Studies On Graphs And Discrete Programming

Studies on Graphs and Discrete Programming

In the context of sports leagues scheduling (SLS) several groups' interests must be taken into account. This book treats requirements for sport leagues schedules to be realizable from an operational and a security point of view, attractive for spectators and TV channels, and fair for the competing teams. Formal problem definitions as well as integer programming models are presented and analyzed.

This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.

Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances,especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume,cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decades.

In 1988, the news of Egmont Köhler's untimely death at the age of 55 reached his friends and colleagues. It was widely felt that a lasting memorial tribute should be organized. The result is the present volume, containing forty-two articles, mostly in combinatorial design theory and graph theory, and all in memory of Egmont Köhler. Designs and graphs were his areas of particular interest; he will long be remembered for his research on cyclic designs, Skolem sequences, t-designs and the Oberwolfach problem. Professors Lenz and Ringel give a detailed appreciation of Köhler's research in the first article of this volume. There is, however, one aspect of Egmont Köhler's biography that merits special attention. Before taking up the study of mathematics at the age of 31, he had completed training as a musician (studying both composition and violoncello at the Musikhochschule in Berlin), and worked as a cellist in a symphony orchestra for some years. This accounts for his interest in the combinatorial aspects of music. His work and lectures in this direction had begun to attract the interest of many musicians, and he had commenced work on a book on mathematical aspects of musical theory. It is tragic indeed that his early death prevented the completion of his work; the surviving paper on the classification and complexity of chords indicates the loss that his death meant to the area, as he was almost uniquely qualified to bring mathematics and music together, being a professional in both fields.

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION "This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list."-Optima "A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such formulations, as well as for understanding the structure of and solving the resulting integer programming problems."-Computing Reviews "[This book] can serve as a basis for various graduate courses on discrete optimization as well as a reference book for researchers and practitioners."-Mathematical Reviews "This comprehensive and wide-ranging book will undoubtedly become a standard reference book for all those in the field of combinatorial optimization."-Bulletin of the London Mathematical Society "This text should be required reading for anybody who intends to do research in this area or even just to keep abreast of developments."-Times Higher Education Supplement, London Also of interest . . . INTEGER PROGRAMMING Laurence A. Wolsey Comprehensive and self-contained, this intermediate-level guide to integer programming provides readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively. 1998 (0-471-28366-5) 260 pp.

Through key research papers from Palgrave's Journal of Operational Research, this book showcases how Operational Research can be applied to sports in a variety of ways, including: timetabling fixtures; scheduling officials; forecasting outcomes; optimizing tactics and strategy; analyzing the effects of rules and laws; planning issues, and performance measurement. The introductory chapter provides a broad overview with an examination of how this area has developed over time, and a look at its wide ranging applications to sports including football, tennis and cricket etc.