A Combinatorial Construction of Almost-Ramanujan Graphs Using the Zig-Zag Product
نویسندگان
چکیده
منابع مشابه
The zig-zag product
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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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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Reingold et al. introduced the notion zig-zag product on two different graphs, and presented a fully explicit construction of dregular expanders with the second largest eigenvalue O(d−1/3). In the same paper, they ask whether or not the similar technique can be used to construct expanders with the second largest eigenvalue O(d−1/2). Such graphs are called Ramanujan graphs. Recently, zig-zag pro...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2011
ISSN: 0097-5397,1095-7111
DOI: 10.1137/080732651