Hello all, This is the presentation of Graph Colouring in Graph theory and application. Use this presentation as a reference if you have any doubt you can comment here.
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Hello all, This is the presentation of Graph Colouring in Graph theory and application. Use this presentation as a reference if you have any doubt you can comment here.
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Map Coloring and Some of Its Applications MD SHAH ALAM
This is a research paper which I have conducted at the final year of undergrad study and got 4.00/4.00. It is mainly related to graph theory and has many applications in practical life.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
Graph coloring is a special case of graph labeling. it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring.
Map Coloring and Some of Its Applications MD SHAH ALAM
This is a research paper which I have conducted at the final year of undergrad study and got 4.00/4.00. It is mainly related to graph theory and has many applications in practical life.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.Graph theory is also important in real life.
Graph coloring is a special case of graph labeling. it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring.
Talk given at neo4j conference "Graph Connect" - discussing some graph theory (old and new), and why knowing your stuff can come in handy on a software project.
This presentation is about applications of graph theory applications....it is updated version it was given at international conference at applications of graph theory at KAULALAMPUR MALYSIA 2OO7
Basic introduction and countermeasures to ransomware threats presentationDarwish Ahmad
Abstract-- Malware or malicious software are exist everywhere, internet or locally. This paper present a category of malware which cybercriminals (hackers, crackers, etc.) currently using for monetizing around the world via internet. Ransomware is the name of this category of malware and it has a variety of families inside it. There are two famous basic types crypto ransomware and locker ransomware. Crypto ransomware usually encrypt personal files of the victims with different cryptography algorithms according how crypto ransomware is designed. These cryptographic alogorithm might be symmetric (single key) or asymmetric (double key, public key). The second type of ransomware lock the victim device (personal computer, mobile device, etc) and prevent the user from accessing it. The countermeasures how to keep secure and safe our systems or network against this dangerous type of malware will be discuss also.
Designing Countermeasures For Tomorrows Threats : DocumentationDarwish Ahmad
Abstract:
Internet and network security is the most important and top priority issues for almost all types of organizations, for instance, military divisions, ministries, banks, other public and private sectors, and even to everyone who concerns it.
These organizations may use security mechanisms to protect their assets safe against evil and attackers, but most of the security countermeasures that they use are based on known attacks, threats and vulnerabilities. They hardly pay attention to protect their assets against unknown and new types of attacks, threats and vulnerabilities. Most of the organizations faced to challenges the new types of unknown attacks and threats.
This research paper's main aim is to focus and study approaches and solutions against the unknown attacks and threats, and therefore, titled Designing Countermeasures for Tomorrows Threats to make the organizations enable to detect new types attacks, threats or vulnerabilities before they damage their assets or systems.
In addition, the outcome of this research paper will give the chance to the organizations to learn who is attacking their systems, how they are being attacked, and what the attackers are trying to achieve. The concepts that this research paper (thesis) used for Designing Countermeasures for Tomorrows Threats are Honeypot and Honeynet systems.
Honeypot and Honeynet Systems are one of the most interesting and well-known concepts for all the security professionals to know their enemies and identify their weakness. Worth mentioning that most of the countries i.e. Iran, Pakistan, India, Saudi Arabia, Germany and Polish are using these concepts to protect their internal networks and assets against the attackers. Besides, there are a great number of security organizations and communities that use these concepts for research to learn and educate public about new types of attacks, threats and vulnerabilities naming Honeynet Project, Norse, FireEye, WorldMap and Global Botnet Threat Activity.
This thesis implemented most of the existed-based technologies on the concept of Honeypot and Honeynet systems both open source and close source. Finally suggest and recommend the best solution for Afghanistan to protect its internal networks especially important organizations like Ministry of Interior and other ministries and sectors.
Designing Countermeasures For Tomorrows ThreatsDarwish Ahmad
Abstract:
Internet and network security is the most important and top priority issues for almost all types of organizations, for instance, military divisions, ministries, banks, other public and private sectors, and even to everyone who concerns it.
These organizations may use security mechanisms to protect their assets safe against evil and attackers, but most of the security countermeasures that they use are based on known attacks, threats and vulnerabilities. They hardly pay attention to protect their assets against unknown and new types of attacks, threats and vulnerabilities. Most of the organizations faced to challenges the new types of unknown attacks and threats.
This research paper's main aim is to focus and study approaches and solutions against the unknown attacks and threats, and therefore, titled Designing Countermeasures for Tomorrows Threats to make the organizations enable to detect new types attacks, threats or vulnerabilities before they damage their assets or systems.
In addition, the outcome of this research paper will give the chance to the organizations to learn who is attacking their systems, how they are being attacked, and what the attackers are trying to achieve. The concepts that this research paper (thesis) used for Designing Countermeasures for Tomorrows Threats are Honeypot and Honeynet systems.
Honeypot and Honeynet Systems are one of the most interesting and well-known concepts for all the security professionals to know their enemies and identify their weakness. Worth mentioning that most of the countries i.e. Iran, Pakistan, India, Saudi Arabia, Germany and Polish are using these concepts to protect their internal networks and assets against the attackers. Besides, there are a great number of security organizations and communities that use these concepts for research to learn and educate public about new types of attacks, threats and vulnerabilities naming Honeynet Project, Norse, FireEye, WorldMap and Global Botnet Threat Activity.
This thesis implemented most of the existed-based technologies on the concept of Honeypot and Honeynet systems both open source and close source. Finally suggest and recommend the best solution for Afghanistan to protect its internal networks especially important organizations like Ministry of Interior and other ministries and sectors.
Königsberg, Euler and the origins of graph theorypupbroeders
A slidecast explaining the origins of graph theory and the solution to the 7 bridges problem of Königsberg. I discuss some modern applications of graph theory too.
Design and Implementation of a Procedural Content Generation Web Application ...Juan Quiroz
This paper was presented at the 25th International Conference on Software Engineering and Data Engineering (SEDE 2016) in Denver. We present a web application for the procedural generation of transformations of 3D models. We generate the transformations by algorithmically generating the vertex shaders of the 3D models. The vertex shaders are created with an interactive genetic algorithm, which displays to the user the visual effect caused by each vertex shader, allows the user to select the visual effect the user likes best, and produces a new generation of vertex shaders using the user feedback as the fitness measure of the genetic algorithm. We use genetic programming to represent each vertex shader as a computer program. This paper presents details of requirements specification, software architecture, high and low-level design, and prototype user interface. We discuss the project’s current status and development challenges.
Introduction to Graphs
Topics:
Definition: Graph
Related Definitions
Applications
Teaching material for the course of "Tecniche di Programmazione" at Politecnico di Torino in year 2012/2013. More information: http://bit.ly/tecn-progr
An analysis between different algorithms for the graph vertex coloring problem IJECEIAES
This research focuses on an analysis of different algorithms for the graph vertex coloring problem. Some approaches to solving the problem are discussed. Moreover, some studies for the problem and several methods for its solution are analyzed as well. An exact algorithm (using the backtracking method) is presented. The complexity analysis of the algorithm is discussed. Determining the average execution time of the exact algorithm is consistent with the multitasking mode of the operating system. This algorithm generates optimal solutions for all studied graphs. In addition, two heuristic algorithms for solving the graph vertex coloring problem are used as well. The results show that the exact algorithm can be used to solve the graph vertex coloring problem for small graphs with 30-35 vertices. For half of the graphs, all three algorithms have found the optimal solutions. The suboptimal solutions generated by the approximate algorithms are identical in terms of the number of colors needed to color the corresponding graphs. The results show that the linear increase in the number of vertices and edges of the analyzed graphs causes a linear increase in the number of colors needed to color these graphs.
Initial Graphulo Graph Analytics Expressed in GraphBLAS:
GraphBLAS is an effort to define standard building blocks for graph algorithms in the language of linear algebra. Graphulo is a project to implement the GraphBLAS using Accumulo.
Graph coloring is an important concept in graph theory. It is a special kind of problem in which we have assign colors to certain elements of the graph along with certain constraints. Suppose we are given K colors, we have to color the vertices in such a way that no two adjacent vertices of the graph have the same color, this is known as vertex coloring, similarly we have edge coloring and face coloring. The coloring problem has a huge number of applications in modern computer science such as making schedule of time table , Sudoku, Bipartite graphs , Map coloring, data mining, networking. In this paper we are going to focus on certain applications like Final exam timetabling, Aircraft Scheduling, guarding an art gallery.
Distributed coloring with O(sqrt. log n) bitsSubhajit Sahu
Distributed Coloring with O˜(√log n) Bits
K Kothapalli, M Onus, C Scheideler, C Schindelhauer
Proc. of IEEE International Parallel and Distributed Processing Symposium …
We consider the well-known vertex coloring problem: given a graph G, find a coloring of its vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree∆ can be colored with∆+ 1 colors, and distributed algorithms that find a (∆+ 1)-coloring in a logarithmic number of communication rounds, with high probability, are known since more than a decade. This is in general the best possible if only a constant number of bits can be sent along every edge in each round. In fact, we show that for the n-node cycle the bit complexity of the coloring problem is
Ω (log n). More precisely, if only one bit can be sent along each edge in a round, then every distributed coloring algorithm (ie, algorithms in which every node has the same initial state and initially only knows its own edges) needs at least Ω (log n) rounds, with high probability, to color the n–node cycle, for any finite number of colors. But what if the edges have orientations, ie, the endpoints of an edge agree on its orientation (while bits may still flow in both directions)? Edge orientations naturally occur in dynamic networks where new nodes establish connections to old nodes. Does this allow one to provide faster coloring algorithms?
A VERY high level over view of Graph Analytics concepts and techniques, including structural analytics, Connectivity Analytics, Community Analytics, Path Analytics, as well as Pattern Matching
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
UiPath Test Automation using UiPath Test Suite series, part 4
Introduction to Graph and Graph Coloring
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Theoretical Section
Practical Section
INTRODUCTION TO GRAPH AND GRAPH
COLORING PROBLEM
Design Methods and Analysis of Algorithm
Darwish Ahmad Herati
St. Joseph’s College (Autonomous)
Computer Science Department
MSc (Computer Science)
SUPERVISOR
Prof. Ms. Mrinmoyee Bhattacharya
September 1, 2015
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Contents
1 Theoretical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
2 Practical Section
Examples
Implementation
Simulation Technologies
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Terminologies of Graphs:
Spanning Tree of a Graph: A spanning tree of an
undirected graph is a subgraph that contains all the
vertices, and no cycles. If we add any edge to the spanning
tree, it forms a cycle, and the tree becomes a graph.
It is possible to define a spanning tree for directed graphs,
however the definition is rather complicated and will not be
discussed here.
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Terminologies of Graphs:
Chromatic Number: The chromatic number of a graph G
is the smallest number k for which a k-coloring of the
vertices of G is possible.We will use the notation x(G) to
denote the chromatic number of G.
k-coloring: A k-coloring of a graph G is a coloring of the
vertices of G using k colors and satisfying the requirement
that adjacent vertices are colored with different colors.
Optimal Coloring: An optimal coloring of a graph G is a
coloring of the vertices of G using the fewest possible
number of colors.
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Introduction to Graph Coloring
Graph coloring is one of the oldest concepts in the theory
of graphs,
A graph G = (V, E) consists two sets where one is the set
of vertices and another is the set of edges such that each
edges is associated with an un ordered pair of vertices and
graph coloring is one of the most useful models in graph
theory. Graph coloring is the way of coloring the vertices of
a graph with the minimum number of colors such that no
two adjacent vertices share the same color.
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Greedy Algorithm for Graph Coloring:
Step 1. Assign the first color (c1) to the first vertex (v1).
Step 2. Vertex v2 is assigned color c1 if it is not adjacent
to v1; otherwise it gets assigned color c2.
Steps 3,4,...,n. Vertex v1 is assigned the first possible
color in the priority list of colors (i.e. the first color that has
not been assigned to one of the already colored neighbors
of vi ).
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Analysis of Graph Coloring:
An Upper bound on the computing time of MCOLORING
can arrived by finding the number of internal nodes in the
state space tree is:
At each internal node, O(mn) time is spent by Next Value
to determine the children corresponding to legal coloring.
Hence the total time is bounded by:
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Aircraft Scheduling:
Aircraft scheduling: Assume that we have k aircrafts,
and we have to assign them to n flights, where the ith flight
is during the time interval (ai, bi). Clearly, if two flights
overlap, then we cannot assign the same aircraft to both
flights. The vertices of the conflict graph correspond to the
flights, two vertices are connected if the corresponding
time intervals overlap. Therefore the conflict graph is an
interval graph, which can be colored optimally in
polynomial time.
Darwish Ahmad Herati Design Methods and analysis of Algorithm
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Making Schedule or Time Table:
Making Schedule or Time Table: Suppose we want to
make am exam schedule for a university. We have list
different subjects and students enrolled in every subject.
Many subjects would have common students (of same
batch, some backlog students, etc). How do we schedule
the exam so that no two exams with a common student are
scheduled at same time? How many minimum time slots
are needed to schedule all exams? This problem can be
represented as a graph where every vertex is a subject
and an edge between two vertices mean there is a
common student. So this is a graph coloring problem
where minimum number of time slots is equal to the
chromatic number of the graph.
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Theoretical Section
Practical Section
Introduction
History
Definitions
Algorithm
Complexity
Applications
Mobile Radio Frequency Assignment:
Mobile Radio Frequency Assignment: When
frequencies are assigned to towers, frequencies assigned
to all towers at the same location must be different. How to
assign frequencies with this constraint? What is the
minimum number of frequencies needed? This problem is
also an instance of graph coloring problem where every
tower represents a vertex and an edge between two towers
represents that they are in range of each other.
Darwish Ahmad Herati Design Methods and analysis of Algorithm