Hardness Of Approximation Between P And Np
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Hardness Of Approximation Between P And Np
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Author : Aviad Rubinstein
language : en
Publisher: Morgan & Claypool
Release Date : 2019-06-07
Hardness Of Approximation Between P And Np written by Aviad Rubinstein and has been published by Morgan & Claypool this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-07 with Computers categories.
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.
P Np And Np Completeness
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Author : Oded Goldreich
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-16
P Np And Np Completeness written by Oded Goldreich and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Computers categories.
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.
Approximation Algorithms For Np Hard Problems
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Author : Dorit S. Hochbaum
language : en
Publisher: Course Technology
Release Date : 1997
Approximation Algorithms For Np Hard Problems written by Dorit S. Hochbaum and has been published by Course Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
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.
Approximation And Online Algorithms
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Author : Evripidis Bampis
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-02
Approximation And Online Algorithms written by Evripidis Bampis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-02 with Computers categories.
The 6th Workshop on Approximation and Online Algorithms (WAOA 2008) focused on the design and analysis of algorithms for online and computati- ally hard problems. Both kinds of problems have a large number of appli- tions from a variety of ?elds. WAOA 2008 took place in Karlsruhe, Germany, during September 18–19, 2008. The workshop was part of the ALGO 2008 event that also hosted ESA 2008, WABI 2008, and ATMOS 2008. The pre- ous WAOA workshops were held in Budapest (2003), Rome (2004), Palma de Mallorca (2005), Zurich (2006), and Eilat (2007). The proceedings of these p- viousWAOA workshopsappearedasLNCS volumes2909,3351,3879,4368,and 4927, respectively. Topics of interest for WAOA 2008 were: algorithmic game theory, appro- mation classes, coloring and partitioning, competitive analysis, computational ?nance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms for design and analysis of approximationand online algorithms, randomizationtechniques, real-world applications, and scheduling problems. In response to the call for - pers,wereceived56submissions.Eachsubmissionwasreviewedbyatleastthree referees, and the vast majority by at least four referees. The submissions were mainly judged on originality, technical quality, and relevance to the topics of the conference. Based on the reviews, the Program Committee selected 22 papers. We are grateful to Andrei Voronkov for providing the EasyChair conference system,whichwasusedtomanagetheelectronicsubmissions,thereviewprocess, and the electronic PC meeting. It made our task much easier. We would also like to thank all the authors who submitted papers to WAOA 2008 as well as the local organizers of ALGO 2008.
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques
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Author : Maria Serna
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-19
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Maria Serna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Computers categories.
This book constitutes the joint refereed proceedings of the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010, and the 14th International Workshop on Randomization and Computation, RANDOM 2010, held in Barcelona, Spain, in September 2010. The 28 revised full papers of the APPROX 2010 workshop and the 29 revised full papers of the RANDOM 2010 workshop included in this volume, were carefully reviewed and selected from 66 and 61 submissions, respectively. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.
Approximation Algorithms For Combinatorial Optimization
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Author : Klaus Jansen
language : en
Publisher: Springer
Release Date : 2003-07-31
Approximation Algorithms For Combinatorial Optimization written by Klaus Jansen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.
This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques
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Author : Sanjeev Arora
language : en
Publisher: Springer
Release Date : 2003-12-15
Approximation Randomization And Combinatorial Optimization Algorithms And Techniques written by Sanjeev Arora and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-15 with Computers categories.
This book constitutes the joint refereed proceedings of the 6th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2003 and of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, held in Princeton, NY, USA in August 2003. The 33 revised full papers presented were carefully reviewed and selected from 74 submissions. Among the issues addressed are design and analysis of randomized and approximation algorithms, online algorithms, complexity theory, combinatorial structures, error-correcting codes, pseudorandomness, derandomization, network algorithms, random walks, Markov chains, probabilistic proof systems, computational learning, randomness in cryptography, and various applications.
Walcom Algorithms And Computation
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Author : NAOKI KATOH
language : en
Publisher: Springer
Release Date : 2011-02-10
Walcom Algorithms And Computation written by NAOKI KATOH and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Computers categories.
This book constitutes the proceedings of the 5th International Workshop on Algorithms and Computation, WALCOM 2011, held in New Delhi, India, in February 2011. The 20 papers presented in this volume were carefully reviewed and selected from 57 submissions. The papers are grouped in topical sections on approximation algorithms, hardness, algorithm engineering, computational geometry, string algorithms, and graph algorithms.
Approximation And Online Algorithms
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Author : Thomas Erlebach
language : en
Publisher: Springer
Release Date : 2013-12-11
Approximation And Online Algorithms written by Thomas Erlebach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Computers categories.
This book constitutes the thoroughly refereed post workshop proceedings of the 10th International Workshop on Approximation and Online Algorithms, WAOA 2012, held in Ljubljana, Slovenia, in September 2012 as part of the ALGO 2012 conference event. The 22 revised full papers presented together with invited talk were carefully reviewed and selected from 60 submissions. The workshop covered areas such as geometric problems, online algorithms, scheduling, algorithmic game theory, and approximation algorithms.
Algorithms Esa 2002
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Author : Rolf Möhring
language : en
Publisher: Springer
Release Date : 2003-08-02
Algorithms Esa 2002 written by Rolf Möhring and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-02 with Computers categories.
This volume contains the 74 contributed papers and abstracts of 4 of the 5 invited talks presented at the 10th Annual European Symposium on Algorithms (ESA 2002), held at the University of Rome “La Sapienza”, Rome, Italy, 17-21 September, 2002. For the ?rst time, ESA had two tracks, with separate program committees, which dealt respectively with: – the design and mathematical analysis of algorithms (the “Design and An- ysis” track); – real-world applications, engineering and experimental analysis of algorithms (the “Engineering and Applications” track). Previous ESAs were held in Bad Honnef, Germany (1993); Utrecht, The Neth- lands (1994); Corfu, Greece (1995); Barcelona, Spain (1996); Graz, Austria (1997); Venice, Italy (1998); Prague, Czech Republic (1999); Saarbruc ̈ ken, Ger- ? many (2000), and Arhus, Denmark (2001). The predecessor to the Engineering and Applications track of ESA was the Annual Workshop on Algorithm En- neering (WAE). Previous WAEs were held in Venice, Italy (1997), Saarbruc ̈ ken, ? Germany (1998), London, UK (1999), Saarbru ̈cken, Germany (2000), and Arhus, Denmark (2001). The proceedings of the previous ESAs were published as Springer LNCS volumes 726, 855, 979, 1284, 1461, 1643, 1879, and 2161. The proceedings of WAEs from 1999 onwards were published as Springer LNCS volumes 1668, 1982, and 2161.