The zig-zag product

نویسنده

  • Neil Olver
چکیده

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 essentially as large as possible. So why do we need some other expander construction? One reason is the consideration of vertex expansion. Define

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Zig-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...

متن کامل

On Construction of Almost-Ramanujan Graphs

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...

متن کامل

Testing Conductance in General Graphs

In this paper, we study the problem of testing the conductance of a given graph in the general graph model. Given distance parameter ε and any constant σ > 0, there exists a tester whose running time isO( (1+σ)/2·logn·log ε ε·Φ2 ), where n is the number of vertices andm is the number of edges of the input graph. With probability at least 2/3, the tester accepts all graphs of conductance at leas...

متن کامل

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...

متن کامل

Theoretical and Experimental Investigation of Optical Properties of ZnS Zig-Zag Thin Films

Zigzag ZnS thin films prepared by thermal evaporation method using glancing angle deposition (GLAD) technique. ZnS films with zigzag structure were produced at deposition angles of 0˚, 60˚ and 80˚ at room temperature on glass substrates. Surface morphology of the films w:as char:acterized by using field emission scanning electron microscopy (FESEM). The optical properties of the specimens were i...

متن کامل

Effects of Surface Topography on Formation of Zig-zag Defects in Ssflc Devices

The cause for wide variations in the zig-zag defect density in SSFLC devices using the same alignment layer material is investigated. In this paper, we show how the topography of the surface layer due to imperfect coating techniques and materials promotes the formation of zig-zag defects. We show that if the alignment surface slope is greater than the pretilt, high densities of zig-zag defects ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010