{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,8]],"date-time":"2023-10-08T06:43:34Z","timestamp":1696747414602},"reference-count":5,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8167,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1984,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article presents two sorting procedures with computational complexity <jats:italic>O<\/jats:italic>(nk<jats:sup>2<\/jats:sup> log(<jats:italic>k<\/jats:italic>)) and <jats:italic>O<\/jats:italic>(<jats:italic>nk<\/jats:italic><jats:sup>2<\/jats:sup>) to perform the generalized vector product <jats:italic>A<\/jats:italic> <jats:sub>1<\/jats:sub>\u2297 <jats:italic>A<\/jats:italic><jats:sub>2<\/jats:sub>\u2297 \u20db \u2297 <jats:italic>A<\/jats:italic><jats:sub>n<\/jats:sub>, where each vector <jats:italic>A<\/jats:italic><jats:sub>i<\/jats:sub> has <jats:italic>k<\/jats:italic> distinct elements arranged in strictly increasing order. The vector product identifies the <jats:italic>k<\/jats:italic> minimal sums, each sum being defined as having one addend from each vector.<\/jats:p>","DOI":"10.1002\/net.3230140207","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T18:18:21Z","timestamp":1178907501000},"page":"269-273","source":"Crossref","is-referenced-by-count":0,"title":["Sorting algorithms for the implementation of a generalized vector product"],"prefix":"10.1002","volume":"14","author":[{"given":"Alberto","family":"Garcia\u2010Diaz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donald K.","family":"Friesen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donald J.","family":"Bagert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho A. V.","year":"1974"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"L. H.Harper T. H.Payne J. E.Savage andE.Straus Sorting X+Y.Comm. ACM(1975)347\u2013349.","DOI":"10.1145\/360825.360869"},{"key":"e_1_2_1_4_2","volume-title":"Optimization Algorithms for Networks and Graphs","author":"Minieka E.","year":"1978"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"E.MiniekaandD.Shier A note on an algebra for theKbest routes in a network.J. Inst. Math. Appl.(1973)145\u2013149.","DOI":"10.1093\/imamat\/11.2.145"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230060303"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230140207","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230140207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,7]],"date-time":"2023-10-07T11:59:07Z","timestamp":1696679947000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230140207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1984,6]]}},"alternative-id":["10.1002\/net.3230140207"],"URL":"https:\/\/doi.org\/10.1002\/net.3230140207","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,6]]}}}