{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:25:14Z","timestamp":1787340314739,"version":"build-2736575974"},"reference-count":3,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1981,5]]},"abstract":"<jats:p>Consider the implementation of two stacks by letting them grow towards each other in a table of size m. Suppose a random sequence of insertions and deletions is executed, with each instruction having a fixed probability $p(0 &lt; p &lt; \\frac{1}{2})$ to be a deletion. Let $A_p (m)$ denote the expected value of $\\max \\{ x,y\\} $, where x and y are the stack heights when the table first becomes full. We shall prove that, as $m \\to \\infty $, $A_p (m) = m\/2 + \\sqrt{m\/(2\\pi (1 - 2p))} + O((\\log m)^2 \/\\sqrt m )$. This gives a solution to an open problem in Knuth [The Art of Computer Programming, Vol. 1, Exercise 2.2.2-13].<\/jats:p>","DOI":"10.1137\/0210029","type":"journal-article","created":{"date-parts":[[2005,2,24]],"date-time":"2005-02-24T06:24:20Z","timestamp":1109226260000},"page":"398-403","source":"Crossref","is-referenced-by-count":26,"title":["An Analysis of a Memory Allocation Scheme for Implementing Stacks"],"prefix":"10.1137","volume":"10","author":[{"given":"Andrew C.","family":"Yao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,2]]},"reference":[{"key":"R1","volume-title":"An introduction to probability theory and its applications. Vol. I","author":"Feller William","year":"1968"},{"key":"R2","volume-title":"The art of computer programming, vol. 1","author":"Knuth Donald E.","year":"1975"},{"key":"R3","volume-title":"Foundations of probability","author":"R\u00e9nyi Alfr\u00e9d","year":"1970"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0210029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:36Z","timestamp":1787336976000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0210029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,5]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1981,5]]}},"alternative-id":["10.1137\/0210029"],"URL":"https:\/\/doi.org\/10.1137\/0210029","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1981,5]]}}}