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In this article, the authors propose a maximum flow algorithm based on flow matrix. The algorithm only requires the effort to reduce the capacity of the underutilized arcs to that of the respective flow. The optimality of the algorithm is proved by the max-flow min-cut theorem. The algorithm is table-based, thus avoiding augmenting path and residual network concepts. The authors used numerical examples and computational comparisons to demonstrate the efficiency of the algorithm. These examples and comparisons revealed that the proposed algorithm is capable of computing exact solutions while using few iterations as compared to some existing algorithms.<\/p>","DOI":"10.4018\/ijamc.322436","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T20:20:01Z","timestamp":1683318001000},"page":"1-16","source":"Crossref","is-referenced-by-count":1,"title":["Extreme Min \u2013 Cut Max \u2013 Flow Algorithm"],"prefix":"10.4018","volume":"14","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2665-9711","authenticated-orcid":true,"given":"Trust","family":"Tawanda","sequence":"first","affiliation":[{"name":"National University of Science and Technology, Zimbabwe"}]},{"given":"Philimon","family":"Nyamugure","sequence":"additional","affiliation":[{"name":"National University of Science and Technology, Zimbabwe"}]},{"given":"Elias","family":"Munapo","sequence":"additional","affiliation":[{"name":"North West University, South Africa"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9321-5622","authenticated-orcid":true,"given":"Santosh","family":"Kumar","sequence":"additional","affiliation":[{"name":"RMIT University, Australia"}]}],"member":"2432","reference":[{"key":"IJAMC.322436-0","first-page":"41","article-title":"An efficient algorithm for finding maximum flow in a network-flow.","volume":"19","author":"F.Ahmed","year":"2014","journal-title":"The Journal of Physiological Sciences; JPS"},{"key":"IJAMC.322436-1","doi-asserted-by":"publisher","DOI":"10.1007\/s12597-012-0106-1"},{"key":"IJAMC.322436-2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2022.04.012"},{"key":"IJAMC.322436-3","doi-asserted-by":"publisher","DOI":"10.2298\/YJOR220415038B"},{"key":"IJAMC.322436-4","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2004.60"},{"key":"IJAMC.322436-5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611977554.ch95"},{"issue":"2","key":"IJAMC.322436-6","first-page":"455","article-title":"Developing algorithm to obtain the maximum flow in a network flow problem.","volume":"11","author":"P.Dash","year":"2019","journal-title":"Journal of Advanced Research in Dynamic and Control Systems"},{"key":"IJAMC.322436-7","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/2349712"},{"key":"IJAMC.322436-8","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-023-05210-y"},{"issue":"9","key":"IJAMC.322436-9","first-page":"6595","article-title":"Fuzzy type-2 in shortest path and maximal flow problems.","volume":"13","author":"B. 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