Sketching and streaming algorithms are in the forefront of current research
directions for cut problems in graphs. In the streaming model, we show that
(1−ϵ)-approximation for Max-Cut must use n1−O(ϵ) space;
moreover, beating 4/5-approximation requires polynomial space. For the
sketching model, we show that r-uniform hypergraphs admit a
(1+ϵ)-cut-sparsifier (i.e., a weighted subhypergraph that
approximately preserves all the cuts) with O(ϵ−2n(r+logn))
edges. We also make first steps towards sketching general CSPs (Constraint
Satisfaction Problems)