Question

The key idea of this paper is to develop single-pass streaming algorithms for finding minimum cuts in graphs, specifically improving space complexity compared to existing cut sparsification techniques. They achieve an Õ(n/ε) space algorithm for approximating the minimum cut, which is more efficient than algorithms producing a general cut sparsifier. This is accomplished by developing a for-each spectral sparsifier in the streaming setting. The paper also addresses exact minimum cuts in random order streams, finding them in Õ(n) space, and provides matching lower bounds for some settings. Furthermore, the paper explores approximating all-pairs effective resistances in the streaming model, alongside a way of improving the post-processing time of recursive contraction algorithms using sketching.