Design and Analysis of Approximation Algorithms
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It is most likely impossible to solve such problems efficiently, so our aim is to give an approximate solution that can be computed in polynomial time and that at the same time has provable guarantees on its cost relative to the optimum.
This course assumes knowledge of a standard undergraduate Algorithms course, and particularly emphasizes algorithms that can be designed using linear programming, a favorite and amazingly successful technique in this area. By taking this course, you will be exposed to a range of problems at the foundations of theoretical computer science, and to powerful design and analysis techniques. Upon completion, you will be able to recognize, when faced with a new combinatorial optimization problem, whether it is close to one of a few known basic problems, and will be able to design linear programming relaxations and use randomized rounding to attempt to solve your own problem.
The course content and in particular the homework is of a theoretical nature without any programming assignments.
Design and Analysis of Approximation Algorithms
This is the first of a two-part course on Approximation Algorithms. Vertex cover and Linear Programming -We introduce the course topic by a typical example of a basic problem, called Vertex Cover, for which we will design and analyze a state-of-the-art approximation algorithm using two basic techniques, called Linear Programming Relaxation and Rounding. It is a simple, elementary application of powerful techniques.
Knapsack and Rounding -This module shows the power of rounding by using it to design a near-optimal solution to another basic problem: the Knapsack problem.
Bin Packing, Linear Programming and Rounding -This module shows the sophistication of rounding by using a clever variant for another basic problem: bin packing. This is a more advanced module.
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Set Cover and Randomized Rounding -This module introduces a simple and powerful variant of rounding, based on probability: randomized rounding. Its power is applied to another basic problem, the Set Cover problem. Multiway Cut and Randomized Rounding -This module deepens the understanding of randomized rounding by developing a sophisticated variant and applying it to another basic problem, the Multiway Cut problem.
Taught by Claire Mathieu. Introduction to approximation algorithms. Introduction to the techniques: Set cover.
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Description This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc.
In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way. Product details Format Paperback pages Dimensions x x Illustrations note XII, p.
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