Investigations Of Finding All Stable Solutions Of Stable Marriage Problem

In 1962, David Gale and Lloyd Shapley proved that, for any equal number of men and women, and each man and each woman give a strict order of preference to the opposite sex, they can always solve for at least one stable marriage solution. What they didn't tell us is how to find all stable solutions. In this paper, I will demonstrate how to find every stable solution to a stable marriage problem. And I will discover the expected number of the stable matching for the stable marriage problem. Moreover, I will use the scoring system to quantify how much a man or a woman prefer the opposite sex, denoted as h̀̀appiness score''. Then we can use the scoring system to present every matching on the $xy$-plane and look at the distribution of matchings.

'This is a very stimulating book!' - N. G. de Bruijn. 'This short book will provide extremely enjoyable reading to anyone with an interest in discrete mathematics and algorithm design' - ""Mathematical Reviews"". 'This book is an excellent (and enjoyable) means of sketching a large area of computer science for specialists in other fields: It requires little previous knowledge, but expects of the reader a degree of mathematical facility and a willingness to participate. It is really neither a survey nor an introduction; rather, it is a paradigm, a fairly complete treatment of a single example used as a synopsis of a larger subject' - ""SIGACT News"". 'Anyone would enjoy reading this book. If one had to learn French first, it would be worth the effort!' - ""Computing Reviews"". The above citations are taken from reviews of the initial French version of this text - a series of seven expository lectures that were given at the University of Montreal in November of 1975.The book uses the appealing 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. The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included.The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms. Donald E. Knuth is one of the most prominent figures of modern computer science. His works in ""The Art of Computer Programming"" are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science.

Annotation This volume constitutes the refereed proceedings of the 11th Pacific Rim Conference on Artificial Intelligence, PRICAI 2010, held in Daegu, Korea, in August/September 2010. The 48 revised full papers presented together with 21 short papers in this volume were carefully reviewed and selected from 191 submissions. The volume concentrates on AI theories, technologies and their applications in the areas of social and economic importance for countries in the Pacific Rim.

This book constitutes the refereed proceedings of the 8th International Symposium on Algorithmic Game Theory, SAGT 2015, held in Saarbrücken, Germany, in September 2015. The 22 full papers presented together with one extended abstract and 6 brief announcements were carefully reviewed and selected from 63 submissions. They cover various important aspects of algorithmic game theory, such as matching under preferences; cost sharing; mechanism design and social choice; auctions; networking; routing and fairness; and equilibrium computation.

LC copy bound in 2 v.: v. 1, p. 1-509; v. 2, p. [509]-1153.

The two-volume set LNAI 12033 and 11034 constitutes the refereed proceedings of the 12th Asian Conference on Intelligent Information and Database Systems, ACIIDS 2020, held in Phuket, Thailand, in March 2020. The total of 105 full papers accepted for publication in these proceedings were carefully reviewed and selected from 285 submissions. The papers of the first volume are organized in the following topical sections: Knowledge Engineering and Semantic Web, Natural Language Processing, Decision Support and Control Systems, Computer Vision Techniques, Machine Learning and Data Mining, Deep Learning Models, Advanced Data Mining Techniques and Applications, Multiple Model Approach to Machine Learning. The papers of the second volume are divided into these topical sections: Application of Intelligent Methods to Constrained Problems, Automated Reasoning with Applications in Intelligent Systems, Current Trends in Arti cial Intelligence, Optimization, Learning,and Decision-Making in Bioinformatics and Bioengineering, Computer Vision and Intelligent Systems, Data Modelling and Processing for Industry 4.0, Intelligent Applications of Internet of Things and Data AnalysisTechnologies, Intelligent and Contextual Systems, Intelligent Systems and Algorithms in Information Sciences, Intelligent Supply Chains and e-Commerce, Privacy, Security and Trust in Arti cial Intelligence, Interactive Analysis of Image, Video and Motion Data in LifeSciences.

This book constitutes the refereed proceedings of the 19th International Conference on Knowledge Engineering and Knowledge Management, EKAW 2014, held in Linköping, Sweden, in November 2014. The 24 full papers and 21 short papers presented were carefully reviewed and selected from 138 submissions. The papers cover all aspects of eliciting, acquiring, modeling, and managing knowledge, the construction of knowledge-intensive systems and services for the Semantic Web, knowledge management, e-business, natural language processing, intelligent information integration, personal digital assistance systems, and a variety of other related topics.

This book constitutes the refereed conference proceedings of the 11th International Conference on Algorithms and Complexity, CIAC 2019, held in Rome, Italy, in May 2019. The 30 full papers were carefully reviewed and selected from 95 submissions. The International Conference on Algorithms and Complexity is intended to provide a forum for researchers working in all aspects of computational complexity and the use, design, analysis and experimentation of efficient algorithms and data structures. The papers present original research in the theory and applications of algorithms and computational complexity.