{"title":"Linear programming and convex hulls made easy","authors":"R. Seidel","doi":"10.1145/98524.98570","DOIUrl":null,"url":null,"abstract":"We present two randomized algorithms. One solves linear programs involving <italic>m</italic> constraints in <italic>d</italic> variables in expected time <italic>&Ogr;</italic>(<italic>m</italic>). The other constructs convex hulls of <italic>n</italic> points in R<italic><supscrpt>d</supscrpt>, d</italic> > 3, in expected time <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>⌈<italic>d</italic>/2⌉</supscrpt>). In both bounds <italic>d</italic> is considered to be a constant. In the linear programming algorithm the dependence of the time bound on <italic>d</italic> is of the form <italic>d</italic>!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.","PeriodicalId":113850,"journal":{"name":"SCG '90","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"206","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SCG '90","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/98524.98570","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 206
Abstract
We present two randomized algorithms. One solves linear programs involving m constraints in d variables in expected time &Ogr;(m). The other constructs convex hulls of n points in Rd, d > 3, in expected time &Ogr;(n⌈d/2⌉). In both bounds d is considered to be a constant. In the linear programming algorithm the dependence of the time bound on d is of the form d!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses.
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