THE DESIGN OF APPROXIMATION ALGORITHMS

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The Design Of Approximation Algorithms

Author : David P. Williamson
ISBN : 9781139498173
Genre : Computers
File Size : 30.96 MB
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Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
Category: Computers

Design And Analysis Of Approximation Algorithms

Author : Ding-Zhu Du
ISBN : 9781461417019
Genre : Mathematics
File Size : 27.67 MB
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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. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. 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.
Category: Mathematics

New Rounding Techniques For The Design And Analysis Of Approximation Algorithms

Author : Shayan Oveis Gharan
ISBN : OCLC:857650575
Genre :
File Size : 24.46 MB
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We study two of the most central classical optimization problems, namely the Traveling Salesman problems and Graph Partitioning problems and develop new approximation algorithms for them. We introduce several new techniques for rounding a fractional solution of a continuous relaxation of these problems into near optimal integral solutions. The two most notable of those are the maximum entropy rounding by sampling method and a novel use of higher eigenvectors of graphs.
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Handbook Of Approximation Algorithms And Metaheuristics

Author : Teofilo F. Gonzalez
ISBN : 1420010743
Genre : Computers
File Size : 20.54 MB
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Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems.
Category: Computers

Approximation Algorithms

Author : Vijay V. Vazirani
ISBN : 9783662045657
Genre : Computers
File Size : 73.66 MB
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Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.
Category: Computers

Approximation Algorithms For Combinatorial Optimization

Author : Klaus Jansen
ISBN : 3540647368
Genre : Computers
File Size : 71.14 MB
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Computer simulation has become a basic tool in many branches of physics such as statistical physics, particle physics, or materials science. The application of efficient algorithms is at least as important as good hardware in large-scale computation. This volume contains didactic lectures on such techniques based on physical insight. The emphasis is on Monte Carlo methods (introduction, cluster algorithms, reweighting and multihistogram techniques, umbrella sampling), efficient data analysis and optimization methods, but aspects of supercomputing, the solution of stochastic differential equations, and molecular dynamics are also discussed. The book addresses graduate students and researchers in theoretical and computational physics.
Category: Computers

Analysis And Design Of Algorithms

Author : A.A.Puntambekar
ISBN : 8184313772
Genre :
File Size : 55.17 MB
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What is an algorithm ? Fundamentals of algorithmic problem solving, Important problem types, Fundamental data structures.Fundamentals of the Analysis of Algorithm Efficiency : Analysis framework.Asymptotic notations and basic efficiency classes, Mathematical analysis of nonrecursive and recursive algorithms, Example - Fibonacci numbers.Brute Force : Selection sort and bubble sort, Sequential search and brute-force string matching, Exhaustive search.Divide and Conquer : Mergesort, Quicksorst, Binary search. Binary tree traversals and related properties, Multiplication of large integers and Stressen's matrix multiplication.Decrease and Conquer : Insertion sort, Depth first search, Breadth first search, Topological sorting.Algorithms for generating combinatorial objects.Transform and Conquer : Presorting, Balanced search trees, Heaps and heapsort, Problem reduction.Space and Time Tradeoffs : Sorting by counting, Input enhancement in string matching, Hashing.Dynamic Programming : Computing a binomial coefficient, Warshall's and Floyd's algorithms, The Knapsack problem and memory functions.Greedy Technique : Prim's algorithm, Kruskal's algorithm, Dujkstra's algorithm, Huffman trees.Limitations of Algorithm Power : Lower-bound arguments, Decision trees., P, NP and NP-complete problems.Coping with the Limitations of Algorithm Power : Backtracking, Branch-and-bound, Approximation algorithms for NP-hard problems.
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Algorithmics For Hard Problems

Author : Juraj Hromkovič
ISBN : 9783662046166
Genre : Computers
File Size : 79.83 MB
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An introduction to the methods of designing algorithms for hard computing tasks, concentrating mainly on approximate, randomized, and heuristic algorithms, and on the theoretical and experimental comparison of these approaches according to the requirements of the practice. This is the first book to systematically explain and compare all the main possibilities of attacking hard computing problems. It also closes the gap between theory and practice by providing at once a graduate textbook and a handbook for practitioners dealing with hard computing problems.
Category: Computers

Approximation Algorithms For Np Hard Problems

Author : Edited By Dorit S Hochbaum
ISBN : UOM:39015058079271
Genre : Mathematics
File Size : 56.38 MB
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This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book.
Category: Mathematics