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Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Numbers, Information and Complexity is a collection of about 50 articles in honour of Rudolf Ahlswede. His main areas of research are represented in the three sections, `Numbers and Combinations', `Information Theory (Channels and Networks, Combinatorial and Algebraic Coding, Cryptology, with the related fields Data Compression, Entropy Theory, Symbolic Dynamics, Probability and Statistics)', and `Complexity'. Special attention was paid to the interplay between the fields. Surveys on topics of current interest are included as well as new research results. The book features surveys on Combinatorics about topics such as intersection theorems, which are not yet covered in textbooks, several contributions by leading experts in data compression, and relations to Natural Sciences are discussed.
This book constitutes the refereed proceedings of the 5th Annual International European Symposium on Algorithms, ESA'97, held in Graz, Austria, September 1997. The 38 revised full papers presented were selected from 112 submitted papers. The papers address a broad spectrum of theoretical and applicational aspects in algorithms theory and design. Among the topics covered are approximation algorithms, graph and network algorithms, combinatorial optimization, computational biology, computational mathematics, data compression, distributed computing, evolutionary algorithms, neural computing, online algorithms, parallel computing, pattern matching, and others.
This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Computers and Games, CG 2016, held in Leiden, The Netherlands,in conjunction with the 19th Computer Olympiad and the 22nd World Computer-Chess Championship. The 20 papers presented were carefully reviewed and selected of 30 submitted papers. The 20 papers cover a wide range of computer games and many different research topics in four main classes which determined the order of publication: Monte Carlo Tree Search (MCTS) and its enhancements (seven papers), concrete games (seven papers), theoretical aspects and complexity (five papers) and cognition model (one paper). The paper Using Partial Tablebases in Breakthrough by Andrew Isaac and Richard Lorentz received the Best Paper Award.
With more than 400 illustrations, and detailed maps, this immense and deeply researched account of the history of chess covers not only the modern international game, derived from Persian and Arab roots, but a broad spectrum of variants going back 1500 years, some of which are still played in various parts of the world. The evolution of strategic board games, especially in India, China and Japan, is discussed in detail. Many more recent chess variants (board sizes, new pieces, 3-D, etc.) are fully covered. Instructions for play are provided, with historical context, for every game presented.
This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Computers and Games, CG 2006, co-located with the 14th World Computer-Chess Championship and the 11th Computer Olympiad. The 24 revised papers cover all aspects of artificial intelligence in computer-game playing. Topics addressed are evaluation and learning, search, combinatorial games and theory opening and endgame databases, single-agent search and planning, and computer Go.
This monograph is a thoroughly revised and extended version of the author's PhD thesis, which was selected as the winning thesis of the 2002 ACM Doctoral Dissertation Competition. Venkatesan Guruswami did his PhD work at the MIT with Madhu Sudan as thesis adviser. Starting with the seminal work of Shannon and Hamming, coding theory has generated a rich theory of error-correcting codes. This theory has traditionally gone hand in hand with the algorithmic theory of decoding that tackles the problem of recovering from the transmission errors efficiently. This book presents some spectacular new results in the area of decoding algorithms for error-correcting codes. Specificially, it shows how the notion of list-decoding can be applied to recover from far more errors, for a wide variety of error-correcting codes, than achievable before The style of the exposition is crisp and the enormous amount of information on combinatorial results, polynomial time list decoding algorithms, and applications is presented in well structured form.
The Computers and Games (CG) series began in 1998 with the objective of showcasing new developments in arti?cial intelligence (AI) research that used games as the experimental test-bed. The ?rst two CG conferences were held at Hamamatsu,Japan(1998,2000).ComputersandGames2002(CG2002)wasthe third event in this biennial series. The conference was held at the University of Alberta(Edmonton,Alberta,Canada),July25–27,2002.Theprogramconsisted of the main conference featuring refereed papers and keynote speakers, as well as several side events including the Games Informatics Workshop, the Agents in Computer Games Workshop, the Trading Agents Competition, and the North American Computer Go Champion...