{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:43:46Z","timestamp":1747151026040,"version":"3.40.5"},"reference-count":16,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T00:00:00Z","timestamp":1639440000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Networks"],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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\u2010indexed 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\u2010indexed arc variables, hop\u2010indexed node variables. In this article, we contextualize the linear programming relaxation of these node\u2010based models in terms of the linear programming relaxation of known arc\u2010based models. We show that the linear programming relaxation of a general node\u2010based model is implied by the linear programming relaxation of a straightforward arc\u2010based model.<\/jats:p>","DOI":"10.1002\/net.22086","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T13:24:35Z","timestamp":1639488275000},"page":"178-192","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A comparison of node\u2010based and arc\u2010based hop\u2010indexed formulations for the Steiner tree problem with hop constraints"],"prefix":"10.1002","volume":"80","author":[{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-2355-8926","authenticated-orcid":false,"given":"Bernard","family":"Fortz","sequence":"first","affiliation":[{"name":"Computer Science Department Universit\u00e9 libre de Bruxelles (ULB)  Brussels Belgium"},{"name":"INOCS, INRIA Lille 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Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,12,14]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2015.05.009"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1110.0472"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/net.20274"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-30165-5_19"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2017.08.017"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(95)00090-9"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.10.2.180"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5087-7_2"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.11.029"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2018.09.007"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-009-0297-2"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2015.06.012"},{"key":"e_1_2_8_14_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1120.0500"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/net.21483"},{"key":"e_1_2_8_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-016-0102-1"},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018967121276"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.22086","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/net.22086","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.22086","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T23:37:36Z","timestamp":1692747456000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/net.22086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,14]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["10.1002\/net.22086"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/net.22086","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"type":"print","value":"0028-3045"},{"type":"electronic","value":"1097-0037"}],"subject":[],"published":{"date-parts":[[2021,12,14]]},"assertion":[{"value":"2021-10-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication 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