Extension Complexity of Independent Set Polytopes

We exhibit an $n$-node graph whose independent set polytope requires extended formulations of size exponential in $Ω(n/\log n)$. Previously, no explicit examples of $n$-dimensional $0/1$-polytopes were known with extension complexity larger than exponential in $Θ(\sqrt{n})$. Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth.

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