Computing the Grothendieck constant of some graph classes
Given a graph $G=([n],E)$ and $w\in\R^E$, consider the integer program ${\max}_{x\in \{\pm 1\}^n} \sum_{ij \in E} w_{ij}x_ix_j$ and its canonical semidefinite programming relaxation ${\max} \sum_{ij \in E} w_{ij}v_i^Tv_j$, where the maximum is taken over all unit vectors $v_i\in\R^n$. The integrality gap of this relaxation is known as the Grothendieck constant $\ka(G)$ of $G$. We present … Read more