Sparse topologies with small spectrum size
نویسندگان
چکیده
One of the fundamental properties of a graph is the number of distinct eigenvalues of its adjacency or Laplace matrix. Determining this number is of theoretical interest as well as of practical impact. Sparse graphs with small spectra exhibit excellent structural properties and can act as interconnection topologies. In this paper, for any n we present graphs, for which the product of their vertex degree and the number of di7erent eigenvalues is small. It is known that load balancing can be performed on such graphs in a small number of steps. c © 2003 Elsevier B.V. All rights reserved.
منابع مشابه
Scalable Sparse Topologies with Small Spectrum
One of the fundamental properties of a graph is the number of distinct eigenvalues of its adjacency or Laplacian matrix. Determining this number is of theoretical interest and also of practical impact. Graphs with small spectra exhibit many symmetry properties and are well suited as interconnection topologies. Especially load balancing can be done on such interconnection topologies in a small n...
متن کاملClosNets: a Priori Sparse Topologies for Faster DNN Training
Fully-connected layers in deep neural networks (DNN) are often the throughput and power bottleneck during training. This is due to their large size and low data reuse. Pruning dense layers can significantly reduce the size of these networks, but this approach can only be applied after training. In this work we propose a novel fullyconnected layer that reduces the memory requirements of DNNs wit...
متن کاملA New Dictionary Construction Method in Sparse Representation Techniques for Target Detection in Hyperspectral Imagery
Hyperspectral data in Remote Sensing which have been gathered with efficient spectral resolution (about 10 nanometer) contain a plethora of spectral bands (roughly 200 bands). Since precious information about the spectral features of target materials can be extracted from these data, they have been used exclusively in hyperspectral target detection. One of the problem associated with the detect...
متن کاملLarge-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation
In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...
متن کاملThe impact of connectivity on the memory capacity and the retrieval dynamics of Hopfield-type networks
Most models of neural associative memory have used networks with broad connectivity. However, this seems unrealistic from a neuroanatomical perspective. A simple model of associative memory with emergent properties was introduced by Hopfield [5]. We choose this widely known model to investigate the impact of connectivity on the storage capacity and the retrieval dynamics in artificial associati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 307 شماره
صفحات -
تاریخ انتشار 2003