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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 ...
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 ...
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.
2009: The Gödel Prize for work on the zig-zag product of graphs, a method of combining smaller graphs to produce larger ones used in the construction of expander graphs. [12] 2011: Elected as a member of the American Academy of Arts and Sciences. [13] 2018: Elected as an ACM Fellow for "contributions to theoretical computer science and ...
By Gram Slattery. WASHINGTON (Reuters) - U.S. President Donald Trump said he expects Elon Musk to find hundreds of billions of dollars of fraud and abuse at the Pentagon during an audit that the ...
GMO labeling and the little-known "8" code. According to the IFPS, there is no mandatory global rule requiring genetically modified produce to be labeled with an “8”; however, some companies ...
Simply twist the handle to expand the toe of the shoe to give your foot more space.The bunion expander plugs on each side of the stretcher work to expand the shoe at your foot's widest points ...