There exist several excellent books on linear and integer programming. Yet, I
did not feel it superfluous to write the present book. Most of the existing books
focus on the, very important, algorithmic side of linear and integer programming.
The emphasis of this book is on the more theoretical aspects, and it aims at
complementing the more practically oriented books.
Another reason for writing this book is that during the last few years several
interesting new results have been obtained, which are not yet all covered by
books: Lovasz’s basis reduction met hod, K hachiyan’s ellipsoid method and
Karmarkar’s method for linear programming, Borgwardt’s analysis of the
average speed of the simplex method, Tardos’ and Megiddo’s algorithms for
linear programming, Lenstra’s algorithm for integer linear programming,
Seymour’s decomposition theorem for totally unimodular matrices, and the
theory of total dual integrality