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Local Graph Partitioning using PageRank Vectors
TLDR
An improved algorithm for computing approximate PageRank vectors, which allows us to find a cut with conductance at most oslash and approximately optimal balance in time O(m log4 m/oslash) in time proportional to its size.
Spectral grouping using the Nystrom method
TLDR
The contribution of this paper is a method that substantially reduces the computational requirements of grouping algorithms based on spectral partitioning making it feasible to apply them to very large grouping problems.
Optical orthogonal codes: Design, analysis, and applications
TLDR
Methods for the design and analysis of OOCs, using tools from projective geometry, the greedy algorithm, iterative constructions, algebraic coding theory, block design, and various other combinational disciplines, are discussed.
A random graph model for massive graphs
TLDR
A random graph model is proposed which is a special case of sparse random graphs with given degree sequences which involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.
Quasi-random graphs
TLDR
A large equivalence class of graph properties is introduced, all of which are shared by so-called random graphs, and it is often relatively easy to verify that a particular family of graphs possesses some property in this class.
Some intersection theorems for ordered sets and graphs
Explicit construction of linear sized tolerant networks
Spectral Clustering of Graphs with General Degrees in the Extended Planted Partition Model
TLDR
A spectral clustering algorithm for similarity graphs drawn from a simple random graph model, where nodes are allowed to have varying degrees, is examined, and guarantees on the performance are shown that it outputs the correct partition under a wide range of parameter values.
Concentration Inequalities and Martingale Inequalities: A Survey
We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general
A Random Graph Model for Power Law Graphs
TLDR
A random graph model is proposed which is a special case of sparserandom graphs with given degree sequences which satisfy a power law and involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.
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