{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,3]],"date-time":"2024-08-03T17:36:54Z","timestamp":1722706614529},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":6127,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1990,1]]},"abstract":"Abstract<\/jats:title>We consider the problem of covering a weighted graph G = (V, E<\/jats:italic>) by a set of vertex\u2010disjoint paths, such that the total weight of these paths is maximized. This problem is clearly NP\u2010complete, since it contains the Hamiltonian path problem as a special case. Three approximation algorithms for this problem are presented, exhibiting a complexity\u2010performance trade\u2010off. First, we develop an algorithm for covering undirected graphs. The time complexity of this algorithm is O<\/jats:italic>(|E<\/jats:italic>|log|E<\/jats:italic>|), and its performance\u2010ratio is \u00bd. Second, we present an algorithm for covering undirected graphs, whose performance\u2010ratio is \u2154. This algorithm uses a maximum weight matching algorithm as a subroutine, which dominates the overall complexity of our algorithm. Finally, we develop an algorithm for covering directed graphs, whose performanceratio is \u2154. This algorithm uses a maximum weight bipartite matching algorithm as a subroutine, which dominates the overall complexity of the algorithm.<\/jats:p>","DOI":"10.1002\/net.3230200106","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T08:19:24Z","timestamp":1178957964000},"page":"55-64","source":"Crossref","is-referenced-by-count":15,"title":["Approximation algorithms for covering a graph by vertex\u2010disjoint paths of maximum total weight"],"prefix":"10.1002","volume":"20","author":[{"given":"Shlomo","family":"Moran","sequence":"first","affiliation":[]},{"given":"Ilan","family":"Newman","sequence":"additional","affiliation":[]},{"given":"Yaron","family":"Wolfstahl","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"38","volume-title":"Problems easy for tree\u2010decomposable graphs. Proceedings of the 15th International Colloquium on Automata. Languages and Programming, July 1988, Tampere","author":"Arnborg S.","year":"1988"},{"key":"e_1_2_1_3_2","first-page":"201","volume-title":"On covering the points of a graph with point disjoint paths. Proceedings of the 1972 Capital Conference on Graph Theory and Combinatorics","author":"Boesch F. T.","year":"1974"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/322003.322005"},{"key":"e_1_2_1_5_2","first-page":"105","volume-title":"Dynamic programming on graphs with bounded treewidth. Proceedings of the 15th International Colloquium on Automata. Languages and Programming, July 1988, Tampere","author":"Bodlaender H. L.","year":"1988"},{"key":"e_1_2_1_6_2","first-page":"89","volume-title":"Combinatorial Structures and Their Applications","author":"Edmonds J.","year":"1969"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"H. N.Gabow Z.GalilandT. H.Spencer Efficient implementation of graph algorithms using contraction. Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science New York 1984 347\u2013357.","DOI":"10.1109\/SFCS.1984.715935"},{"key":"e_1_2_1_8_2","first-page":"136","volume-title":"Computers and Intractability: A Guide to the Theory of NP\u2010Completeness","author":"Garey M.","year":"1979"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0205049"},{"key":"e_1_2_1_10_2","article-title":"Optimal covering of cacti by vertex\u2010disjoint paths","author":"Moran S.","journal-title":"Theoretical Computer Science"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01408172"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(81)90009-0"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/6462.6502"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230200106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230200106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T09:27:58Z","timestamp":1697966878000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230200106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,1]]}},"alternative-id":["10.1002\/net.3230200106"],"URL":"https:\/\/doi.org\/10.1002\/net.3230200106","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,1]]}}}