# Sparsification of Binary CSPs

## TL;DR

This paper extends the classification of which binary Boolean CSPs can be sparsified to binary CSPs over arbitrary finite domains, building on the concept of cut sparsifiers in graph theory.

## Contribution

It generalizes previous results from Boolean domains to arbitrary finite domains for binary CSPs, expanding the understanding of sparsifiability.

## Key findings

- Extended the classification of sparsifiable binary CSPs to arbitrary finite domains.
- Connected CSP sparsification to graph cut sparsifiers.
- Provided theoretical foundations for future sparsification algorithms.

## Abstract

A cut $\varepsilon$-sparsifier of a weighted graph $G$ is a re-weighted subgraph of $G$ of (quasi)linear size that preserves the size of all cuts up to a multiplicative factor of $\varepsilon$. Since their introduction by Bencz\'ur and Karger [STOC'96], cut sparsifiers have proved extremely influential and found various applications. Going beyond cut sparsifiers, Filtser and Krauthgamer [SIDMA'17] gave a precise classification of which binary Boolean CSPs are sparsifiable. In this paper, we extend their result to binary CSPs on arbitrary finite domains.