{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T17:09:28Z","timestamp":1791306568001,"version":"4.3.1"},"reference-count":9,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8806,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1982,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The following problem is considered: Given an integer <jats:italic>K<\/jats:italic>, a graph <jats:italic>G<\/jats:italic> with two distinct vertices <jats:italic>s<\/jats:italic> and <jats:italic>t<\/jats:italic>, find the maximum number of disjoint paths of length <jats:italic>K<\/jats:italic> from <jats:italic>s<\/jats:italic> to <jats:italic>t<\/jats:italic>. The problem has several variants: the paths may be vertex\u2010disjoint or edge\u2010disjoint, the lengths of the paths may be equal to <jats:italic>K<\/jats:italic> or bounded by <jats:italic>K<\/jats:italic>, the graph may be undirected or directed. It is shown that except for small values of <jats:italic>K<\/jats:italic> all the problems are NP\u2010complete. Assuming <jats:italic>P<\/jats:italic> \u2260 NP, for each problem, the largest value of <jats:italic>K<\/jats:italic> for which the problem is not NP\u2010complete is found. Whenever a polynomial algorithm exists, an efficient algorithm is described.<\/jats:p>","DOI":"10.1002\/net.3230120306","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T13:25:25Z","timestamp":1178889925000},"page":"277-286","source":"Crossref","is-referenced-by-count":127,"title":["The complexity of finding maximum disjoint paths with length constraints"],"prefix":"10.1002","volume":"12","author":[{"given":"A.","family":"Itai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Y.","family":"Perl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Y.","family":"Shiloach","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"S. A.Cook The complexity of theorem proving procedures. Proc. 3rd Annual ACM Symposium on Theory of Computing (1971)151\u2013185.","DOI":"10.1145\/800157.805047"},{"key":"e_1_2_1_3_2","first-page":"1277","article-title":"Algorithm for solution of a problem of maximum flow in a network with power estimation","volume":"11","author":"Dinic E. A.","year":"1970","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_4_2","volume-title":"Algorithmic Combinatorics","author":"Even S.","year":"1973"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"S.EvenandO.Kariv \u201cAnO(n2.5) algorithm for maximum matching in a general graphs. Proceedings of the 16th Annual Symposium on Foundations of Computer Science Berkeley\u201d (1975)100\u2013102.","DOI":"10.1109\/SFCS.1975.5"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0204043"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/321941.321942"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-2001-2_9"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"S.MicaliandV. V.Vazirani An O(|v||e|) algorithm for finding maximum matching in general graphs. 21st Foundation of Computer Science October1980.","DOI":"10.1109\/SFCS.1980.12"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230040204"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230120306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230120306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T13:19:42Z","timestamp":1699795182000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230120306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,9]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1982,9]]}},"alternative-id":["10.1002\/net.3230120306"],"URL":"https:\/\/doi.org\/10.1002\/net.3230120306","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,9]]}}}