A linear algorithm for computing convex hulls for random lines

Daniel Berend, Vladimir Braverman

Research output: Contribution to journalArticlepeer-review


Finding the convex hull of n points in the plane requires O(n log n) time in general. In Devroye and Toussaint [1993] and Golin et al. [2002] the problem of computing the convex hull of the intersection points of n lineswas considered, where the lines are chosen randomly according to two various models. In both models, linear-time algorithms were developed. Here we improve the results of Devroye and Toussaint [1993] by giving a universal algorithm for a wider range of distributions.

Original languageEnglish
Article number42
JournalACM Transactions on Algorithms
Issue number4
StatePublished - 1 Oct 2009


  • Computational complexity
  • Computational geometry
  • Convex hull
  • Random lines
  • Randomized algorithms

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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