Extension complexity of independent set polytopes

Abstract

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(n). Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth.

Publication Title

SIAM Journal on Computing

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