Single pass sparsification in the streaming model with edge deletions

In this paper we give a construction of cut sparsifiers of Benczúr and Karger in the dynamic streaming setting in a single pass over the data stream. Previous constructions either required multiple passes or were unable to handle edge deletions. We use Õ(1/ǫ) time for each stream update and Õ(n/ǫ) time to construct a sparsifier. Our ǫ-sparsifiers have O(n log n/ǫ) edges. The main tools behind our result are an application of sketching techniques of Ahn et al.[SODA’12] to estimate edge connectivity together with a novel application of sampling with limited independence and sparse recovery to produce the edges of the sparsifier.