Hop-level flow formulation for the hop constrained survivable network design problem

Authors:
Ridha Mahjoub;Luidi Simonetti;Eduardo Uchoa
Affiliations:
Université Paris-Dauphine, Paris Cedex 16, France;Universidade Federal Fluminense, Niterói, Brazil;Universidade Federal Fluminense, Niterói, Brazil
Venue:
INOC'11 Proceedings of the 5th international conference on Network optimization
Year:
2011

Citing 3
Cited 0

The two-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut

Networks - Special Issue on Multicommodity Flows and Network Design
Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs

Mathematical Programming: Series A and B
Approximability of 3- and 4-hop bounded disjoint paths problems

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization

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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.