# Approximating Rectangles by Juntas and Weakly-Exponential Lower Bounds for LP Relaxations of CSPs

arXiv: https://arxiv.org/abs/1610.02704 · HTML: https://mlsanity.com/paper/1610.02704/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2016.

## Built on by (most cited first, 1 of 1)

- [On Differential Privacy and Adaptive Data Analysis with Bounded Space](https://mlsanity.com/paper/2302.05707/) (2023)

## Abstract (arXiv)

We show that for constraint satisfaction problems (CSPs), sub-exponential size linear programming relaxations are as powerful as nOmega(1)-rounds of the Sherali-Adams linear programming hierarchy. As a corollary, we obtain sub-exponential size lower bounds for linear programming relaxations that beat random guessing for many CSPs such as MAX-CUT and MAX-3SAT. This is a nearly-exponential improvement over previous results, previously, it was only known that linear programs of size no(log n) cannot beat random guessing for any CSP (Chan-Lee-Raghavendra-Steurer 2013). Our bounds are obtained by exploiting and extending the recent progress in communication complexity for "lifting" query lower bounds to communication problems. The main ingredient in our results is a new structural result on "high-entropy rectangles" that may of independent interest in communication complexity.