Stable Marriage and Its Relation to Other Combinatorial Problems PDF Download

Author: Donald Ervin Knuth
Publisher: American Mathematical Soc.
ISBN: 0821806033
Category : Mathematics
Languages : en
Pages : 90

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Book Description
Uses the theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.

Author: Dan Gusfield
Publisher: MIT Press (MA)
ISBN: 9780262071185
Category : Computers
Languages : en
Pages : 240

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Book Description
This book probes the stable marriage problem and its variants as a rich source of problems and ideas that illustrate both the design and analysis of efficient algorithms. It covers the most recent structural and algorithmic work on stable matching problems, simplifies and unifies many earlier proofs, strengthens several earlier results, and presents new results and more efficient algorithms. The authors develop the structure of the set of stable matchings in the stable marriage problem in a more general and algebraic context than has been done previously; they discuss the problem's structure in terms of rings of sets, which allows many of the most useful features to be seen as features of a more general set of problems. The relationship between the structure of the stable marriage problem and the more general stable roommates problem is demonstrated, revealing many commonalities. The results the authors obtain provide an algorithmic response to the practical, and political, problems created by the asymmetry inherent in the Gale Shapley solutions, leading to alternative methods and better compromises than are provided by the Gale Shapley method. And, in contrast to Donald Knuth's earlier work which primarily focused on the application of mathematics to the analysis of algorithms, this book illustrates the productive and almost inseparable relationship between mathematical insight and the design of efficient algorithms. Dan Gusfield is Associate Professor of Computer Science at the University of California, Davis. Robert W. Irving is Senior Lecturer in Computing Science at the University of Glasgow. The Stable Marriage Problem is included in the Foundations of Computing Series, edited by Michael Garey and Albert Meyer.

Author: John Harris
Publisher: Springer Science & Business Media
ISBN: 0387797114
Category : Mathematics
Languages : en
Pages : 392

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Book Description
These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Author: Alvin E. Roth
Publisher: Cambridge University Press
ISBN: 1107782430
Category : Business & Economics
Languages : en
Pages : 288

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Book Description
Two-sided matching provides a model of search processes such as those between firms and workers in labor markets or between buyers and sellers in auctions. This book gives a comprehensive account of recent results concerning the game-theoretic analysis of two-sided matching. The focus of the book is on the stability of outcomes, on the incentives that different rules of organization give to agents, and on the constraints that these incentives impose on the ways such markets can be organized. The results for this wide range of related models and matching situations help clarify which conclusions depend on particular modeling assumptions and market conditions, and which are robust over a wide range of conditions. 'This book chronicles one of the outstanding success stories of the theory of games, a story in which the authors have played a major role: the theory and practice of matching markets ... The authors are to be warmly congratulated for this fine piece of work, which is quite unique in the game-theoretic literature.' From the Foreword by Robert Aumann

Author: David F. Manlove
Publisher: World Scientific
ISBN: 9814425257
Category : Mathematics
Languages : en
Pages : 524

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Book Description
Matching problems with preferences are all around us OCo they arise when agents seek to be allocated to one another on the basis of ranked preferences over potential outcomes. Efficient algorithms are needed for producing matchings that optimise the satisfaction of the agents according to their preference lists.In recent years there has been a sharp increase in the study of algorithmic aspects of matching problems with preferences, partly reflecting the growing number of applications of these problems worldwide. This book describes the most important results in this area, providing a timely update to The Stable Marriage Problem: Structure and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in connection with stable matching problems, whilst also broadening the scope to include matching problems with preferences under a range of alternative optimality criteria."

Author: Bela Bollobas
Publisher: Springer Science & Business Media
ISBN: 1461206197
Category : Mathematics
Languages : en
Pages : 408

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Book Description
An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.

Author: Dimitris Fotakis
Publisher: Springer Nature
ISBN: 3030304736
Category : Computers
Languages : en
Pages : 401

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Book Description
This book constitutes the refereed proceedings of the 12th International Symposium on Algorithmic Game Theory, SAGT 2019, held in Athens, Greece, in September/October 2019. The 25 full papers presented together with 3 invited talks and one abstract paper were carefully reviewed and selected from 55 submissions. The papers are organized in topical sections named: Algorithmic Mechanism Design; Auctions and Markets; Computational Aspects of Games; Network Games and Congestion Games; Social Choice; and Matchings and Fair Division.

Author: Dimitrios M. Thilikos
Publisher: Springer
ISBN: 3642169260
Category : Computers
Languages : en
Pages : 349

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Book Description
The 36th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2010) took place in Zar ́ os, Crete, Greece, June 28–30, 2010. About 60 mathematicians and computer scientists from all over the world (Australia, Canada, Czech Republic, France, Germany, Greece, Hungary, Israel, Japan, The Netherlands, Norway, Poland, Switzerland, the UK, and the USA) attended the conference. WG has a long tradition. Since 1975, WG has taken place 21 times in Germany, four times in The Netherlands, twice in Austria, twice in France and once in the Czech Republic, Greece, Italy, Norway, Slovakia, Switzerland, and the UK. WG aims at merging theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications. The goal is to presentemergingresearchresultsand to identify and exploredirections of future research.The conference is well-balanced with respect to established researchers and young scientists. There were 94 submissions, two of which where withdrawn before entering the review process. Each submission was carefully reviewed by at least 3, and on average 4.5, members of the Program Committee. The Committee accepted 28 papers, which makes an acceptance ratio of around 30%. I should stress that, due to the high competition and the limited schedule, there were papers that were not accepted while they deserved to be.

Author: Lars Arge
Publisher: Springer
ISBN: 3540755209
Category : Computers
Languages : en
Pages : 782

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Book Description
This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.

Author: Joe Celko
Publisher: Elsevier
ISBN: 0080491685
Category : Computers
Languages : en
Pages : 347

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Book Description
Joe Celko's SQL Puzzles and Answers, Second Edition, challenges you with his trickiest puzzles and then helps solve them with a variety of solutions and explanations. Author Joe Celko demonstrates the thought processes that are involved in attacking a problem from an SQL perspective to help advanced database programmers solve the puzzles you frequently face. These techniques not only help with the puzzle at hand, but also help develop the mindset needed to solve the many difficult SQL puzzles you face every day. This updated edition features many new puzzles; dozens of new solutions to puzzles; and new chapters on temporal query puzzles and common misconceptions about SQL and RDBMS that leads to problems. This book is recommended for database programmers with a good knowledge of SQL. A great collection of tricky SQL puzzles with a variety of solutions and explanations Uses the proven format of puzzles and solutions to provide a user-friendly, practical look into SQL programming problems - many of which will help users solve their own problems New edition features: Many new puzzles added!, Dozens of new solutions to puzzles, and using features in SQL-99, Code is edited to conform to SQL STYLE rules, New chapter on temporal query puzzles, New chapter on common misconceptions about SQL and RDBMS that leads to problems