This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a class of problems, namely, the NP-complete proble
Computers and Intractability: A Guide to the Theory of NP-Completeness
โ Scribed by Michael R. Garey, David S. Johnson
- Tongue
- English
- Leaves
- 351
- Category
- Library
No coin nor oath required. For personal study only.
โฆ Synopsis
This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a class of problems, namely, the NP-complete problems: if you can prove that a problem is in this class, then it has no known polynomial-time solution that is guaranteed to work in general. This quality implies that the problem is difficult to deal with in practice. The focus of this book is to teach the reader how to identify, deal with, and understand the essence of NP-complete problems; Computers and Intractability does all of those things effectively. In a readable yet mathematically rigorous manner, the book covers topics such as how to prove that a given problem is NP-complete and how to cope with NP-complete problems. (There is even a chapter on advanced topics, with numerous references.) Computers and Intractability also contains a list of more than 300 problems--most of which are known to be NP-complete--with comments and references.
โฆ Table of Contents
Cover......Page __sk_0000.djvu
Copyright......Page __sk_0002.djvu
Contents......Page __sk_0003.djvu
Preface......Page __sk_0007.djvu
1.1 Introduction......Page __sk_0011.djvu
1.2 Problems, Algorithms, and Complexity......Page __sk_0014.djvu
1.3 Polynomial Time Algorithms and Intractable Problems......Page __sk_0016.djvu
1.4 Provably Intractable Problems......Page __sk_0021.djvu
1.5 NP-Complete Problems......Page __sk_0023.djvu
1.6 An Outline of the Book......Page __sk_0024.djvu
2 The Theory of NP-Completeness......Page __sk_0027.djvu
2.1 Decision Problems, Languages, and Encoding Schemes......Page __sk_0028.djvu
2.2 Deterministic Turing Machines and the Class P......Page __sk_0033.djvu
2.3 Nondeterministic Computation and the Class NP......Page __sk_0037.djvu
2.4 The Relationship Between P and NP......Page __sk_0042.djvu
2.5 Polynomial Transformations and NP-Completeness......Page __sk_0044.djvu
2.6 Cook's Theorem......Page __sk_0048.djvu
3 Proving NP-Completeness Results......Page __sk_0055.djvu
3.1 Six Basic NP-Complete Problems......Page __sk_0056.djvu
3.1.1 3-SATISFIABILITY......Page __sk_0058.djvu
3.1.2 3-DIMENSIONAL MATCHING......Page __sk_0060.djvu
3.1.3 VERTEX COVER and CLIQUE......Page __sk_0063.djvu
3.1.4 HAMILTONIAN CIRCUIT......Page __sk_0066.djvu
3.1.5 PARTITION......Page __sk_0070.djvu
3.2.1 Restriction......Page __sk_0073.djvu
3.2.2 Local Replacement......Page __sk_0076.djvu
3.2.3 Component Design......Page __sk_0082.djvu
3.3 Some Suggested Exercises......Page __sk_0084.djvu
4 Using NP-Completeness to Analyze Problems......Page __sk_0087.djvu
4.1 Analyzing Subproblems......Page __sk_0090.djvu
4.2 Number Problems and Strong NP-Completeness......Page __sk_0100.djvu
4.2.1 Some Additional Definitions......Page __sk_0102.djvu
4.2.2 Proving Strong NP-Completeness Results......Page __sk_0105.djvu
4.3 Time Complexity as a Function of Natural Parameters......Page __sk_0116.djvu
5.1 Turing Reducibility and NP-Hard Problems......Page __sk_0119.djvu
5.2 A Terminological History......Page __sk_0128.djvu
6 Coping with NP-Complete Problems......Page __sk_0131.djvu
6.1 Performance Guarantees for Approximation Algorithms......Page __sk_0133.djvu
6.2 Applying NP-Completeness to Approximation Problems......Page __sk_0147.djvu
6.3 Performance Guarantees and Behavior "In Practice"......Page __sk_0158.djvu
7 Beyond NP-Completeness......Page __sk_0163.djvu
7.1 The Structure of NP......Page __sk_0164.djvu
7.2 The Polynomial Hierarchy......Page __sk_0171.djvu
7.3 The Complexity of Enumeration Problems......Page __sk_0177.djvu
7.4 Polynomial Space Completeness......Page __sk_0180.djvu
7.5 Logarithmic Space......Page __sk_0187.djvu
7.6 Proofs of Intractability and P vs. NP......Page __sk_0191.djvu
Appendix: A List of NP-Complete Problems......Page __sk_0197.djvu
A1.1 Covering and Partitioning......Page __sk_0200.djvu
A1.2 Subgraphs and Supergraphs......Page __sk_0204.djvu
A1.3 Vertex Ordering......Page __sk_0209.djvu
A1.4 Iso- and Other Morphisms......Page __sk_0212.djvu
Al.5 Miscellaneous......Page __sk_0213.djvu
A2.1 Spanning Trees......Page __sk_0216.djvu
A2.2 Cuts and Connectivity......Page __sk_0219.djvu
A2.3 Routing Problems......Page __sk_0221.djvu
A2.4 Flow Problems......Page __sk_0224.djvu
A2.5 Miscellaneous......Page __sk_0228.djvu
A3.1 Covering, Hitting, and Splitting......Page __sk_0231.djvu
A3.2 Weighted Set Problems......Page __sk_0233.djvu
A4.1 Data Storage......Page __sk_0236.djvu
A4.2 Compression and Representation......Page __sk_0238.djvu
A4.3 Database Problems......Page __sk_0242.djvu
A5.1 Sequencing on One Processor......Page __sk_0246.djvu
A5.2 Multiprocessor Scheduling......Page __sk_0248.djvu
A5.3 Shop Scheduling......Page __sk_0251.djvu
A5.4 Miscellaneous......Page __sk_0253.djvu
A6 Mathematical Programming......Page __sk_0255.djvu
A7.1 Divisibility Problems......Page __sk_0259.djvu
A7.2 Solvability of Equations......Page __sk_0260.djvu
A7.3 Miscellaneous......Page __sk_0262.djvu
A8 Games and Puzzles......Page __sk_0264.djvu
A9.1 Propositional Logic......Page __sk_0269.djvu
A9.2 Miscellaneous......Page __sk_0271.djvu
A10.1 Automata Theory......Page __sk_0275.djvu
AlO.2 Formal Languages......Page __sk_0277.djvu
A11.1 Code Generation......Page __sk_0282.djvu
Al1.2 Programs and Schemes......Page __sk_0285.djvu
A12 Miscellaneous......Page __sk_0289.djvu
A13 Open Problems......Page __sk_0295.djvu
Symbol Index......Page __sk_0299.djvu
Reference and Author Index......Page __sk_0301.djvu
Subject Index......Page __sk_0337.djvu
Update for the Current Printing......Page __sk_0349.djvu
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This book's introduction features a humorous story of a man with a line of people behind him, who explains to his boss, "I can't find an efficient algorithm, but neither can all these famous people." This man illustrates an important quality of a class of problems, namely, the NP-complete proble
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