Connectivity Upgrade Models for Survivable Network Design
Operations Research
Color-Coding Algorithms to the Balanced Path Problem: Computational Issues
INFORMS Journal on Computing
On the k edge-disjoint 2-hop-constrained paths polytope
Operations Research Letters
The k edge-disjoint 3-hop-constrained paths polytope
Discrete Optimization
Benders Decomposition for the Hop-Constrained Survivable Network Design Problem
INFORMS Journal on Computing
Characterization of facets of the hop constrained chain polytope via dynamic programming
Discrete Applied Mathematics
Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks
Journal of Combinatorial Optimization
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Given a graph G with distinguished nodes s and t, a cost on each edge of G, and a fixed integer L \geq 2, the two edge-disjoint hop-constrained paths problem is to find a minimum cost subgraph such that between s and t there exist at least two edge-disjoint paths of length at most L. In this paper, we consider that problem from a polyhedral point of view. We give an integer programming formulation for the problem when L = 2,3. An extension of this result to the more general case where the number of required paths is arbitrary and L = 2,3 is also given. We discuss the associated polytope, P(G,L), for L = 2,3. In particular, we show in this case that the linear relaxation of P(G,L), Q(G,L), given by the trivial, the st-cut, and the so-called L-path-cut inequalities, is integral. As a consequence, we obtain a polynomial time cutting plane algorithm for the problem when L = 2,3. We also give necessary and sufficient conditions for these inequalities to define facets of P(G,L) for L \geq 2 when G is complete. We finally investigate the dominant of P(G,L) and give a complete description of this polyhedron for L \geq 2 when P(G,L) = Q(G,L).