Algorithmics of Matching Under Preferences

Abstract

A new book by Dr David Manlove of the School of Computing Science has recently been published by World Scientific as part of their Series on Theoretical Computer Science. This book, called “Algorithmics of Matching Under Preferences”, deals with algorithms and complexity issues surrounding the matching of agents to one another when preferences are involved. \n \nFor example, in several countries, centralised matching schemes handle the annual allocation of intending junior doctors to hospitals based on their preferences over one another. Efficient algorithms required to solve the underlying theoretical matching problems. Similar examples arise in the allocation of pupils to schools, students to projects, kidney patients to donors, and so on. \n \nThe book surveys algorithmic results for a range of matching problems involving preferences, with practical applications areas including those mentioned above. It covers the classical Stable Marriage, Hospitals/Residents and Stable Roommates problems, where so-called stable matchings are sought, thereby providing an update to “The Stable Marriage problem, Structure and Algorithms”, by Dan Gusfield and Rob Irving, published by MIT Press in 1989. It also extends the coverage to the House Allocation problem, where stability is no longer the key requirement for a matching, and other definitions of optimality hold. \n \nThis book builds on the author’s prior research in this area, and also his practical experience of developing, with colleagues including Rob Irving and Gregg O’Malley, algorithms for matching kidney patients to donors in the UK (collaborating with NHS Blood and Transplant), for assigning medical students to hospitals in Scotland (in collaboration with NHS Education for Scotland), and for allocating students to elective courses and projects (within the Schools of Medicine and Computing Science at the University of Glasgow, respectively). \n \nThe book is also timely, as the research area recently came to the forefront in 2012 following the award of the Nobel Prize in Economic Sciences to Alvin Roth and Lloyd Shapley, two leading contributors to the field of matching theory and its application in practical settings, whose work is described in detail throughout the book. \n \nA Foreword is contributed by Kurt Mehlhorn of Max-Planck Institut fur Informatik, Saarbrucken, who wrote: “This book covers the research area in its full breadth and beauty. Written by one of the foremost experts in the area, it is a timely update to “The Stable Marriage Problem: Structure and Algorithms” (D. Gusfield and R.W. Irving, 1989). This book will be required reading for anybody working on the subject; it has a good chance of becoming a classic.”

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