A standard algorithm for finding vertex elimination orders, whose treewidth provides a good upper bound for the minimal treewidth of a graph, is known as the QuickBB algorithm. It was first proposed by Vibhav Gogate and Rina Dechter in their 2004 paper "A complete Anytime Algorithm for Treewidth". The paper along with a binary implementation of the algorithm is provided here. Here we provide a julia wrapper for their binary which requires a linux OS.
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brenjohn/QuickBB.jl
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