{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T17:39:25Z","timestamp":1648834765358},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p> The Knapsack Node Weighted Steiner Tree Problem (KNWSTP) is a generalization of the Steiner Tree Problem on graphs, which takes into account the classical cost function defined on the edges, as well as a prize function defined on the vertices and a limit on the size of the solution. It has several applications to network design. We propose an exact branch-and-bound algorithm for this problem, based on a relax-and-cut approach: the algorithm relaxes an exponential family of generalized subtour elimination constraints and takes into account only the violated ones as the computation proceeds. The performance of the algorithm has been tested on a wide set of benchmark problems, up to three hundred vertices, whose structure reflects the features of the most likely applications (sparse graphs with Euclidean costs) and covers different cases with respect to the prize function (only positive, or both positive and negative prizes) and the weight threshold. <\/jats:p>","DOI":"10.1142\/s0217595908001791","type":"journal-article","created":{"date-parts":[[2008,7,18]],"date-time":"2008-07-18T10:21:41Z","timestamp":1216376501000},"page":"373-391","source":"Crossref","is-referenced-by-count":1,"title":["A RELAX-AND-CUT ALGORITHM FOR THE KNAPSACK NODE WEIGHTED STEINER TREE PROBLEM"],"prefix":"10.1142","volume":"25","author":[{"given":"ROBERTO","family":"CORDONE","sequence":"first","affiliation":[{"name":"DTI \u2014 Universit\u00e0 degli Studi di Milano, via Bramante, 65, Crema, 26013, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARCO","family":"TRUBIAN","sequence":"additional","affiliation":[{"name":"DSI \u2014 Universit\u00e0 degli Studi di Milano, via Comelico 39\/41, Milano, 20135, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230190102"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0120697"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230170309"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0037(199801)31:1<11::AID-NET2>3.0.CO;2-N"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230240103"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6089-0"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793242618"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1287\/opre.13.3.462"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1287\/opre.18.6.1138"},{"key":"rf13","first-page":"155","volume":"7","author":"Jonsson O.","journal-title":"Asia-Pacific Journal of Operational Research"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1995.1029"},{"key":"rf15","first-page":"2","volume":"21","author":"Lucena A.","journal-title":"COAL Bulletin"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(03)00380-9"},{"key":"rf17","doi-asserted-by":"crossref","unstructured":"T. L.\u00a0Magnanti and L. A.\u00a0Wolsey, Network Models, Handbooks in Operations Research and Management Science\u00a07 (North-Holland, 1995)\u00a0pp. 503\u2013615.","DOI":"10.1016\/S0927-0507(05)80126-4"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230170102"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595908001791","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:01:21Z","timestamp":1565186481000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595908001791"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":15,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1142\/S0217595908001791"],"URL":"https:\/\/doi.org\/10.1142\/s0217595908001791","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}