{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:28Z","timestamp":1740144508581,"version":"3.37.3"},"reference-count":13,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2020,2,21]]},"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p>We present three different mixed integer linear models with a polynomial number of variables and constraints for the Steiner tree problem in graphs. The linear relaxations of these models are compared to show that a good (strong) linear relaxation can be a good approximation for the problem. We present computational results for the STP OR-Library (J.E. Beasley) instances of type <jats:italic>b<\/jats:italic>, <jats:italic>c<\/jats:italic>, <jats:italic>d<\/jats:italic> and <jats:italic>e<\/jats:italic>.<\/jats:p>","DOI":"10.1051\/ro\/2020023","type":"journal-article","created":{"date-parts":[[2020,2,25]],"date-time":"2020-02-25T08:56:47Z","timestamp":1582621007000},"page":"S343-S350","source":"Crossref","is-referenced-by-count":1,"special_numbering":"Supplement","title":["Using multiflow formulations to solve the Steiner tree problem in graphs"],"prefix":"10.1051","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8175-8320","authenticated-orcid":false,"given":"Laura","family":"Bahiense","sequence":"first","affiliation":[]},{"given":"Arthur","family":"Besso","sequence":"additional","affiliation":[]},{"given":"Rogerio","family":"Tostas","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3897-3356","authenticated-orcid":false,"given":"Nelson","family":"Maculan","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s10107-002-0357-3","volume":"94","author":"Bahiense","year":"2002","journal-title":"Math. 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In: Publication 315, Centre de Recherche sur les Transports, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al (1983).","key":"R5"},{"key":"R6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/net.3230230104","volume":"23","author":"Goemans","year":"1993","journal-title":"Networks"},{"unstructured":"Hwang F.K., Richards D.S. and Winter P., The Steiner tree problem. In: Vol. 53 of Annals of Discrete Mathematics. North-Holland, Amsterdam (1992).","key":"R7"},{"unstructured":"Karp R.M., Reducibility among combinatorial problems, edited by Miller R.E., Thatcher J.W. and Bohlinger J.D.. In: Complexity of Computer Computations. The IBM Research Symposia Series. Springer, New York, NY (1972) 85\u2013103.","key":"R8"},{"key":"R9","first-page":"185","volume":"31","author":"Maculan","year":"1987","journal-title":"Ann. Discrete Math."},{"key":"R10","first-page":"109","volume":"7","author":"Maculan","year":"1988","journal-title":"Comput. Appl. 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