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The use of all nodes is not mandatory and each connection between the root and a terminal aims to satisfy the quality of service according to the limits established for each metric. The objective is to maximize the number of serviced terminals according to the network's quality of service metrics. We present an integer programming formulation and four Lagrangian relaxations, to obtain good primal and dual bounds. We also develop a local search applied during the resolution of the Lagrangian relaxations. These methodologies were subjected to computational experiments with a set of 40 instances generated with characteristics of vehicular ad hoc networks. Statistical analyses were performed to compare the performance between methodologies, where the model achieved optimal values for 29 instances, and the Lagrangian relaxations rendered competitive bounds, especially for large\u00a0instances.<\/jats:p>","DOI":"10.1111\/itor.13200","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T09:29:46Z","timestamp":1660123786000},"page":"140-166","update-policy":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lagrangian relaxation for maximum service in multicast routing with QoS constraints"],"prefix":"10.1111","volume":"31","author":[{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0001-7331-9782","authenticated-orcid":false,"given":"Carlos Victor Dantas","family":"Ara\u00fajo","sequence":"first","affiliation":[{"name":"Department of Computer Theory Institute of Computing University of Campinas  Campinas 13083\u2010852 Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-5945-0845","authenticated-orcid":false,"given":"Cid Carvalho","family":"de Souza","sequence":"additional","affiliation":[{"name":"Department of Computer Theory Institute of Computing University of Campinas  Campinas 13083\u2010852 Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/orcid.org\/0000-0002-8972-080X","authenticated-orcid":false,"given":"F\u00e1bio Luiz","family":"Usberti","sequence":"additional","affiliation":[{"name":"Department of Computer Theory Institute of Computing University of Campinas  Campinas 13083\u2010852 Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,8,10]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnca.2012.01.023"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysarc.2013.04.004"},{"key":"e_1_2_10_4_1","first-page":"1","article-title":"Statistical comparisons of classifiers over multiple data sets","volume":"7","author":"Dem\u0161ar J.","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/598675"},{"volume-title":"Computers and Intractability; A Guide to the Theory of NP\u2010Completeness","year":"1990","author":"Garey M.R.","key":"e_1_2_10_6_1"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/MPRV.2008.80"},{"key":"e_1_2_10_8_1","first-page":"33","volume-title":"Column Generation","author":"Irnich S.","year":"2006"},{"issue":"1","key":"e_1_2_10_9_1","first-page":"364","article-title":"Vanet: superior system for content distribution in vehicular network applications","volume":"1","author":"Karim R.","year":"2008","journal-title":"Technical Report"},{"issue":"1","key":"e_1_2_10_10_1","first-page":"110","article-title":"Evaluation of intelligent transport system in road safety","volume":"1","author":"Khorasani G.","year":"2013","journal-title":"International Journal of Chemical, Environmental & Biological Sciences"},{"key":"e_1_2_10_11_1","unstructured":"Libraries B.C. 29\/20\/2020.Boost c++$++$libraries. 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