{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T02:06:07Z","timestamp":1769825167838,"version":"3.49.0"},"reference-count":10,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":9628,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1980,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider a connected undirected graph <jats:italic>G[N; E<\/jats:italic>] with <jats:italic>N = S \u222a P<\/jats:italic>, the set of nodes, where <jats:italic>P<\/jats:italic> is designated as the set of Steiner points. A weight is associated with each edge <jats:italic>e<\/jats:italic><jats:sub>i<\/jats:sub> of the set <jats:italic>E<\/jats:italic>. The problem of obtaining a minimal weighted tree which spans the set <jats:italic>S<\/jats:italic> of nodes has been termed in literature as the Steiner problem in graphs. A specialized integer programming (set covering) formulation is presented for the problem. The number of constraints in this formulation grows exponentially with the size of the problem. A method called the row generation scheme is developed to solve the above problem. The method requires knowing the constraints only implicitly. Several other problems which can be put in a similar framework can also be handled by the above scheme. The generality of the scheme and its efficiency is discussed. Finally the computational result is demonstrated.<\/jats:p>","DOI":"10.1002\/net.3230100207","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T11:36:41Z","timestamp":1178883401000},"page":"167-178","source":"Crossref","is-referenced-by-count":105,"title":["An integer linear programming approach to the steiner problem in graphs"],"prefix":"10.1002","volume":"10","author":[{"given":"Y. P.","family":"Aneja","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1957.tb01515.x"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1956-0078686-7"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01949715"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230010302"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230010203"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.23.6.652"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.3.194"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.19.4.998"},{"key":"e_1_2_1_10_2","volume-title":"Integer Programming","author":"Garfinkel R. S.","year":"1972"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/0109047"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230100207","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230100207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:19:21Z","timestamp":1699787961000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230100207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1980,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1980,6]]}},"alternative-id":["10.1002\/net.3230100207"],"URL":"https:\/\/doi.org\/10.1002\/net.3230100207","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1980,6]]}}}