Results 1  10
of
1,869
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
Abstract

Cited by 507 (8 self)
 Add to MetaCart
then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
Graphcut textures: Image and video synthesis using graph cuts
 ACM Transactions on Graphics, SIGGRAPH 2003
, 2003
"... This banner was generated by merging the source images in Figure 6 using our interactive texture merging technique. In this paper we introduce a new algorithm for image and video texture synthesis. In our approach, patch regions from a sample image or video are transformed and copied to the output a ..."
Abstract

Cited by 490 (9 self)
 Add to MetaCart
. Unlike dynamic programming, our graph cut technique for seam optimization is applicable in any dimension. We specifically explore it in 2D and 3D to perform video texture synthesis in addition to regular image synthesis. We present approximative offset search techniques that work well in conjunction
A Random Graph Model for Massive Graphs
 STOC 2000
, 2000
"... We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from t ..."
Abstract

Cited by 406 (26 self)
 Add to MetaCart
We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and loglog growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
Abstract

Cited by 506 (0 self)
 Add to MetaCart
the family of radial basis kernels. It can also be used to define kernels in the form of joint Gibbs probability distributions. Kernels can be built from hidden Markov random elds, generalized regular expressions, pairHMMs, or ANOVA decompositions. Uses of the method lead to open problems involving
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
Abstract

Cited by 1397 (38 self)
 Add to MetaCart
? To recover x 0 , we consider the solution x to the 1 regularization problem where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x 0 is sufficiently sparse, then the solution is within the noise level As a first example
Models of Random Regular Graphs
 IN SURVEYS IN COMBINATORICS
, 1999
"... In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular g ..."
Abstract

Cited by 215 (33 self)
 Add to MetaCart
In a previous paper we showed that a random 4regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random dregular
EIGENVALUES AND EXPANDERS
 COMBINATORICA
, 1986
"... Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian mani ..."
Abstract

Cited by 400 (20 self)
 Add to MetaCart
Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian
Efficient erasure correcting codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2001
"... We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discretetime random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both si ..."
Abstract

Cited by 360 (26 self)
 Add to MetaCart
We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discretetime random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both
Stochastic Models for the Web Graph
, 2000
"... The web may be viewed as a directed graph each of whose vertices is a static HTML web page, and each of whose edges corresponds to a hyperlink from one web page to another. In this paper we propose and analyze random graph models inspired by a series of empirical observations on the web. Our graph m ..."
Abstract

Cited by 291 (12 self)
 Add to MetaCart
when these earlier models are generalized to account for the arrival of vertices over time. In particular, the sparse random graphs in our models exhibit properties that do not arise in far denser random graphs generated by ErdosR'enyi models.
Sparse regular random graphs: Spectral density and eigenvectors
"... Abstract. We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges to ..."
Abstract

Cited by 26 (2 self)
 Add to MetaCart
Abstract. We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of vertices, the empirical spectral distribution converges
Results 1  10
of
1,869