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Mark de Berg
Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example, because the problems are NP-hard. The goal of the Approximation Algorithms course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations.
Prerequisites:
Read more
Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example, because the problems are NP-hard. The goal of the Approximation Algorithms course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations.
Prerequisites:
Read more
Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example, because the problems are NP-hard. The goal of the Approximation Algorithms course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations.
Prerequisites:
In order to successfully take this course, you should already have a basic knowledge of algorithms and mathematics. Here's a short list of what you are supposed to know:
- O-notation, Ω-notation, Θ-notation; how to analyze algorithms
- Basic calculus: manipulating summations, solving recurrences, working with logarithms, etc.
- Basic probability theory: events, probability distributions, random variables, expected values etc.
- Basic data structures: linked lists, stacks, queues, heaps
- (Balanced) binary search trees
- Basic sorting algorithms, for example MergeSort, InsertionSort, QuickSort
- Graph terminology, representations of graphs (adjacency lists and adjacency matrix), basic graph algorithms (BFS, DFS, topological sort, shortest paths)
The material for this course is based on the course notes that can be found under the resources tab.
Register for this course and see more details by visiting:
OpenCourser.com/course/kvtd1s/approximation
What's inside
Syllabus
Introduction to Approximation algorithms
In the module the motivation for studying approximation algorithms will be given. We will discuss what optimization problems are, and what the difference between heuristics and approximation algorithms is. Finally, we will introduce the concept of approximation ratio, which plays a central role in the analysis of the quality of approximation algorithms.
Read more
Syllabus
Introduction to Approximation algorithms
In the module the motivation for studying approximation algorithms will be given. We will discuss what optimization problems are, and what the difference between heuristics and approximation algorithms is. Finally, we will introduce the concept of approximation ratio, which plays a central role in the analysis of the quality of approximation algorithms.
Read more
The Load Balancing problem
In this module we will study various approximation algorithms for the load balancing problem. This problems asks to distribute a given set of jobs, each with a certain processing time, over a number of machine. The goal is to do this such that all jobs are finished as soon as possible. We will analyze the quality of the computed solutions computed using the concept of rho-approximation, which we saw in the previous lecture. In this analysis we will see that lower bounds on the optimal solution play a crucial role in the analysis (or, for maximization problems: upper bounds).
LP Relaxation
In this module we will introduce the technique of LP relaxation to design approximation algorithms, and explain how to analyze the approximation ratio of an algorithm based in LP relaxation. We will do this using the (weighted) Vertex Cover problem as an example. Before we explain the technique of LP relaxation, however, we first give a simple 2-approximation algorithm for the unweighted Vertex Cover problem.
Polynomial-time approximation schemes
In this module we will introduce the concept of Polynomial-Time Approximation Scheme (PTAS), which are algorithms that can get arbitrarily close to an optimal solution. We describe a general technique to design PTASs, and apply it to the famous Knapsack problem. Finally we will see how to analyze PTASs that are designed with the general technique.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Explores approximation algorithms, which is a key concept in optimization
Taught by Mark de Berg, who is an esteemed professor in the field of algorithms
Develops practical skills in designing and analyzing approximation algorithms, which are valuable in various domains
Requires prerequisites in algorithms and mathematics, making it suitable for learners with a solid foundation in these areas
Save this course
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Reviews summary
Approximation algorithms: highly praised
learners say this course is an insightful and thorough introduction to approximation algorithms. Highly received, students praise its clear explanations, engaging assignments, and informative presentations. Additionally, learners commend the course's excellent instructor, Professor Mark de Berg.
The material is explained very clearly
"The material is explained very clearly."
"The examples are very useful."
"Short but compact course that discusses important topics."
Challenging assignments to reinforce learning
"The quizes and programming homeworks are challenging enough to help to check your studying procedure."
Professor Mark de Berg is an amazing instructor
"Prof. Mark de Berg is an amazing instructor and gives clear lecture videos."
"Professor speaks english very well and hence no one will face any problem related to language."
Discussion forums remain unanswered
"All the questions in discussion forums remains unanswered."
"Mentors of this course are sitting idle."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Approximation Algorithms with these
activities:
Organize Course Materials
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Organization of course materials will aid in review and retrieval of information, enhancing understanding.
Browse courses on
Organization
Show steps
-
Gather all course notes, assignments, and resources.
-
Create a system for organizing and storing the materials (e.g., folders, binders, digital files).
-
Review the materials regularly to reinforce learning.
Review: 'Approximation Algorithms' by Vijay Vazirani
Show steps
Reading and reviewing this book will provide a comprehensive understanding of approximation algorithms, their techniques, and applications.
View
Approximation Algorithms
on Amazon
Show steps
-
Read the book and take notes on key concepts and algorithms.
-
Summarize the main ideas and techniques presented in the book.
-
Evaluate the strengths and weaknesses of the algorithms discussed.
Solve Approximation Algorithm Problems
Show steps
Solve approximation algorithm problems to reinforce the concepts and techniques covered in the course and improve problem-solving skills.
Browse courses on
Load Balancing
Show steps
-
Review the course notes and identify key approximation algorithms.
-
Practice solving problems related to load balancing.
-
Solve problems related to the weighted vertex cover problem.
-
Work on problems involving polynomial-time approximation schemes (PTAS).
Four other activities
Expand to see all activities and additional details
Show all seven activities
Attend a Workshop on Approximation Algorithms
Show steps
Attending a workshop will allow for in-depth exploration of approximation algorithms and interactions with experts.
Browse courses on
Approximation Algorithms
Show steps
-
Identify and register for a relevant workshop on approximation algorithms.
-
Actively participate in the workshop sessions and ask questions.
-
Network with other attendees and experts in the field.
Explain an Approximation Algorithm
Show steps
Creating an explanation of an approximation algorithm will enhance understanding and communication skills.
Browse courses on
Load Balancing
Show steps
-
Choose an approximation algorithm covered in the course.
-
Prepare an outline of the explanation, including the algorithm's purpose, steps, and analysis.
-
Develop a clear and concise explanation in your preferred format (e.g., written document, presentation, video).
-
Share the explanation with peers or instructors for feedback.
Mentor a Peer on Approximation Algorithms
Show steps
Mentoring others will reinforce your understanding of approximation algorithms while assisting peers.
Browse courses on
Approximation Algorithms
Show steps
-
Identify a peer who would benefit from guidance on approximation algorithms.
-
Offer your assistance and establish regular mentoring sessions.
-
Review course concepts and work through problems together.
-
Provide feedback and support to enhance their understanding.
Develop an Approximation Algorithm for a Novel Problem
Show steps
Developing an approximation algorithm for a novel problem fosters critical thinking, problem-solving, and algorithmic design skills.
Browse courses on
Approximation Algorithms
Show steps
-
Identify a real-world problem that could benefit from an approximation algorithm.
-
Research existing approximation algorithms and techniques.
-
Design and implement your own approximation algorithm.
-
Analyze the performance of your algorithm and compare it to known bounds.
-
Write a technical report or paper describing your algorithm and findings.
Organize Course Materials
Show steps
Organization of course materials will aid in review and retrieval of information, enhancing understanding.
Browse courses on
Organization
Show steps
Show steps
Show steps
- Gather all course notes, assignments, and resources.
- Create a system for organizing and storing the materials (e.g., folders, binders, digital files).
- Review the materials regularly to reinforce learning.
Review: 'Approximation Algorithms' by Vijay Vazirani
Show steps
Reading and reviewing this book will provide a comprehensive understanding of approximation algorithms, their techniques, and applications.
View
Approximation Algorithms
on Amazon
Show steps
Show steps
Show steps
- Read the book and take notes on key concepts and algorithms.
- Summarize the main ideas and techniques presented in the book.
- Evaluate the strengths and weaknesses of the algorithms discussed.
Solve Approximation Algorithm Problems
Show steps
Solve approximation algorithm problems to reinforce the concepts and techniques covered in the course and improve problem-solving skills.
Browse courses on
Load Balancing
Show steps
Show steps
Show steps
- Review the course notes and identify key approximation algorithms.
- Practice solving problems related to load balancing.
- Solve problems related to the weighted vertex cover problem.
- Work on problems involving polynomial-time approximation schemes (PTAS).
Four other activities
Expand to see all activities and additional details
Show all seven activities
Attend a Workshop on Approximation Algorithms
Show steps
Attending a workshop will allow for in-depth exploration of approximation algorithms and interactions with experts.
Browse courses on
Approximation Algorithms
Show steps
Show steps
Show steps
- Identify and register for a relevant workshop on approximation algorithms.
- Actively participate in the workshop sessions and ask questions.
- Network with other attendees and experts in the field.
Explain an Approximation Algorithm
Show steps
Creating an explanation of an approximation algorithm will enhance understanding and communication skills.
Browse courses on
Load Balancing
Show steps
Show steps
Show steps
- Choose an approximation algorithm covered in the course.
- Prepare an outline of the explanation, including the algorithm's purpose, steps, and analysis.
- Develop a clear and concise explanation in your preferred format (e.g., written document, presentation, video).
- Share the explanation with peers or instructors for feedback.
Mentor a Peer on Approximation Algorithms
Show steps
Mentoring others will reinforce your understanding of approximation algorithms while assisting peers.
Browse courses on
Approximation Algorithms
Show steps
Show steps
Show steps
- Identify a peer who would benefit from guidance on approximation algorithms.
- Offer your assistance and establish regular mentoring sessions.
- Review course concepts and work through problems together.
- Provide feedback and support to enhance their understanding.
Develop an Approximation Algorithm for a Novel Problem
Show steps
Developing an approximation algorithm for a novel problem fosters critical thinking, problem-solving, and algorithmic design skills.
Browse courses on
Approximation Algorithms
Show steps
Show steps
Show steps
- Identify a real-world problem that could benefit from an approximation algorithm.
- Research existing approximation algorithms and techniques.
- Design and implement your own approximation algorithm.
- Analyze the performance of your algorithm and compare it to known bounds.
- Write a technical report or paper describing your algorithm and findings.
Career center
Learners who complete Approximation Algorithms will develop knowledge and skills
that may be useful to these careers:
Investigador de Operaciones
Investigador de Operaciones
Los Investigadores de Operaciones utilizan técnicas matemáticas y analíticas para resolver problemas complejos en una variedad de industrias, como finanzas, atención médica y logística. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas necesarios para resolver problemas de optimización que surgen en estos campos. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son esenciales para una carrera exitosa como Investigador de Operaciones.
Científico de datos
Científico de datos
Los Científicos de Datos utilizan herramientas y técnicas estadísticas y de aprendizaje automático para extraer información valiosa de grandes conjuntos de datos. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos de optimización y análisis de datos que son esenciales para una carrera exitosa como Científico de Datos. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Científicos de Datos.
Ingeniero de Software
Ingeniero de Software
Los Ingenieros de Software diseñan, desarrollan y mantienen sistemas de software. El curso de Algoritmos de Aproximación proporciona una base sólida en los fundamentos teóricos de la ciencia computacional que son esenciales para una carrera exitosa como Ingeniero de Software. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Ingenieros de Software.
Analista de negocios
Analista de negocios
Los Analistas de Negocios identifican y analizan las necesidades comerciales y desarrollan soluciones para mejorar los procesos y el rendimiento. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Analista de Negocios. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Analistas de Negocios.
Gestor de proyectos
Gestor de proyectos
Los Gestores de Proyectos planifican, organizan y gestionan proyectos para alcanzar objetivos específicos. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Gestor de Proyectos. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Gestores de Proyectos.
Consultor de gestión
Consultor de gestión
Los Consultores de Gestión ayudan a las empresas a identificar y resolver problemas comerciales. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Consultor de Gestión. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Consultores de Gestión.
Analista Financiero
Analista Financiero
Los Analistas Financieros analizan y hacen recomendaciones sobre inversiones y decisiones financieras. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Analista Financiero. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Analistas Financieros.
Actuario
Actuario
Los Actuarios utilizan principios matemáticos y estadísticos para evaluar y gestionar el riesgo. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Actuario. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Actuarios.
Matemático
Matemático
Los Matemáticos investigan y desarrollan teorías y principios matemáticos. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Matemático. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Matemáticos.
Estadístico
Estadístico
Los Estadísticos recopilan, analizan e interpretan datos para obtener información valiosa. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Estadístico. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Estadísticos.
Analista de investigación de operaciones
Analista de investigación de operaciones
Los Analistas de Investigación de Operaciones utilizan técnicas matemáticas y analíticas para resolver problemas complejos en una variedad de industrias. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Analista de Investigación de Operaciones. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Analistas de Investigación de Operaciones.
Ingeniero Industrial
Ingeniero Industrial
Los Ingenieros Industriales diseñan, implementan y mejoran sistemas integrados de personas, materiales y equipos. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Ingeniero Industrial. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Ingenieros Industriales.
Analista de Sistemas
Analista de Sistemas
Los Analistas de Sistemas analizan y mejoran los sistemas de información. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Analista de Sistemas. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Analistas de Sistemas.
Programador
Programador
Los Programadores diseñan, desarrollan y mantienen aplicaciones y sistemas de software. El curso de Algoritmos de Aproximación proporciona una base sólida en los fundamentos teóricos de la ciencia computacional que son esenciales para una carrera exitosa como Programador. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Programadores.
Profesor de matemáticas
Profesor de matemáticas
Los Profesores de Matemáticas enseñan conceptos y principios matemáticos a estudiantes en diversos niveles educativos. El curso de Algoritmos de Aproximación proporciona una base sólida en los conceptos y técnicas de optimización que son esenciales para una carrera exitosa como Profesor de Matemáticas. Al aprender sobre aproximación de algoritmos, los estudiantes desarrollan habilidades analíticas y de resolución de problemas que son necesarias para abordar los desafíos complejos que enfrentan los Profesores de Matemáticas.
For more career information including salaries, visit:
OpenCourser.com/course/kvtd1s/approximation
Reading list
We've selected 13 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Approximation Algorithms.
Provides a comprehensive overview of the design of approximation algorithms. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of approximation algorithms for NP-hard problems. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Is another classic textbook on algorithms. It covers a wide range of topics, from basic data structures to advanced algorithms. It valuable reference for students and practitioners in the field.
Provides a comprehensive overview of randomized algorithms. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Save
Provides a comprehensive overview of graph algorithms. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of combinatorial optimization. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of integer programming. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of nonlinear programming. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of optimization by vector space methods. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of multi-objective optimization. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Save
Provides a comprehensive overview of robust optimization. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Provides a comprehensive overview of stochastic optimization. It covers a wide range of topics, from basic concepts to advanced techniques. It valuable reference for researchers and practitioners in the field.
Save
Classic textbook on algorithms. It covers a wide range of topics, from basic data structures to advanced algorithms. It valuable reference for students and practitioners in the field.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/kvtd1s/approximation
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Good to know
Explores approximation algorithms, which is a key concept in optimization
Taught by Mark de Berg, who is an esteemed professor in the field of algorithms
Develops practical skills in designing and analyzing approximation algorithms, which are valuable in various domains
Requires prerequisites in algorithms and mathematics, making it suitable for learners with a solid foundation in these areas
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