Abstract

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 isdO(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 ofnpoints and finding the maximum volume ellipsoid in the intersection ofnhalfspaces.

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