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Algorithmics Of Matching Under Preferences
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Book Synopsis Algorithmics of Matching Under Preferences by : David F. Manlove
Download or read book Algorithmics of Matching Under Preferences written by David F. Manlove and published by World Scientific. This book was released on 2013 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Algorithmics Of Matching Under Preferences by : David Manlove
Download or read book Algorithmics Of Matching Under Preferences written by David Manlove and published by World Scientific. This book was released on 2013-03-20 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matching problems with preferences are all around us: 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. The importance of the research area was recognised in 2012 through the award of the Nobel Prize in Economic Sciences to Alvin Roth and Lloyd Shapley.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.
Book Synopsis Theory and Algorithms for Matching Problems Under Preferences by : Changyong Hu
Download or read book Theory and Algorithms for Matching Problems Under Preferences written by Changyong Hu and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matching under preferences involves matching agents to one another, subject to various optimality criteria such as stability, popularity, and Pareto-optimality, etc. Each agent expresses ordinal preferences over a subset of the others. Real-life applications include assigning graduating medical students to hospitals, high school students to colleges, public houses to applicants, and so on. We consider various matching problems with preferences. In this dissertation, we present efficient algorithms to solve them, prove hardness results, and develop linear programming theory around them. In the first part of this dissertation, we present two characterizations for the set of super-stable matchings. Super-stability is one of the optimality criteria when the preference lists contain ties. The first algorithm computes irreducible super-stable matchings in the super-stable matching lattice. The second algorithm takes O(mn) time, where m denotes the number of edges and n denotes the number of vertices and gives an explicit rotation poset that can be used to construct all super-stable matchings. In the second part, we present a polyhedral characterization of the set of all super-stable matchings, i.e. a linear system that is integral and describes the super-stable matching polytope. We also give alternative proof for the integrality of the strongly stable matching polytope. We also use linear programming techniques to solve an application of the stable matching problem. In the third part, we present NC algorithms for the popular matching problem. Popularity is another optimality criterion, where each agent gives a vote and the outcome matching has majority votes. In the last part, we consider envy-freeness, a relaxation of stability in the Hospitals/Residents setting, which allows blocking pairs involving a resident and an empty position of a hospital. Envy-free matching might not exist. We prove NP-hardness results of minimizing envy (if envy is inevitable) in terms of envy-pairs and envy-residents in the Hospitals/Residents Problem with Lower Quota
Book Synopsis Efficient Algorithms for Optimal Matching Problems Under Preferences by : Augustine Kwanashie
Download or read book Efficient Algorithms for Optimal Matching Problems Under Preferences written by Augustine Kwanashie and published by . This book was released on 2015 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Efficient Algorithms for Bipartite Matching Problems with Preferences by : Colin Sng
Download or read book Efficient Algorithms for Bipartite Matching Problems with Preferences written by Colin Sng and published by . This book was released on 2008 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Two-Sided Matching by : Alvin E. Roth
Download or read book Two-Sided Matching written by Alvin E. Roth and published by Cambridge University Press. This book was released on 1992-06-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Complexity and Algorithms in Matching Problems Under Preferences by : Ágnes Cseh
Download or read book Complexity and Algorithms in Matching Problems Under Preferences written by Ágnes Cseh and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Stable Marriage Problem by : Dan Gusfield
Download or read book The Stable Marriage Problem written by Dan Gusfield and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matching Mechanisms in Theory and Practice by : Andreas Zweifel
Download or read book Matching Mechanisms in Theory and Practice written by Andreas Zweifel and published by GRIN Verlag. This book was released on 2010 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bachelor Thesis from the year 2009 in the subject Economics - Other, grade: 5.0, University of Zurich (Sozialökonomisches Institut (SOI)), language: English, abstract: Matching is the part of economics that deals with the question of who gets what, e.g. who gets which jobs, who goes to which university, who receives which organ or who marries whom. During the second part of the last century, many markets have been discovered to have failed in providing the necessary conditions for efficient matches. These market failures have partly evolved on ethical or institutional grounds, but are more generally attributed to congestion or coordination problems caused by the inability of the market to make it safe for participants to act on their private information. For this reason, a variety of allocation mechanisms have been developed and subsequently tested in field and laboratory experiments for possible implementation in real-world applications. This work attempts at giving a condensed review of different matching mechanisms and the performance of algorithms that have been implemented for solving the problems in their respective environments. The theoretical properties of these mechanisms as described in the increasingly vast literature on matching design will be used as a benchmark to compare their relative performance in terms of overall efficiency. The results yield some basic insights in the varying success of the competing algorithms in practice, indicating that both the quality of theoretical predictions and the actual performance of the algorithms decrease with the complexity of market environments. In particular, they show that imperfections of markets such as information asymmetry and incentive problems can have far-reaching consequences with respect to the effective working of matching procedures.
Book Synopsis Trends in Computational Social Choice by : Ulle Endriss
Download or read book Trends in Computational Social Choice written by Ulle Endriss and published by Lulu.com. This book was released on 2017 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of computer science and economics. The central question studied in computational social choice is that of how best to aggregate the individual points of view of several agents, so as to arrive at a reasonable compromise. Examples include tallying the votes cast in an election, aggregating the professional opinions of several experts, and finding a fair manner of dividing a set of resources amongst the members of a group -- Back cover.
Book Synopsis Algorithms for Stable Matching with Indifferences by : Chi Kit Lam
Download or read book Algorithms for Stable Matching with Indifferences written by Chi Kit Lam and published by . This book was released on 2019 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the stable matching problem, given a two-sided matching market where each agent has ordinal preferences over the agents on the other side, we would like to find a bipartite matching such that no pair of agents prefer each other to their partners. Indifferences in preferences of the agents arise naturally in large-scale centralized matching schemes. We consider stable matching models where indifferences may occur in the preferences and address some of the related algorithmic challenges. In the first part of this dissertation, we study group strategyproofness and Pareto-stability in the stable matching market with indifferences. We present Pareto-stable mechanisms that are group strategyproof for one side of the market. Our key technique involves modeling the stable matching market as a generalized assignment game. In the second part of this dissertation, we study the problem of finding maximum stable matchings when preference lists are incomplete and contain one-sided ties. We present a polynomial algorithm that achieves an approximation ratio of 1 + (1 - [1 over L]) [superscript L], where L is the maximum tie length. Our algorithm is based on a proposal process in which numerical priorities are adjusted according to the solution of a linear program, and are used for tie-breaking purposes. Our main idea is to use an infinitesimally small step size for incrementing the priorities. Our analysis involves a charging argument and an infinite-dimensional factor-revealing linear program. We also show that the same ratio of 1 + (1 - [1 over L]) [superscript L], is an upper bound on the integrality gap, which matches the known lower bound. For the case of one-sided ties where the maximum tie length is two, our result implies an approximation ratio and integrality gap of [5 over 4], which matches the known UG-hardness result
Book Synopsis Efficient Algorithms for Bipartite Matching Problems with Preferences by : Colin Sng
Download or read book Efficient Algorithms for Bipartite Matching Problems with Preferences written by Colin Sng and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Computational Social Choice by : Felix Brandt
Download or read book Handbook of Computational Social Choice written by Felix Brandt and published by Cambridge University Press. This book was released on 2016-04-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.
Book Synopsis Stable Marriage and Its Relation to Other Combinatorial Problems by : Donald Ervin Knuth
Download or read book Stable Marriage and Its Relation to Other Combinatorial Problems written by Donald Ervin Knuth and published by American Mathematical Soc.. This book was released on 1997 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Online Matching and Ad Allocation by : Aranyak Mehta
Download or read book Online Matching and Ad Allocation written by Aranyak Mehta and published by . This book was released on 2013-10-01 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matching is a classic problem with a rich history and a significant impact on both the theory of algorithms and in practice. Recently, there has been a surge of interest in the online version of matching and its generalizations. This is due to the important new application domain of Internet advertising. The theory of online matching and allocation has played a critical role in designing algorithms for ad allocation. Online Matching and Ad Allocation surveys the key problems, models, and algorithms from online matchings, as well as their implication in the practice of ad allocation. It provides a classification of the problems in this area, an introduction into the techniques used, a glimpse into the practical impact, and ponders some of the open questions that will be of interest in the future. Matching continues to find core applications in diverse domains, and the advent of massive online and streaming data emphasizes the future applicability of the algorithms and techniques surveyed here. Online Matching and Ad Allocation is an ideal primer for anyone interested in matching, and particularly in the online version of the problem, in bipartite graphs.
Book Synopsis Programming in Networks and Graphs by : Ulrich Derigs
Download or read book Programming in Networks and Graphs written by Ulrich Derigs and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network flow and matching are often treated separately in the literature and for each class a variety of different algorithms has been developed. These algorithms are usually classified as primal, dual, primal-dual etc. The question the author addresses in this work is that of the existence of a common combinatorial principle which might be inherent in all those apparently different approaches. It is shown that all common network flow and matching algorithms implicitly follow the so-called shortest augmenting path. This can be interpreted as a greedy-like decision rule where the optimal solution is built up through a sequence of local optimal solutions. The efficiency of this approach is realized by combining this myopic decision rule with an anticipant organization. The approach of this work is organized as follows. For several standard flow and matching problems the common solution procedures are first reviewed. It is then shown that they all reduce to a common basic principle, that is, they all perform the same computational steps if certain conditions are set properly and ties are broken according to a common rule. Recognizing this near-equivalence of all commonly used algorithms the question of the best method has to be modified - all methods are (only) different implementations of the same algorithm obtained by different views of the problem.
Book Synopsis Twenty Lectures on Algorithmic Game Theory by : Tim Roughgarden
Download or read book Twenty Lectures on Algorithmic Game Theory written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2016-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
