Blocking pairs of polyhedra arising from network flows

Edge-Directions of Standard Polyhedra with Applications to Network Flows

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 x u}, tightening a standard...

Multicommodity Flows and Polyhedra

Seymour s conjecture on binary clutters with the so called weak or Q max ow min cut property implies if true a wide variety of results in combinatorial optimization about objects ranging from matchings to mul ticommodity ows and disjoint paths In this paper we review in particular the relation between classes of multicommodity ow problems for which the so called cut condition is su cient and cl...

On Blocking and Anti-Blocking Polyhedra in Infinite Dimensions

We consider the natural generalizations of blocking and antiblocking polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. Using appropriate finite truncations we give conditions under which complementary slackness holds for primal-dual pairs of the infinite linear programming problems associated with infinite blocking and anti-b...

Lattice Polyhedra and Submodular Flows

Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain suband supermodularity constraints. Lattice polyhedra provide one of the most general frameworks of total dual integral systems. So far no combinatorial algorithm has been found for the ...

Notes on Combinatorial Mathematics: Anti-blocking Polyhedra