The Sharpest Cut is written in honor of Manfred Padberg, who has made fundamental contributions to both the theoretical and computational sides of integer programming and combinatorial optimization. This outstanding collection presents recent results in these areas that are closely connected to Padberg's research. His deep commitment to the geometrical approach to combinatorial optimization can be felt throughout this volume; his search for increasingly better and computationally efficient cutting planes gave rise to its title. The peer-reviewed papers contained here are based on invited lectures given at a workshop held in October 2001 to celebrate Padberg's 60th birthday. Grouped by topic (packing, stable sets, and perfect graphs; polyhedral combinatorics; general polytopes; semidefinite programming; computation), many of the papers set out to solve challenges set forth in Padberg's work. The book also shows how Padberg's ideas on cutting planes have influenced modern commercial optimization software. In addition, the volume contains a short curriculum vitae, a personal account of Padberg's work by Laurence Wolsey, and an appendix with reflections from Egon Balas, Claude Berge, and Harold Kuhn.
Preface Part I: Manfred Padberg: Curriculum Vitae and Survey of His Work Chapter 1: Manfred Padberg: Curriculum Vitae Chapter 2: Time for Old and New Faces, L. Wolsey Part II: Packing, Stable Sets, and Perfect Graphs Chapter 3: Combinatorial Packing Problems, R. Borndoerfer Chapter 4: Bicolorings and Equitable Bicolorings of Matrices, M. Conforti, G. Cornuejols, and G. Zambelli Chapter 5: The Clique-Rank of 3-Chromatic Perfect Graphs, J. Fonlupt Chapter 6: On the Way to Perfection: Primal Operations for Stable Sets in Graphs, C. Gentile, U.-U. Haus, M. Koeppe, G. Rinaldi, R. Weismantel Chapter 7: Relaxing Perfectness: Which Graphs Are "Almost" Perfect?, A.K. Wagler Part III: Polyhedral Combinatorics Chapter 8: Cardinality Homogeneous Set Systems, Cycles in Matroids, and Associated Polytopes, M. Groetschel Chapter 9: (1,2)-Survivable Networks: Facets and Branch-and-Cut, H. Kerivin, A.R. Mahjoub, and C. Nocq Chapter 10: The Domino Inequalities for the Symmetric Traveling Salesman Problem, C. Naddef Chapter 11: Computing Optimal Consecutive Ones Matrices, M. Oswald and G. Reinelt Chapter 12: Protein Folding on Lattices: An Integer Programming Approach, V. Chandru, M.R. Rao, and G. Swaminathan Part IV: General Polytopes, Chapter 13: On the Expansion of Graphs of 0/1-Polytopes, V. Kaibel Chapter 14: Typical and Extremal Linear Programs, G.M. Ziegler Part V: Semidefinite Programming Chapter 15: A Cutting Plane Algorithm for Large Scale Semidefinite Relaxations, C. Helmberg Chapter 16: Semidefinite Relaxations for Max-Cut, M. Laurent Part VI: Computation Chapter 17: The Steinberg Wiring Problem, N.W. Brixius and K.M. Anstreicher Chapter 18: Mixed-Integer Programming: A Progress Report, R.E. Bixby, M. Fenelon, Z. Gu, E. Rothberg, and R. Wunderling Chapter 19: Graph Drawing: Exact Optimization Helps!, P. Muntzel and M. Juenger Part VII: Appendix Chapter 20: Dinner Speeches Index.
