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The goal is to design an algorithm for these inputs so that eventually the expected running time will be optimal for the input distribution $\\mathcal{D}=\\prod_i\\mathcal{D}_i$. We give such self-improving algorithms for two problems: (i) sorting a sequence of numbers and (ii) computing the Delaunay triangulation of a planar point set. Both algorithms achieve optimal expected limiting complexity. The algorithms begin with a training phase during which they collect information about the input distribution, followed by a stationary regime in which the algorithms settle to their optimized incarnations.<\/jats:p>","DOI":"10.1137\/090766437","type":"journal-article","created":{"date-parts":[[2011,4,6]],"date-time":"2011-04-06T15:08:56Z","timestamp":1302102536000},"page":"350-375","source":"Crossref","is-referenced-by-count":19,"title":["Self-Improving Algorithms"],"prefix":"10.1137","volume":"40","author":[{"given":"Nir","family":"Ailon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernard","family":"Chazelle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenneth L.","family":"Clarkson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ding","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Mulzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Seshadhri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2011,4,5]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"P. 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