In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience.

The volume contains the papers selected for presentation at IPCO 2008, the 13th International Conference on Integer Programming and Combinatorial - timization that was held in Bertinoro (Italy), May 26-28, 2008. The IPCO series of conferences, sponsored by the Mathematical Progr- ming Society, highlights recent developments in theory, computation, and app- cation of integer programming and combinatorial optimization. The ?rst conf- ence took place in 1990; starting from IPCO 1995, the proceedings are published in the Lecture Notes in Computer Science series. The 12 previous IPCO conferences were held in Waterloo (Canada) 1990, Pittsburgh (USA) 1992, Erice (Italy) 1993, Copenhagen (Denmark) 1995 [LNCS 920], Vancouver (Canada) 1996 [LNCS 1084], Houston (USA) 1998 [LNCS 1412], Graz (Austria) 1999 [LNCS 1610], Utrecht (The Netherlands) 2001 [LNCS 2081], Boston (USA) 2002 [LNCS 2337], New York (USA) 2004 [LNCS 2986], Berlin (Germany) 2005 [LNCS 3509], and Ithaca (USA) 2007 [LNCS 4168]. The c- ference is not held in the years when the International Symposium of the Ma- ematical Programming Society takes place.

This book is dedicated to Jack Edmonds in appreciation of his ground breaking work that laid the foundations for a broad variety of subsequent results achieved in combinatorial optimization. The main part consists of 13 revised full papers on current topics in combinatorial optimization, presented at Aussois 2001, the Fifth Aussois Workshop on Combinatorial Optimization, March 5-9, 2001, and dedicated to Jack Edmonds. Additional highlights in this book are an account of an Aussois 2001 special session dedicated to Jack Edmonds including a speech given by William R. Pulleyblank as well as newly typeset versions of three up-to-now hardly accessible classical papers: - Submodular Functions, Matroids, and Certain Polyhedra   by Jack Edmonds - Matching: A Well-Solved Class of Integer Linear Programs   by Jack Edmonds and Ellis L. Johnson - Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems   by Jack Edmonds and Richard M. Karp.

This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Symposium on Combinatorial Optimization, ISCO 2018, held in Marrakesh, Marocco, in April 2018. The 35 revised full papers presented in this book were carefully reviewed and selected from 75 submissions. The symposium aims to bring together researchers from all the communities related to combinatorial optimization, including algorithms and complexity, mathematical programming and operations research.

This book aims to present some fundamental pillars that must be taken into account for the design and construction of a medical record system. The work does not claim to be exhaustive, as the spirit of the book is to propose to reason out on some issues that have to be considered as the main features to take in consideration in the design and deployment of medical record systems, trying to bring positive issues to the general discussion. The first challenge has been to face the issues proposed in a co-productive way, in which the point of views of different actors (technicians, doctors, policy makers) are harmonised in shared visions, where the requirements that must be posed and considered become opportunities and challenges to overcome, also offering different shared solutions based on technology, organisational changes, medical actions and workflow in a unitary way.