Sparsification of Binary CSPs

Abstract

A cut ε-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 ε. Since their introduction by Benczúr 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.