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Full Description
AlegendsaysthatJackEdmondsshouted"Eureka-youshrink!"whenhefound a good characterization for matching (and the matching algorithm) in 1963, the daybeforehistalkatasummerworkshopatRANDCorporationwithcelebrities like George Dantzig, Ralph Gomory, and Alan Ho?man in the audience. During Aussois 2001, Jack con?rmed: "'Eureka - you shrink!' is really true, except that instead of 'Eureka' it maybe was some less digni?ed word." Aussois 2001 was the ?fth in an annual series of workshops on combinatorial optimization that are alternately organized by Thomas Liebling, Denis Naddef, andLaurenceWolsey-theinitiatorsofthisseries-inevenyearsandtheeditors of this book in odd years (except 1997). We decided to dedicate Aussois 2001 to Jack Edmonds in appreciation of his groundbreaking work that laid the foundations of much of what combinatorial optimizers have done in the last 35 years. Luckily, Jack is a regular participant of the Aussois workshops and, as ever, he cares a lot for young combinatorial optimizers who traditionally play a major r ole in the Aussois series. Fig.1.
Handout for the Aussois 2001 participants VI Preface Highlights of Aussois 2001 included a special session entitled "Eureka - you shrink!" in honor of Jack and a special lecture by Jack on "Submodular Fu- tions, Matroids, and Certain Polyhedra" that closed the workshop. In this book, we give an account of the "Eureka - you shrink!" session as well as reprints of three hardly accessible papers that Jack gave as a handout to the Aussois 2001 participants and that were originally published in theProceedings oftheCalgaryInternationalConferenceonCombinatorialStructuresandTheir Applications 1969, Gordon and Breach (1970) - newly typeset by the editors and reprinted by permission.
Contents
"Eureka — You Skrink!".- "Eureka — You Shrink!".- Submodular Functions, Matroids, and Certain Polyhedra.- Matching: A Well-Solved Class of Integer Linear Programs.- Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems.- Connected Matchings.- Hajós' Construction and Polytopes.- Algorithmic Characterization of Bipartite b-Matching and Matroid Intersection.- Solving Real-World ATSP Instances by Branch-and-Cut.- The Bundle Method for Hard Combinatorial Optimization Problems.- The One-Commodity Pickup-and-Delivery Travelling Salesman Problem.- Reconstructing a Simple Polytope from Its Graph.- An Augment-and-Branch-and-Cut Framework for Mixed 0-1 Programming.- A Procedure of Facet Composition for the Symmetric Traveling Salesman Polytope.- Constructing New Facets of the Consecutive Ones Polytope.- A Simplex-Based Algorithm for 0-1 Mixed Integer Programming.- Mixed-Integer Value Functions in Stochastic Programming.- Exact Algorithms for NP-Hard Problems: A Survey.
