{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T06:10:54Z","timestamp":1697955054329},"reference-count":10,"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":6798,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1988,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we study the probabilistic behavior of the farthest neighbor heuristic for finding the longest Hamiltonian tour in a graph. We assume the edge weights are independent random variables uniformly distributed in [0,1]. If F, is the length of the heuristic tour and L, the optimal tour then F<jats:sub>n<\/jats:sub>\/L<jats:sub>n<\/jats:sub> \u2192 1 a.s. as n \u2192 \u03b1. We also show that L<jats:sub>n<\/jats:sub>\/n \u2192 1 a.s. as n \u2192 \u221e.<\/jats:p>","DOI":"10.1002\/net.3230180103","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T22:51:38Z","timestamp":1178923898000},"page":"13-18","source":"Crossref","is-referenced-by-count":1,"title":["Probabilistic analysis of the longest hamiltonian tour problem"],"prefix":"10.1002","volume":"18","author":[{"given":"Rakesh V.","family":"Vohra","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728174"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.27.4.799"},{"key":"e_1_2_1_4_2","unstructured":"A. M.Frieze Worst case analysis of algorithms for travelling salesman problems. Technical Report Department of Computer Science Queen Mary College London (1978)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.10.5.647"},{"key":"e_1_2_1_6_2","volume-title":"Introduction to Mathematical Statistics","author":"Hogg R. V.","year":"1978"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1975.151"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0210024"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1956.10501314"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/0209041"},{"key":"e_1_2_1_11_2","unstructured":"R.VohraandD.Foster A probabalistic analysis of the K\u2010Location problem.Working paper Ohio State University(1986)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230180103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230180103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T20:16:42Z","timestamp":1697919402000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230180103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1988,3]]}},"alternative-id":["10.1002\/net.3230180103"],"URL":"https:\/\/doi.org\/10.1002\/net.3230180103","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,3]]}}}