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 −2 n(r + log n)) edges. We also make first steps towards sketching general CSPs (Constraint Satisfaction Problems).
Kogan and Krauthgamer REF generalized the method of Benczúr and Karger [3] and showed that any r-uniform hypergraph admits an -cut sparsifier of O(n(r + log n)/ 2 ) hyperedges.
Sketching Cuts in Graphs and Hypergraphs
ITCS '15
Mathematics Computer Science