Sparsification Of Binary Csps

A cut epsilon-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 epsilon. Since their introduction by Benczur 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.