A comparison of node‐based and arc‐based hop‐indexed formulations for the Steiner tree problem with hop constraints. Issue 2 (14th December 2021)

• Record Type: Journal Article
• Authors: Fortz, Bernard; Gouveia, Luis; Moura, Pedro
• Is Part Of: Networks. Volume 80:Issue 2(2022)
• Page Start: 178
• Page End: 192
• Publication Date: 2021-12-14
• Subjects: hop constraint -- hop‐indexed model -- integer programming -- linear programming relaxation -- network design -- Steiner tree; Network analysis (Planning) -- Periodicals; 658.4032
• DOI: 10.1002/net.22086
• Languages: English
• ISSNs: 0028-3045

Abstract

Abstract: We study the relation between the linear programming relaxation of two classes of models for the Steiner tree problem with hop constraints. One class is characterized by having hop‐indexed arc variables. Although such models have proved to have a very strong linear programming bound, they are not easy to use because of the huge number of variables. This has motivated some studies with models involving fewer variables that use, instead of the hop‐indexed arc variables, hop‐indexed node variables. In this article, we contextualize the linear programming relaxation of these node‐based models in terms of the linear programming relaxation of known arc‐based models. We show that the linear programming relaxation of a general node‐based model is implied by the linear programming relaxation of a straightforward arc‐based model.