{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T07:58:39Z","timestamp":1709625519653},"reference-count":14,"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":9445,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1980,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A recursive algorithm is developed for finding the probability that not all nodes are connected in a graph with arcs that can fail. The number of multiplications required by the algorithm when applied to a complete graph on <jats:italic>n<\/jats:italic> nodes is shown to be of order 3<jats:sup><jats:italic>n<\/jats:italic>\u20101<\/jats:sup>, substantially less than other published algorithms. Further, it is shown that the algorithm enables other reliability measures related to the connection of nodes in a graph to be determined with minimal extra multiplications. The algorithm can also form the basis of methods for calculating the reliability measures of graphs with unreliable nodes and unreliable arcs. The complexity is then at worst 4<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> and, in most cases, of order 3<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup>.<\/jats:p>","DOI":"10.1002\/net.3230100404","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T11:45:00Z","timestamp":1178883900000},"page":"311-327","source":"Crossref","is-referenced-by-count":44,"title":["A recursive algorithm for finding reliability measures related to the connection of nodes in a graph"],"prefix":"10.1002","volume":"10","author":[{"given":"J. A.","family":"Buzacott","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"M. O.Ball \u201cNetwork Reliability Analysis: Algorithms and Complexity \u201dPh.D. thesis Cornell University January1977."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70726-X"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.27.4.823"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.4.2.132"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/1267324"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1970.5216433"},{"key":"e_1_2_1_8_2","unstructured":"J. A.Buzacott \u201cA Recursive Algorithm for Finding the Probability that a Graph is Disconnected \u201dWorking Paper No. 76\u2013016 Department of Industrial Engineering University of Toronto August1976."},{"key":"e_1_2_1_9_2","unstructured":"J. A.Buzacott andS. K.Chang \u201cPartitions and Partitioning\u2010Decomposition for Network Reliability Analysis \u201dWorking Paper No. 79\u2010017 Department of Industrial Engineering University of Toronto July 1979."},{"key":"e_1_2_1_10_2","unstructured":"L.Fratta andU.Montanari \u201cDecomposition Techniques for Evaluating Network Reliability \u201d IBM Research Report RC\u20105923 (#25618) 3\/26\/76 IBM Thomas J. Watson Research Center Yorktown Heights NY."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177706098"},{"key":"e_1_2_1_12_2","unstructured":"T. D.Murchland andD. R.Shier \u201cCalculating the Probability that an Unreliable Graph is Disconnected \u201d unpublished report TDM\u2010186 1973:S:21 Planning and Transport Research and Computation London England 1973."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0132031"},{"key":"e_1_2_1_14_2","unstructured":"N.Spyratos \u201cDecomposition Techniques for Computing Reliability Measures in Large Systems \u201dPh.D. thesis Department of Systems Engineering Carleton University 1975."},{"key":"e_1_2_1_15_2","first-page":"619","volume-title":"Reliability and Fault Tree Analysis","author":"Van Slyke R. M.","year":"1975"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230100404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230100404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T07:25:26Z","timestamp":1697700326000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230100404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1980,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1980,12]]}},"alternative-id":["10.1002\/net.3230100404"],"URL":"https:\/\/doi.org\/10.1002\/net.3230100404","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1980,12]]}}}