# Hardness of approximation between P and NP (Record no. 383497)

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000 -LEADER | |
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fixed length control field | 06458nam a22005777a 4500 |

003 - CONTROL NUMBER IDENTIFIER | |

control field | APU |

005 - DATE AND TIME OF LATEST TRANSACTION | |

control field | 20221101135833.0 |

008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |

fixed length control field | 210804s2019 enka b 001 0 eng d |

015 ## - NATIONAL BIBLIOGRAPHY NUMBER | |

National bibliography number | GBB9F5834 |

Source | bnb |

016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER | |

Record control number | 019535884 |

Source | Uk |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

International Standard Book Number | 9781947487222 (epub) |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

International Standard Book Number | 9781947487215 (pdf) |

040 ## - CATALOGING SOURCE | |

Original cataloging agency | Uk |

Language of cataloging | eng |

Transcribing agency | APU |

Modifying agency | SF |

042 ## - AUTHENTICATION CODE | |

Authentication code | ukblsr |

050 ## - LIBRARY OF CONGRESS CALL NUMBER | |

Classification number | QA267.7 |

Item number | .R83 2019eb |

082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |

Classification number | 511.352 |

Edition number | 23 |

100 1# - MAIN ENTRY--PERSONAL NAME | |

Personal name | Rubinstein, Aviad, |

9 (RLIN) | 47440 |

245 10 - TITLE STATEMENT | |

Title | Hardness of approximation between P and NP |

Medium | [electronic resources] / |

Statement of responsibility, etc | Aviad Rubinstein. |

260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |

Place of publication, distribution, etc | [New York] : |

Name of publisher, distributor, etc | Association for Computing Machinery, |

Date of publication, distribution, etc | c2019. |

300 ## - PHYSICAL DESCRIPTION | |

Extent | 1 online resources (xv, 301 pages) : |

Other physical details | illustrations (chiefly color). ; |

490 0# - SERIES STATEMENT | |

Series statement | ACM books ; |

Volume number/sequential designation | #24 |

International Standard Serial Number | 2374-6777 ; |

500 ## - GENERAL NOTE | |

General note | Revision of author's thesis (doctoral)--University of California, Berkeley, 2017. |

504 ## - BIBLIOGRAPHY, ETC. NOTE | |

Bibliography, etc | Includes bibliographical references and index. |

505 0# - FORMATTED CONTENTS NOTE | |

Formatted contents note | part I. Overview -- 1. The frontier of intractability -- 1.1. PPAD : finding a needle you know is in the haystack -- 1.2. Quasi-polynomial time and the birthday paradox -- 1.3. Approximate Nash equilibrium |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 2. Preliminaries -- 2.1. Nash equilibrium and relaxations -- 2.2. PPAD and end-of-a-line -- 2.3. Exponential time hypotheses -- 2.4. PCP theorems -- 2.5. Learning theory -- 2.6. Information theory -- 2.7. Useful lemmata |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | part II. Communication complexity -- 3. Communication complexity of approximate Nash equilibrium -- 3.1. Uncoupled dynamics -- 3.2. Techniques -- 3.3. Additional related literature -- 3.4. Proof overview -- 3.5. Proofs -- 3.6. An open problem : correlated equilibria in 2-player games |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 4. Brouwer's fixed point -- 4.1. Brouwer with �[infinity] -- 4.2. Euclidean Brouwer |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | part III. PPAD -- 5. PPAD-hardness of approximation |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 6. The generalized circuit problem -- 6.1. Proof overview -- 6.2. From Brouwer to [epsilon]-Gcircuit -- 6.3. Gcircuit with fan-out 2 |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 7. Many-player games -- 7.1. Graphical, polymatrix games -- 7.2. Succinct games |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 8. Bayesian Nash equilibrium -- 9. Market equilibrium -- 9.1. Why are non-monotone markets hard? -- 9.2. High-level structure of the proof -- 9.3. Adaptations for constant factor inapproximability -- 9.4. Non-monotone markets : proof of inapproximability |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 10. CourseMatch -- 10.1. The course allocation problem -- 10.2. A-CEEI is PPAD-hard -- 10.3. A-CEEI [epsilon] PPAD |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | part IV. Quasi-polynomial time -- 11. Birthday repetition -- 11.1. Warm-up : best [epsilon]-Nash |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 12. Densest k-subgraph -- 12.1. Construction (and completeness) -- 12.2. Soundness |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 13. Community detection -- 13.1. Related works -- 13.2. Overview of proofs -- 13.3. Hardness of counting communities -- 13.4. Hardness of detecting communities |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 14. VC and Littlestone's dimensions -- 14.1. Discussion -- 14.2. Techniques -- 14.3. Related Work -- 14.4. Inapproximability of the VC dimension -- 14.5. Inapproximability of Littlestone's dimension -- 14.6. Quasi-polynomial algorithm for Littlestone's dimension |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | 15. Signaling -- 15.1. Techniques -- 15.2. Near-optimal signaling is hard |

505 8# - FORMATTED CONTENTS NOTE | |

Formatted contents note | part V. Approximate Nash equilibrium -- 16. 2-player approximate Nash equilibrium -- 16.1. Technical overview -- 16.2. End-of-a-line with local computation -- 16.3. Holographic proof -- 16.4. Polymatrix WeakNash -- 16.5. From Polymatrix to Bimatrix. |

520 ## - SUMMARY, ETC. | |

Summary, etc | 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. |

538 ## - SYSTEM DETAILS NOTE | |

System details note | Mode of access: World Wide Web. |

538 ## - SYSTEM DETAILS NOTE | |

System details note | System requirements: Adobe Acrobat Reader. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | NP-complete problems. |

9 (RLIN) | 47441 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Equilibrium. |

9 (RLIN) | 47442 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Computer algorithms. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Programming (Mathematics) |

9 (RLIN) | 488 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Game theory. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Computational complexity. |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematical optimization. |

856 ## - ELECTRONIC LOCATION AND ACCESS | |

Uniform Resource Identifier | https://dl-acm-org.ezproxy.apu.edu.my/doi/book/10.1145/3241304 |

Public note | Available in ACM Digital Library. Requires Log In to view full text. |

942 ## - ADDED ENTRY ELEMENTS (KOHA) | |

Source of classification or shelving scheme | |

Koha item type | E-Book |

Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Home library | Current library | Shelving location | Date acquired | Source of acquisition | Total Checkouts | Full call number | Date last seen | Copy number | Price effective from | Koha item type |
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Not Withdrawn | Available | Not Damaged | Available for loan | E-Book | APU Library | APU Library | Online Database | 08/03/2022 | OTHERS | QA267.7 .R83 2019eb | 08/03/2022 | 1 | 08/03/2022 | General Circulation |