We give a new lower bound on the expansion coefficient of an edge-vertex graph of a d-regular graph. As a consequence, we obtain an improvement on the lower bound on relative minimum distance of the expander codes constructed by Sipser and Spielman. We also derive some improved results on the vertex expansion of graphs that help us in improving the parameters of the expander codes of Alon, Bruc...

It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of automata for which the same is true. However, we also show that some automata in this class do not give rise to expander graphs.

Expander graphs are one of the deepest tools of theoretical computer science and discrete mathematics, popping up in all sorts of contexts since their introduction in the 1970s. Here’s a list of some of the things that expander graphs can be used to do. Don’t worry if not all the items on the list make sense: the main thing to take away is the sheer range of areas in which expanders can be appl...

We show that r pseudo-random bits can be obtained by concatenating t blocks of r/t pseudo-random bits, where the blocks are generated in parallel. This can be considered as a parallel version of [a] recycling random bits by doing a random walk on an expander. The proof is based on the fact that t simultaneous independent random walks on an expander graph is equivalent to a random walk on a much...

Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess’s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess’s paradox i...

We compute the mixing rate of a non-backtracking random walk on a regular expander. Using some properties of Chebyshev polynomials of the second kind, we show that this rate may be up to twice as fast as the mixing rate of the simple random walk. The closer the expander is to a Ramanujan graph, the higher the ratio between the above two mixing rates is. As an application, we show that if G is a...

Informally, an expander is an undirected graph that has relatively sparse density, but whose vertices are nevertheless highly connected. Consequently, expanders have the property that any small subset of the vertices has a large set of neighbors outside of the set. This simple graph property has led to highly useful results in a number of branches of computer science. In addition, the study of ...

Primary skin closure after surgery for club foot in children can be difficult especially in revision operations. Between 1990 and 1996 a soft-tissue expander was implanted in 13 feet before such procedures. Two were primary operations and 11 were revisions. A standard technique was used for implantation of the expander. Skin augmentation was successful in 11 cases. There was failure of one expa...