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 littleknown connection between extended formulations and (monotone) circuit depth.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 DOI:
 10.48550/arXiv.1604.07062
 arXiv:
 arXiv:1604.07062
 Bibcode:
 2016arXiv160407062G
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics