On Linear-Time Deterministic Algorithms for Optimization Problems in Fixed Dimension

Bernard Chazelle, Jiří Matoušek

Research output: Contribution to journalArticlepeer-review

126 Scopus citations


We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a linear-time deterministic algorithm. The constant of proportionality is dO(d), which is better than those for previously known algorithms. We show that the algorithm works in a fairly general abstract setting, which allows us to solve various other problems, e.g., computing the minimum-volume ellipsoid enclosing a set of n points and finding the maximum volume ellipsoid in the intersection of n halfspaces.

Original languageEnglish (US)
Pages (from-to)579-597
Number of pages19
JournalJournal of Algorithms
Issue number3
StatePublished - Nov 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics


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