Asia Pacific University Library catalogue


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

000 -LEADER
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
Holdings
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
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