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Sketching Cuts in Graphs and Hypergraphs

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 n{1-O(ε)} space; moreover, beating 4/5-approximation requires polynomial space. For the sketching model, we show that every r-uniform hypergraph admits a (1+ ε)-cut-sparsifier (i.e., a weighted subhypergraph that approximately preserves all the cuts) with O(ε-2n(r+log n)) edges. We also make first steps towards sketching general CSPs (Constraint Satisfaction Problems).