Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
A quantitative approach to logical inference
Decision Support Systems
Extended Horn sets in propositional logic
Journal of the ACM (JACM)
Lehman's forbidden minor characterization of ideal 0–1 matrices
Discrete Mathematics
Journal of Combinatorial Theory Series B
A class of logic problems solvable by linear programming
Journal of the ACM (JACM)
Resolution and the integrality of satisfiability problems
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Perfect and Ideal 0, ±1 Matrices
Mathematics of Operations Research
Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour
SIAM Journal on Discrete Mathematics
A short proof of Guenin's characterization of weakly bipartite graphs
Journal of Combinatorial Theory Series B
Integral Polyhedra Related to Even-Cycle and Even-Cut Matroids
Mathematics of Operations Research
On Combinatorial Properties of Binary Spaces
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
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The Operations Research model known as the Set Covering Problem has a wide range of applications. See for example the survey by Ceria, Nobili and Sassano and edited by Dell'Amico, Maffioli and Martello (Annotated Bibliographies in Combinatorial Optimization, Wiley, New York, 1997). Sometimes, due to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution that is integer, thus solving the problem. Under which conditions do such integrality properties hold? This question is of both theoretical and practical interest. On the theoretical side, polyhedral combinatorics and graph theory come together in this rich area of discrete mathematics. In this tutorial, we present the state of the art and open problems on this question.