{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T14:46:59Z","timestamp":1791038819610,"version":"4.1.0"},"reference-count":12,"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":7984,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1984,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the following problem: Given an integer <jats:italic>k<\/jats:italic> and a network <jats:italic>G<\/jats:italic> with two distinct vertices <jats:italic>s<\/jats:italic> and <jats:italic>t<\/jats:italic>, find a maximum number of vertex disjoint paths from <jats:italic>s<\/jats:italic> to <jats:italic>t<\/jats:italic> of length bounded by <jats:italic>k<\/jats:italic>. In a recent work [9] it was shown that for length greater than four this problem is <jats:italic>NP<\/jats:italic>\u2010hard. In this paper we present a polynomial heuristic algorithm for the problem for general length. The algorithm is proved to give optimal solution for length less than five. Experiments show very good results for the algorithm.<\/jats:p>","DOI":"10.1002\/net.3230140405","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T18:47:03Z","timestamp":1178909223000},"page":"531-544","source":"Crossref","is-referenced-by-count":24,"title":["Heuristics for finding a maximum number of disjoint bounded paths"],"prefix":"10.1002","volume":"14","author":[{"given":"D.","family":"Ronen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Y.","family":"Perl","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","unstructured":"B. V.Cherkasky Algorithm for construction of maximal flow in networks with complexity ofO(V2E1\/2) operations.Math. Methods of Solution of Economical Problems(1977)117\u2013125(in Russian)."},{"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 estimations","volume":"11","author":"Dinic E. A.","year":"1970","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_4_2","first-page":"233","volume-title":"Information Technology","author":"Even S.","year":"1978"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0204043"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207176708921826"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"Z.Galil A new algorithm for the maximal flow problem.Proc. 19th Symp. on Foundations of Computer Science(1978)231\u2013245.","DOI":"10.1109\/SFCS.1978.5"},{"key":"e_1_2_1_8_2","volume-title":"Computers and Intractability: A Guide to the Theory of NP\u2010Completeness","author":"Garry M. R.","year":"1979"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"Z.GalilandA.Naamad Network flow and generalized path compression.Proc. 11th Annual ACM Symp. on Theory of Computing(1979)13\u201326.","DOI":"10.1145\/800135.804394"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230120306"},{"key":"e_1_2_1_11_2","first-page":"434","article-title":"Determining the maximal flow in a network by the method of preflows","volume":"15","author":"Karzanov A. V.","year":"1974","journal-title":"Soviet Math. Dokl."},{"key":"e_1_2_1_12_2","unstructured":"D.Ronen A heuristic algorithm for finding a maximum number of disjoint bounded paths in a network M.Sc. thesis Department of Mathematics and Computer Science Bar\u2010IIan Univ. 1981."},{"key":"e_1_2_1_13_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.3230140405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230140405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T15:57:55Z","timestamp":1697817475000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230140405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1984,12]]}},"alternative-id":["10.1002\/net.3230140405"],"URL":"https:\/\/doi.org\/10.1002\/net.3230140405","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,12]]}}}