This monograph presents new and elegant proofs of  classical results and makes difficult results accessible. The integer  programming models known as set packing and set covering have a wide  range of applications. Sometimes, owing to the special structure of  the constraint matrix, the natural linear programming relaxation  yields an optimal solution that is integral, thus solving the  problem. Sometimes, both the linear programming relaxation and its  dual have integral optimal solutions. Under which conditions do such  integrality conditions hold? This question is of both theoretical and  practical interest. Min-max theorems, polyhedral combinatorics, and  graph theory all come together in this rich area of discrete  mathematics. This monograph presents several of these beautiful  results as it introduces mathematicians to this active area of  research.    To encourage research on the many intriguing open problems that  remain, Dr. Cornuéjols is offering a $5000 prize to the first paper  solving or refuting each of the 18 conjectures described in the  book. To claim one of the prizes mentioned in the preface, papers must  be accepted by a quality refereed journal (such as Journal of  Combinatorial Theory B, Combinatorica, SIAM Journal on Discrete  Mathematics, or others to be determined by Dr. Cornuéjols) before  2020. Claims must be sent to Dr. Cornuéjols at Carnegie Mellon  University during his lifetime.

Combinatorial Optimization: Packing and Covering PDF

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