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The zigzag product was introduced by Reingold, Vadhan & Wigderson (2000). When the zig-zag product was first introduced, it was used for the explicit construction of constant degree expanders and extractors. Later on, the zig-zag product was used in computational complexity theory to prove that symmetric logspace and logspace are equal ...
In mathematics, a rotation map is a function that represents an undirected edge-labeled graph, where each vertex enumerates its outgoing neighbors.Rotation maps were first introduced by Reingold, Vadhan and Wigderson (“Entropy waves, the zig-zag graph product, and new constant-degree expanders”, 2002) in order to conveniently define the zig-zag product and prove its properties.
Roughly speaking, the zig-zag product of two expander graphs produces a graph with only slightly worse expansion. Therefore, a zig-zag product can also be used to construct families of expander graphs. If G is a (n, d, λ 1)-graph and H is an (m, d, λ 2)-graph, then the zig-zag product G H is a (nm, d 2, φ(λ 1, λ 2))-graph where φ has the ...
One of the main contributions of his work is a new type of graph product, called the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of ...
Zig-zag product This page was last edited on 18 December 2020, at 00:02 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ...
A palatal expander Upper and lower jaw functional expanders. A palatal expander is a device in the field of orthodontics which is used to widen the upper jaw [1] so that the bottom and upper teeth will fit together better. [2] [3] This is a common orthodontic procedure. The use of an expander is most common in children and adolescents 8–18 ...
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