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(√n). Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth.
Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Goos, M., Jain, R., & Watson, T. (2016). Extension Complexity of Independent Set Polytopes. Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2016-December, 565-572. https://doi.org/10.1109/FOCS.2016.67