{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T05:52:35Z","timestamp":1698213155282},"reference-count":7,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4485,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1994,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider a network on <jats:italic>n<\/jats:italic> + 1 vertices and two <jats:italic>s<\/jats:italic> \u2010 <jats:italic>t<\/jats:italic>\u2010flows <jats:italic>f<\/jats:italic> and <jats:italic>f<\/jats:italic> * of equal value. <jats:italic>f<\/jats:italic> * is called a <jats:italic>flow spanner<\/jats:italic> of <jats:italic>f<\/jats:italic> if <jats:italic>f<\/jats:italic> *(<jats:italic>e<\/jats:italic>) \u2a7d <jats:italic>f<\/jats:italic>(<jats:italic>e<\/jats:italic>) for every edge <jats:italic>e<\/jats:italic>. In this note, we prove that every integral flow <jats:italic>f<\/jats:italic> of value <jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>\u2010\u03b5 (0 \u2a7d \u03b5 \u2a7d 2) has a flow spanner <jats:italic>f<\/jats:italic> * that uses at most <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>\u2010\u03b5\/2) many edges. A sequence of examples shows that this result is asymptotically optimal. \u00a9 1994 by John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/net.3230240409","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T18:21:57Z","timestamp":1178994117000},"page":"263-266","source":"Crossref","is-referenced-by-count":0,"title":["Note: Small integral flows need only sparse networks"],"prefix":"10.1002","volume":"24","author":[{"given":"Ingo","family":"Alth\u00f6fer","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":"10.1007\/BF02189308"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/4221.4227"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"L. P.Chew There is a planar graph almost as good as the complete graph. Proceedings of the 2nd ACM Symposium on Computational Geometry (1986)169\u2013177.","DOI":"10.1145\/10515.10534"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130114"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"D.PelegandE.Upfal A tradeoff between space and efficiency for routing tables.Proceedings of the 20th Symposium on Theory of Computing(1988)43\u201352.","DOI":"10.1145\/62212.62217"},{"key":"e_1_2_1_7_2","unstructured":"J.Soares Graph spanners: A survey. Preprint (1992)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","unstructured":"R. E.Tarjan Data structures and network algorithms. SIAM Philadelphia PA (1983).","DOI":"10.1137\/1.9781611970265"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230240409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230240409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T04:09:37Z","timestamp":1698120577000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230240409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,7]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,7]]}},"alternative-id":["10.1002\/net.3230240409"],"URL":"https:\/\/doi.org\/10.1002\/net.3230240409","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,7]]}}}