Extension Complexity of Independent Set Polytopes
Abstract
We exhibit an $n$-node graph whose independent set polytope requires extended formulations of size exponential in $\Omega(n/\log n)$. Previously, no explicit examples of $n$-dimensional $0/1$-polytopes were known with extension complexity larger than exponential in $\Theta(\sqrt{n})$. Our construction is inspired by a relatively little-known connection between extended formulations and (monotone) circuit depth.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2016
- DOI:
- 10.48550/arXiv.1604.07062
- arXiv:
- arXiv:1604.07062
- Bibcode:
- 2016arXiv160407062G
- Keywords:
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- Computer Science - Computational Complexity;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics