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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-21527-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21526-1
Online ISBN: 978-3-642-21527-8
eBook Packages: Computer ScienceComputer Science (R0)