{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T22:57:56Z","timestamp":1769813876315,"version":"3.49.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2011,10,5]],"date-time":"2011-10-05T00:00:00Z","timestamp":1317772800000},"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":[[2011,11]]},"abstract":"<jats:p>We consider the problem of selecting sequentially a <jats:italic>unimodal subsequence<\/jats:italic> from a sequence of independent identically distributed random variables, and we find that a person doing optimal sequential selection does so within a factor of the square root of two as well as a prophet who knows all of the random observations in advance of any selections. Our analysis applies in fact to selections of subsequences that have <jats:italic>d<\/jats:italic>+1 monotone blocks, and, by including the case <jats:italic>d<\/jats:italic>=0, our analysis also covers monotone subsequences.<\/jats:p>","DOI":"10.1017\/s0963548311000411","type":"journal-article","created":{"date-parts":[[2011,10,5]],"date-time":"2011-10-05T09:03:59Z","timestamp":1317805439000},"page":"799-814","source":"Crossref","is-referenced-by-count":9,"title":["Optimal Sequential Selection of a Unimodal Subsequence of a Random Sequence"],"prefix":"10.1017","volume":"20","author":[{"given":"ALESSANDRO","family":"ARLOTTO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. MICHAEL","family":"STEELE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,10,5]]},"reference":[{"key":"S0963548311000411_ref7","doi-asserted-by":"crossref","first-page":"612","DOI":"10.2307\/1427625","article-title":"\u2018Wald's lemma\u2019 for sums of order statistics of i.i.d. random variables","volume":"23","author":"Bruss","year":"1991","journal-title":"Adv. Appl. Probab."},{"key":"S0963548311000411_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(80)90021-7"},{"key":"S0963548311000411_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177005586"},{"key":"S0963548311000411_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(01)00122-3"},{"key":"S0963548311000411_ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-99-00307-0"},{"key":"S0963548311000411_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200042856"},{"key":"S0963548311000411_ref9","first-page":"463","article-title":"A combinatorial problem in geometry","volume":"2","author":"Erd\u0151s","year":"1935","journal-title":"Compositio Math."},{"key":"S0963548311000411_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90168-0"},{"key":"S0963548311000411_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2004.09.002"},{"key":"S0963548311000411_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662034.014"},{"key":"S0963548311000411_ref11","unstructured":"[11] Lugosi G. (2009) Concentration-of-measure inequalities. www.econ.upf.edu\/~lugosi\/anu.pdf."},{"key":"S0963548311000411_ref2","volume-title":"Stochastic Optimal Control: The Discrete Time Case","author":"Bertsekas","year":"1978"},{"key":"S0963548311000411_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994265"},{"key":"S0963548311000411_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200017873"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T03:40:52Z","timestamp":1556336452000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000411\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,5]]},"references-count":14,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["S0963548311000411"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000411","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,5]]}}}