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arXiv · 1409.2391

Sketching Cuts in Graphs and Hypergraphs

Dmitry Kogan·Robert Krauthgamer
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Abstract

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

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Dmitry Kogan, Robert Krauthgamer. 2014-09-08. Sketching Cuts in Graphs and Hypergraphs. https://doi.org/10.1145/2688073.2688093

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