Abstract
The HSNDP consists in finding a minimum cost subgraph containing K edge-disjoint paths with length at most H joining each pair of vertices in a given demand set. The only formulation found in the literature that is valid for any K and any H is based on multi-commodity flows over suitable layered graphs (Hop-MCF) and has typical integrality gaps in the range of 5% to 25%. We propose a new formulation called Hop-Level-MCF (in this short paper only for the rooted demands case), having about H times more variables and constraints than Hop-MCF, but being significantly stronger. Typical gaps for rooted instances are between 0% and 6%. Some instances from the literature are solved for the first time.
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References
Bley, A., Neto, J.: Approximability of 3- and 4-hop bounded disjoint paths problems. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 205–218. Springer, Heidelberg (2010)
Botton, Q., Fortz, B., Gouveia, L., Poss, M.: Benders decomposition for the hop-constrained network design problem, Optimization on-line, report ULB (2010)
Gouveia, L., Simonetti, L., Uchoa, E.: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs. Mathematical Programming, Online first (2009)
Huygens, D., Labbé, M., Mahjoub, A.R., Pesneau, P.: Two-edge connected hop-constrained network design problem: valid inequalities and branch-and-cut. Networks 49, 116–133 (2007)
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Mahjoub, R., Simonetti, L., Uchoa, E. (2011). Hop-Level Flow Formulation for the Hop Constrained Survivable Network Design Problem. In: Pahl, J., Reiners, T., Voß, S. (eds) Network Optimization. INOC 2011. Lecture Notes in Computer Science, vol 6701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21527-8_23
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DOI: https://doi.org/10.1007/978-3-642-21527-8_23
Publisher Name: Springer, Berlin, Heidelberg
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