{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:31:34Z","timestamp":1787340694619,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1989,8]]},"abstract":"<jats:p>Let $P = ( &lt; _P ,Y)$ be a partial order on a set $Y = \\{ y_1 ,y_2 , \\cdots ,y_n \\} $ of n elements. The problem of P-production is as follows: Given an input of n distinct numbers $Y = x_1 ,x_2 , \\cdots ,x_n $, find a permutation $\\sigma $ of $(1,2, \\cdots ,n)$ such that $y_i &lt; _P y_j $ implies $x_{\\sigma (i)} &lt; x_{\\sigma (j)} $. Let $C(P),\\bar C(P)$ be, respectively, the minimum number and the minimum average number of binary comparisons $x_i :x_j $ needed by any decision-tree algorithm to produce P. It is proved that $C(P) = \\Theta (\\bar C(P))$. As an intermediate result, it is shown that $C(P) = O(\\log _2 ({{n!} \/ {\\mu (P)}}) + n)$, where $\\mu (P)$ is the number of permutations consistent with P, thus proving a conjecture of Saks.<\/jats:p>","DOI":"10.1137\/0218047","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:32:44Z","timestamp":1109226764000},"page":"679-689","source":"Crossref","is-referenced-by-count":8,"title":["On the Complexity of Partial Order Productions"],"prefix":"10.1137","volume":"18","author":[{"given":"Andrew Chi-Chih","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"RAB","volume-title":"Informantion theory and coding","author":"Abramson Norman","year":"1963"},{"key":"RAI","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90197-7"},{"key":"RBFPRT","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(73)80033-9"},{"key":"RD","doi-asserted-by":"publisher","DOI":"10.2307\/1969503"},{"key":"RFR","doi-asserted-by":"publisher","DOI":"10.1145\/360680.360691"},{"key":"RKN","volume-title":"The art of computer programming. Volume 3","author":"Knuth Donald E.","year":"1973"},{"key":"RSA","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5315-4_4"},{"key":"RSCH","volume-title":"Journ\u00e9es algorithmiques (\u00c9cole Norm. Sup., Paris, 1975)","author":"Sch\u00f6nhage A.","year":"1976"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0218047","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:44:27Z","timestamp":1787337867000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0218047"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,8]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1989,8]]}},"alternative-id":["10.1137\/0218047"],"URL":"https:\/\/doi.org\/10.1137\/0218047","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,8]]}}}