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Combinatorial Optimization - Packing and Covering (Paperback)
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Combinatorial Optimization - Packing and Covering (Paperback)
Series: CBMS-NSF Regional Conference Series, No. 74
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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. Cornuejols 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.
Cornuejols) before 2020. Claims must be sent to Dr. Cornuejols at
Carnegie Mellon University during his lifetime.
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