... $S_\mathrm{\scriptscriptstyle mar}'\subseteq S_\mathrm{\scriptscriptstyle sep}$¹

In the rest of this article we will use the symbol $S_\mathrm{\scriptscriptstyle mar}'$ to indicate an earlier computed bound over $S_\mathrm{\scriptscriptstyle mar}'$ with $S_\mathrm{\scriptscriptstyle mar}'\subseteq S_\mathrm{\scriptscriptstyle sep}$.

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... seconds²

We used a computer with a 1 GHz Athlon processor.

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... network³

The data can be downloaded from the Bayesian Network Repository at
http://www.cs.huji.ac.il/labs/compbio/Repository/

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... $\Omega\left(25,000\right)$⁴

We started with $\Omega\left(100\right)$ and gradually increased this value up to 25,000. The bounds obtained with small clusters are used as good starting points for the more time consuming larger clusters.

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