Polyhedral characterization of discrete dynamic programming
Operations Research
Facets of the p-cycle polytope
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
INFORMS Journal on Computing
Two Edge-Disjoint Hop-Constrained Paths and Polyhedra
SIAM Journal on Discrete Mathematics
The two-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut
Networks - Special Issue on Multicommodity Flows and Network Design
Facets of the (s,t)-p-path polytope
Discrete Applied Mathematics
On cardinality constrained cycle and path polytopes
Mathematical Programming: Series A and B
On the k edge-disjoint 2-hop-constrained paths polytope
Operations Research Letters
Using separation algorithms to generate mixed integer model reformulations
Operations Research Letters
Compact vs. exponential-size LP relaxations
Operations Research Letters
On the directed hop-constrained shortest path problem
Operations Research Letters
A note on hop-constrained walk polytopes
Operations Research Letters
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In this paper, we study the hop constrained chain polytope, that is, the convex hull of the incidence vectors of (s,t)-chains using at most k arcs of a given digraph, and its dominant. We use extended formulations (implied by the inherent structure of the Moore-Bellman-Ford algorithm) to derive facet defining inequalities for these polyhedra via projection. Our findings result in characterizations of all facet defining 0/+/-1-inequalities for the hop constrained chain polytope and all facet defining 0/1-inequalities for its dominant. Although the derived inequalities are already known, such classifications were not previously given to the best of our knowledge. Moreover, we use this approach to generalize so called jump inequalities, which have been introduced in a paper by Dahl and Gouveia in 2004.