## On Linear-Time Deterministic Algorithms for Optimization Problems in Fixed Dimension (1992)

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by
Bernard Chazelle
,
Jiri Matousek

Citations: | 91 - 10 self |

### BibTeX

@MISC{Chazelle92onlinear-time,

author = {Bernard Chazelle and Jiri Matousek},

title = {On Linear-Time Deterministic Algorithms for Optimization Problems in Fixed Dimension },

year = {1992}

}

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### Abstract

We show that with recently developed derandomization techniques, one can convert Clarkson's randomized algorithm for linear programming in fixed dimension into a lineartime deterministic one. The constant of proportionality is d O(d) , which is better than for previously known such algorithms. We show that the algorithm works in a fairly general abstract setting, which allows us to solve various other problems (such as finding the maximum volume ellipsoid inscribed into the intersection of n halfspaces) in linear time.