM

7. ACTIVITY DIAGRAM

8. CONTROL FLOW DIAGRAM

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.