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Beschreibung
Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed conjecture that P≠NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial-time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of approximation algorithms.
This book is divided into three parts. Part I covers combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. Part II presents linear programming based algorithms. These are categorized under two fundamental techniques: rounding and the primal-dual schema. Part III covers four important topics: the first is the problem of finding a shortest vector in a lattice; the second is the approximability of counting, as opposed to optimization, problems; the third topic is centered around recent breakthrough results, establishing hardness of approximation for many key problems, and giving new legitimacy to approximation algorithms as a deep theory; and the fourth topic consists of the numerous open problems of this young field.
This book is suitable for use in advanced undergraduate and graduate-level courses on approximation algorithms. An undergraduate course in algorithms and the theory of NP-completeness should suffice as a prerequisite for most of the chapters. This book can also be used as supplementary text in basic undergraduate and graduate algorithms courses.
This book is divided into three parts. Part I covers combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. Part II presents linear programming based algorithms. These are categorized under two fundamental techniques: rounding and the primal-dual schema. Part III covers four important topics: the first is the problem of finding a shortest vector in a lattice; the second is the approximability of counting, as opposed to optimization, problems; the third topic is centered around recent breakthrough results, establishing hardness of approximation for many key problems, and giving new legitimacy to approximation algorithms as a deep theory; and the fourth topic consists of the numerous open problems of this young field.
This book is suitable for use in advanced undergraduate and graduate-level courses on approximation algorithms. An undergraduate course in algorithms and the theory of NP-completeness should suffice as a prerequisite for most of the chapters. This book can also be used as supplementary text in basic undergraduate and graduate algorithms courses.
Most natural optimization problems, including those arising in important application areas, are NP-hard. Therefore, under the widely believed conjecture that P≠NP, their exact solution is prohibitively time consuming. Charting the landscape of approximability of these problems, via polynomial-time algorithms, therefore becomes a compelling subject of scientific inquiry in computer science and mathematics. This book presents the theory of approximation algorithms.
This book is divided into three parts. Part I covers combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. Part II presents linear programming based algorithms. These are categorized under two fundamental techniques: rounding and the primal-dual schema. Part III covers four important topics: the first is the problem of finding a shortest vector in a lattice; the second is the approximability of counting, as opposed to optimization, problems; the third topic is centered around recent breakthrough results, establishing hardness of approximation for many key problems, and giving new legitimacy to approximation algorithms as a deep theory; and the fourth topic consists of the numerous open problems of this young field.
This book is suitable for use in advanced undergraduate and graduate-level courses on approximation algorithms. An undergraduate course in algorithms and the theory of NP-completeness should suffice as a prerequisite for most of the chapters. This book can also be used as supplementary text in basic undergraduate and graduate algorithms courses.
This book is divided into three parts. Part I covers combinatorial algorithms for a number of important problems, using a wide variety of algorithm design techniques. Part II presents linear programming based algorithms. These are categorized under two fundamental techniques: rounding and the primal-dual schema. Part III covers four important topics: the first is the problem of finding a shortest vector in a lattice; the second is the approximability of counting, as opposed to optimization, problems; the third topic is centered around recent breakthrough results, establishing hardness of approximation for many key problems, and giving new legitimacy to approximation algorithms as a deep theory; and the fourth topic consists of the numerous open problems of this young field.
This book is suitable for use in advanced undergraduate and graduate-level courses on approximation algorithms. An undergraduate course in algorithms and the theory of NP-completeness should suffice as a prerequisite for most of the chapters. This book can also be used as supplementary text in basic undergraduate and graduate algorithms courses.
Zusammenfassung
Spreads powerful algorithmic ideas developed in this area to practitionersWill accelerate progress in this areaRaises algorithmic awareness of the scientific community by showing simple ways of expressing complex algorithmic ideasAn indispensable cookbook for all serious mathematical programmers
Inhaltsverzeichnis
1 Introduction.- I. Combinatorial Algorithms.- 2 Set Cover.- 3 Steiner Tree and TSP.- 4 Multiway Cut and k-Cut.- 5 k-Center.- 6 Feedback Vertex Set.- 7 Shortest Superstring.- 8 Knapsack.- 9 Bin Packing.- 10 Minimum Makespan Scheduling.- 11 Euclidean TSP.- II. LP-Based Algorithms.- 12 Introduction to LP-Duality.- 13 Set Cover via Dual Fitting.- 14 Rounding Applied to Set Cover.- 15 Set Cover via the Primal¿Dual Schema.- 16 Maximum Satisfiability.- 17 Scheduling on Unrelated Parallel Machines.- 18 Multicut and Integer Multicommodity Flow in Trees.- 19 Multiway Cut.- 20 Multicut in General Graphs.- 21 Sparsest Cut.- 22 Steiner Forest.- 23 Steiner Network.- 24 Facility Location.- 25 k-Median.- 26 Semidefinite Programming.- III. Other Topics.- 27 Shortest Vector.- 28 Counting Problems.- 29 Hardness of Approximation.- 30 Open Problems.- A An Overview of Complexity Theory for the Algorithm Designer.- A.3.1 Approximation factor preserving reductions.- A.4 Randomized complexity classes.- A.5 Self-reducibility.- A.6 Notes.- B Basic Facts from Probability Theory.- B.1 Expectation and moments.- B.2 Deviations from the mean.- B.3 Basic distributions.- B.4 Notes.- References.- Problem Index.
Details
Erscheinungsjahr: | 2010 |
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Genre: | Informatik, Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Inhalt: |
xix
380 S. 2 s/w Illustr. |
ISBN-13: | 9783642084690 |
ISBN-10: | 3642084699 |
Sprache: | Englisch |
Einband: | Kartoniert / Broschiert |
Autor: | Vazirani, Vijay V. |
Auflage: | Softcover reprint of hardcover 1st edition 2001 |
Hersteller: |
Springer Berlin
Springer Berlin Heidelberg |
Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
Maße: | 235 x 155 x 22 mm |
Von/Mit: | Vijay V. Vazirani |
Erscheinungsdatum: | 08.12.2010 |
Gewicht: | 0,61 kg |