The Zig-Zag product of two graphs, $Z = G \circ H$, was introduced in the seminal work of Reingold, Vadhan, and Wigderson (Ann. of Math. 2002) and has since become a pivotal tool in theoretical computer science. The classical bound, which is used throughout, states that the spectral expansion of ... more >>>

The notion of the derandomized square of two graphs, denoted as $G \circ H$, was introduced by Rozenman and Vadhan as they rederived Reingold's Theorem, $\mathbf{SL} = \mathbf{L}$. This pseudorandom primitive, closely related to the Zig-Zag product, plays a crucial role in recent advancements on space-bounded derandomization. For this and ... more >>>

More than twenty years ago, Capalbo, Reingold, Vadhan and Wigderson gave the first (and up to date only) explicit construction of a bipartite expander with almost full combinatorial expansion. The construction incorporates zig-zag ideas together with extractor technology, and is rather complicated. We give an alternative construction that builds upon ... more >>>

Dinitz, Schapira, and Valadarsky (Algorithmica 2017) introduced the intriguing notion of expanding expanders -- a family of expander graphs with the property that every two consecutive graphs in the family differ only on a small number of edges. Such a family allows one to add and remove vertices with only ... more >>>