Hardness of approximation between P and NP / (Record no. 891)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 06639nam a2200637 i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 9781947287215 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MOCL |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20260609132937.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 190719r20192019nyua ob 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781947287215 |
| Qualifying information | eBook |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781947287222 |
| Qualifying information | ePub |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781947287239 |
| Qualifying information | hardcover |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781947287208 |
| Qualifying information | paperback |
| 024 8# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1145/3241304 |
| Source of number or code | doi |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaBNVSL)thg00979248 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | CaBNVSL |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | CaBNVSL |
| Modifying agency | CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA269 |
| Item number | .R835 2019eb |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.3 |
| Edition information | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Rubinstein, Aviad, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Hardness of approximation between P and NP / |
| Statement of responsibility, etc. | Aviad Rubinstein. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | First edition. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | [New York, New York] : |
| Name of producer, publisher, distributor, manufacturer | Association for Computing Machinery, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2019] |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 PDF (xv, 301 pages) : |
| Other physical details | illustrations (chiefly color). |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | electronic |
| Source | isbdmedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | ACM books, |
| International Standard Serial Number | 2374-6777 ; |
| Volume/sequential designation | #24 |
| 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. |
| 500 ## - GENERAL NOTE | |
| General note | Revision of author's thesis (doctoral)--University of California, Berkeley, 2017. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references (pages [273]-290) 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 3# - 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. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE | |
| Additional physical form available note | Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Title from PDF title page (viewed on July 19, 2019). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Game theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Programming (Mathematics) |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9781947287239 |
| -- | 9781947287208 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | Abstract with links to full text |
| Uniform Resource Identifier | <a href="https://dl.acm.org/citation.cfm?id=3241304">https://dl.acm.org/citation.cfm?id=3241304</a> |
No items available.