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arXiv · 1312.7061

The accessibility of convex bodies and derandomization of the hit and run algorithm

Benoit Collins·Termeh Kousha·Rafał Kulik·Tomasz Szarek·Karol Życzkowski
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Abstract

We introduce the concept of accessibility and prove that any convex body $X$ in $\mathbb R^d$ is accessible with relevant constants depending on $d$ only. This property leads to a new algorithm which may be considered as a natural derandomization of the hit and run algorithm applied to generate a sequence of random points covering $X$ uniformly. We prove stability of the Markov chain generated by the proposed algorithm and provide its rate of convergence.

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Benoit Collins, Termeh Kousha, Rafał Kulik, Tomasz Szarek, Karol Życzkowski. 2013-12-26. The accessibility of convex bodies and derandomization of the hit and run algorithm. https://arxiv.org/abs/1312.7061

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