{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T11:11:05Z","timestamp":1724757065622},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,6,22]],"date-time":"2009-06-22T00:00:00Z","timestamp":1245628800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We consider the minimum-weight path between any pair of nodes of the <jats:italic>n<\/jats:italic>-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about \u03b1* log <jats:italic>n<\/jats:italic> edges, where \u03b1* \u2248 3.5911 is the unique solution of the equation \u03b1 log \u03b1 \u2212 \u03b1 = 1. This answers a question posed by Janson [8].<\/jats:p>","DOI":"10.1017\/s0963548309990204","type":"journal-article","created":{"date-parts":[[2009,6,22]],"date-time":"2009-06-22T10:02:07Z","timestamp":1245664927000},"page":"1-19","source":"Crossref","is-referenced-by-count":8,"title":["The Longest Minimum-Weight Path in a Complete Graph"],"prefix":"10.1017","volume":"19","author":[{"given":"LOUIGI","family":"ADDARIO-BERRY","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NICOLAS","family":"BROUTIN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G\u00c1BOR","family":"LUGOSI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,6,22]]},"reference":[{"key":"S0963548309990204_ref12","volume-title":"Empirical Processes with Applications to Statistics","author":"Shorack","year":"1986"},{"key":"S0963548309990204_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/0471722154"},{"key":"S0963548309990204_ref15","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20141"},{"key":"S0963548309990204_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/2308012"},{"key":"S0963548309990204_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548399003892"},{"key":"S0963548309990204_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5320-4"},{"key":"S0963548309990204_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240050207"},{"key":"S0963548309990204_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00265991"},{"key":"S0963548309990204_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03981-6"},{"key":"S0963548309990204_ref13","first-page":"1","article-title":"A survey of recursive trees","volume":"51","author":"Smythe","year":"1995","journal-title":"Theoret. Probab. Math. Statist."},{"key":"S0963548309990204_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548306007802"},{"key":"S0963548309990204_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01651330"},{"key":"S0963548309990204_ref11","volume-title":"Diffusions, Markov Processes, and Martingales","author":"Rogers","year":"2000"},{"key":"S0963548309990204_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100034241"},{"key":"S0963548309990204_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009176"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548309990204","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,28]],"date-time":"2019-04-28T21:04:31Z","timestamp":1556485471000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548309990204\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,22]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["S0963548309990204"],"URL":"https:\/\/doi.org\/10.1017\/s0963548309990204","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6,22]]}}}