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Design and Analysis of Approximation Algorithms 2012 ed. [Mīkstie vāki]

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  • Formāts: Paperback / softback, 440 pages, height x width: 235x155 mm, weight: 688 g, XII, 440 p., 1 Paperback / softback
  • Sērija : Springer Optimization and Its Applications 62
  • Izdošanas datums: 25-Jan-2014
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1489998446
  • ISBN-13: 9781489998446
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Design and Analysis of Approximation Algorithms 2012 ed.Palielināt
  • Formāts: Paperback / softback, 440 pages, height x width: 235x155 mm, weight: 688 g, XII, 440 p., 1 Paperback / softback
  • Sērija : Springer Optimization and Its Applications 62
  • Izdošanas datums: 25-Jan-2014
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1489998446
  • ISBN-13: 9781489998446
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781489998446.html
Keywords:
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.

Unlike other books on theoretical computer science, this textbook organizes approximation algorithms into chapters based on the design techniques for the algorithms. This allows the reader to study approximation algorithms of the same nature together.

Recenzijas

From the reviews:

This book is intended for graduate courses of different levels, and course plans based on different chapter selections are proposed. Each chapter is accompanied by several pages of exercises and historical notes, setting the material and the references in context. The comprehensive bibliography covers a huge amount of literature in the heuristics and approximations area, as well as specific application problems. The index is detailed. This makes the book a good source for a course on approximation algorithms. ...For the more advanced reader the book seems to be an excellent in-depth resource on approximation algorithms, for their beginning up to the latest developments.

Gudula Runger, Computing Reviews

It contains a large amount of precisely selected topics covering various aspects and design techniques related to approximation algorithms. It has been intended as a textbook for a graduate course in theoretical computer science. it can also be used as a reference book for postgraduate students and researchers in the area of design and analysis of algorithms. It also serves as a reference for established researchers by providing efficient tools for various applied areas like applied mathematics, engineering, medicine, economics, and other sciences. (Vladimķr Lacko, Zentralblatt MATH, Vol. 1237, 2012)

This textbook organizes approximation algorithms into chapters based on the design techniques. this book is particularly suited for students who, possibly starting from scratch, want to first encounter, then absorb, and finally master the main techniques which have emerged as general paradigms in the design of approximation algorithms. This includes self-study by novices but also teaching by experts in standard courses. (Romeo Rizzi, Mathematical Reviews, January, 2013)

Preface v
1 Introduction
1(34)
1.1 Open Sesame
1(7)
1.2 Design Techniques for Approximation Algorithms
8(5)
1.3 Heuristics Versus Approximation
13(1)
1.4 Notions in Computational Complexity
14(3)
1.5 NP-Complete Problems
17(6)
1.6 Performance Ratios
23(12)
Exercises
28(5)
Historical Notes
33(2)
2 Greedy Strategy
35(46)
2.1 Independent Systems
35(5)
2.2 Matroids
40(3)
2.3 Quadrilateral Condition on Cost Functions
43(6)
2.4 Submodular Potential Functions
49(10)
2.5 Applications
59(7)
2.6 Nonsubmodular Potential Functions
66(15)
Exercises
75(5)
Historical Notes
80(1)
3 Restriction
81(42)
3.1 Steiner Trees and Spanning Trees
82(4)
3.2 k-Restricted Steiner Trees
86(3)
3.3 Greedy k-Restricted Steiner Trees
89(13)
3.4 The Power of Minimum Spanning Trees
102(8)
3.5 Phylogenetic Tree Alignment
110(13)
Exercises
115(6)
Historical Notes
121(2)
4 Partition
123(42)
4.1 Partition and Shifting
123(6)
4.2 Boundary Area
129(7)
4.3 Multilayer Partition
136(6)
4.4 Double Partition
142(15)
4.4.1 A Weighted Covering Problem
142(4)
4.4.2 A 2-Approximation for WDS-UDG on a Small Cell
146(5)
4.4.3 A 6-Approximation for WDS-UDG on a Large Cell
151(4)
4.4.4 A (6 + ε)-Approximation for WDS-UDG
155(2)
4.5 Tree Partition
157(8)
Exercises
160(4)
Historical Notes
164(1)
5 Guillotine Cut
165(46)
5.1 Rectangular Partition
165(5)
5.2 1-Guillotine Cut
170(5)
5.3 m-Guillotine Cut
175(9)
5.4 Portals
184(7)
5.5 Quadtree Partition and Patching
191(10)
5.6 Two-Stage Portals
201(10)
Exercises
205(3)
Historical Notes
208(3)
6 Relaxation
211(34)
6.1 Directed Hamiltonian Cycles and Superstrings
211(8)
6.2 Two-Stage Greedy Approximations
219(4)
6.3 Connected Dominating Sets in Unit Disk Graphs
223(5)
6.4 Strongly Connected Dominating Sets in Digraphs
228(7)
6.5 Multicast Routing in Optical Networks
235(3)
6.6 A Remark on Relaxation Versus Restriction
238(7)
Exercises
240(3)
Historical Notes
243(2)
7 Linear Programming
245(52)
7.1 Basic Properties of Linear Programming
245(7)
7.2 Simplex Method
252(7)
7.3 Combinatorial Rounding
259(8)
7.4 Pipage Rounding
267(5)
7.5 Iterated Rounding
272(8)
7.6 Random Rounding
280(17)
Exercises
289(6)
Historical Notes
295(2)
8 Primal-Dual Schema and Local Ratio
297(42)
8.1 Duality Theory and Primal-Dual Schema
297(6)
8.2 General Cover
303(7)
8.3 Network Design
310(5)
8.4 Local Ratio
315(10)
8.5 More on Equivalence
325(14)
Exercises
332(4)
Historical Notes
336(3)
9 Semidefinite Programming
339(32)
9.1 Spectrahedra
339(2)
9.2 Semidefinite Programming
341(4)
9.3 Hyperplane Rounding
345(7)
9.4 Rotation of Vectors
352(6)
9.5 Multivariate Normal Rounding
358(13)
Exercises
363(6)
Historical Notes
369(2)
10 Inapproximability
371(36)
10.1 Many--One Reductions with Gap
371(5)
10.2 Gap Amplification and Preservation
376(4)
10.3 APX-Completeness
380(8)
10.4 PCP Theorem
388(3)
10.5 (ρln n)-Inapproximability
391(5)
10.6 nc-Inapproximability
396(11)
Exercises
399(6)
Historical Notes
405(2)
Bibliography 407(18)
Index 425
Ding-Zhu Du is co-editor of the first and soon-to-be published, second editions, of the Handbook of Combinatorial Optimization. He was also co-author with P.M. Pardalos and W. Wu of the Kluwer publication "Mathematical Theory of Optimization". Du will co-author upcoming Springer publications (2012) entitled "Connected Dominating Set: Theory and Applications" and "Introduction to Combinatorial Optimization". Prof. Du is also the EiC of the Journal of Combinatorial Optimization (Springer).

Ker-I Ko is a well known expert in the field of theoretical computer science. He has authored a single publication with Birkhauser "Computational Complexity of Real Functions" in 1991, with very good reviews. Prof. Du and Ker-I Ko have written several texts together including "Problem Solving in Automata, Languages, and Complexity" John Wiley, 2001; "Theory of Computational Complexity", John Wiley, 2000; Both of these books have received good reviews.

Xiaodong Hu is an expert in combinatorial optimization. He is a member of the editorial boards of Journal of Combinatorial Optimization and Discrete Mathematics, Algorithms and Applications.