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 (1ϵ)(1-\epsilon)-approximation for Max-Cut must use n1O(ϵ)n^{1-O(\epsilon)} space; moreover, beating 4/54/5-approximation requires polynomial space. For the sketching model, we show that rr-uniform hypergraphs admit a (1+ϵ)(1+\epsilon)-cut-sparsifier (i.e., a weighted subhypergraph that approximately preserves all the cuts) with O(ϵ2n(r+logn))O(\epsilon^{-2} n (r+\log n)) edges. We also make first steps towards sketching general CSPs (Constraint Satisfaction Problems)

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