Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders
نویسندگان
چکیده
منابع مشابه
Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors
The main contribution of this work is a new type of graph product, which we call 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 constant-degree expanders of arbitrary size, startin...
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The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...
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A family of expanders is a family of graphs Gn = (Vn, En), |Vn| = n, such that each graph is dn-regular, and the edge-expansion of each graph is at least h, for an absolute constant h independent of n. Ideally, we would like to have such a construction for each n, although it is usually enough for most applications that, for some constant c and every k, there is an n for which the construction ...
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Construction 7.1 (Margulis [Mar]) Fix a positive integerM and let [M ] = {1, 2, . . . ,M}. Define the bipartite graph G = (V,E) as follows. Let V = [M ]2∪ [M ]2, where vertices in the first partite set are denoted (x, y)1 and vertices in the second partite set are denoted (x, y)2. From each vertex (x, y)1, put in edges to (x, y)2, (x, x+ y)2, (x, x+ y+1)2, (x+ y, y)2, and (x+ y+ 1, y)2, where a...
متن کاملZig-zag and replacement product graphs and LDPC codes
It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2002
ISSN: 0003-486X
DOI: 10.2307/3062153