P Np And Np Completeness

Author : Oded Goldreich
Publisher : Cambridge University Press
ISBN 13 : 1139490095
Total Pages : pages
Book Rating : 4.92/5 ( download)

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Download or read book P, NP, and NP-Completeness written by Oded Goldreich and published by Cambridge University Press. This book was released on 2010-08-16 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive, and this is captured by saying that P is different from NP. Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural computational problems arising in many different areas of mathematics and science are NP-complete.

Author : Lance Fortnow
Publisher : Princeton University Press
ISBN 13 : 0691175780
Total Pages : 188 pages
Book Rating : 4.82/5 ( download)

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Download or read book The Golden Ticket written by Lance Fortnow and published by Princeton University Press. This book was released on 2017-02-28 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.64/5 ( download)

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Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author : Thomas H Cormen
Publisher : MIT Press
ISBN 13 : 9780262032933
Total Pages : 1216 pages
Book Rating : 4.37/5 ( download)

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Download or read book Introduction To Algorithms written by Thomas H Cormen and published by MIT Press. This book was released on 2001 with total page 1216 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensively revised edition of a mathematically rigorous yet accessible introduction to algorithms.

Author : Various Authors,
Publisher : Zondervan
ISBN 13 : 0310294142
Total Pages : 6637 pages
Book Rating : 4.46/5 ( download)

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Download or read book Holy Bible (NIV) written by Various Authors, and published by Zondervan. This book was released on 2008-09-02 with total page 6637 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NIV is the world's best-selling modern translation, with over 150 million copies in print since its first full publication in 1978. This highly accurate and smooth-reading version of the Bible in modern English has the largest library of printed and electronic support material of any modern translation.

Author : Cristopher Moore
Publisher : OUP Oxford
ISBN 13 : 0191620807
Total Pages : 1498 pages
Book Rating : 4.05/5 ( download)

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Download or read book The Nature of Computation written by Cristopher Moore and published by OUP Oxford. This book was released on 2011-08-11 with total page 1498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

Author : Bernard M. E. Moret
Publisher : Addison-Wesley Professional
ISBN 13 :
Total Pages : 600 pages
Book Rating : 4.88/5 ( download)

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Download or read book Algorithms from P to NP: Design & efficiency written by Bernard M. E. Moret and published by Addison-Wesley Professional. This book was released on 1991 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Aviad Rubinstein
Publisher : Morgan & Claypool
ISBN 13 : 1947487213
Total Pages : 319 pages
Book Rating : 4.15/5 ( download)

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Download or read book Hardness of Approximation Between P and NP written by Aviad Rubinstein and published by Morgan & Claypool. This book was released on 2019-06-07 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nash equilibrium is the central solution concept in Game Theory. Since Nash’s original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed. Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer’s fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.

Author : Peter Bürgisser
Publisher : Springer Science & Business Media
ISBN 13 : 3662041790
Total Pages : 174 pages
Book Rating : 4.96/5 ( download)

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Download or read book Completeness and Reduction in Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

Author :
Publisher :
ISBN 13 : 0077388496
Total Pages : pages
Book Rating : 4.92/5 ( download)

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Download or read book Algorithms written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: