Theory of linear and integer programming
Theory of linear and integer programming
On the equivalence between some discrete and continuous optimization problems
Annals of Operations Research
Minkowski addition of polytopes: computational complexity and applications to Gro¨bner bases
SIAM Journal on Discrete Mathematics
Directional-quasi-convexity, asymmetric Schur-convexity and optimality of consecutive partitions
Mathematics of Operations Research
0/1-Integer Programming: Optimization and Augmentation are Equivalent
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
The partition bargaining problem
Discrete Applied Mathematics
The partition bargaining problem
Discrete Applied Mathematics
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Recent results show that edge-directions of polyhedra play an important role in (combinatorial) optimization; in particular, a d-dimensional polyhedron with |D| distinct edge-directions has at most O(|D|d-1) vertices. Here, we obtain a characterization of the directions of edges that are adjacent to a given vertex of a standard polyhedron of the form P = {x : Ax = b, l驴 x驴 u, tightening a standard necessary condition which asserts that such directions must be minimal support solutions of the homogenous equation Ax = 0 which are feasible at the given vertex. We specialize the characterization for polyhedra that correspond to network flows, obtaining a graph characterization of circuits which correspond to edge-directions. Applications to partitioning polyhedra are discussed.