, Vertex Isoperimetry and Concentration

@article{Bobkov2000VI,
  title={, Vertex Isoperimetry and Concentration},
  author={Sergey G. Bobkov and Christian Houdr{\'e} and Prasad Tetali},
  journal={Combinatorica},
  year={2000},
  volume={20},
  pages={153-172}
}
. This approach refines results relating the spectral gap of a graph to the so-called magnification of a graph. A concentration result involving is also derived. 
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43 Citations
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43 Citations

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References

SHOWING 1-10 OF 29 REFERENCES
Graph-Theoretic Properties in computational Complexity
  • L. Valiant
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1976
TLDR
The extent to which a set of related graph-theoretic properties can be used to accont for the superlinear complexity of computational problems is explored and certain limited lower bounds can be proved by means of such properties.
Concentration of Measure for Products of Markov Kernels and Graph Products via Functional Inequalities
  • C. Houdré, P. Tetali
  • Computer Science, Mathematics
    Combinatorics, Probability and Computing
  • 2001
We present versions of concentration inequalities for products of Markov kernels and graph products. We also present discussions of a variety of consequences such as sharp upper bounds, in terms of…
Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution
Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every…
lambda1, Isoperimetric inequalities for graphs, and superconcentrators
TLDR
This method uses the second smallest eigenvalue of a certain matrix associated with the graph and it is the discrete version of a method used before for Riemannian manifolds for asymptotic isoperimetric inequalities for families of graphs.
An Asymptotic Isoperimetric Inequality
Abstract. For a finite metric space V with a metric $ \rho $, let V n be the metric space in which the distance between (a1, . . ., an) and (b1, . . ., bn) is the sum $ \sum^{n}_{i = 1} \rho (a_i,…
Sorting inc logn parallel steps
We give a sorting network withcn logn comparisons. The algorithm can be performed inc logn parallel steps as well, where in a parallel step we comparen/2 disjoint pairs. In thei-th step of the…
Time-space tradeoffs for some algebraic problems
  • J. Jaja
  • Computer Science, Mathematics
    STOC '80
  • 1980
TLDR
Several results relating the algebraic properties of a set of functions to the structure of the graph of any straight-line program, that computes this set, are shown.
The Complexity of Testing Whether a Graph is a Superconcentrator
TLDR
A very surprising result due to Valiant is the existence of superconcentrators with n inputs and O(n) edges.
Explicit Constructions of Linear-Sized Superconcentrators
TLDR
A direct way to construct a family of l inear concentrators using Pinsker’s linear concentrators and disproved a conjecture that superconcentrators require more than a linear number of edges.
Time-Space Tradeoffs for Computing Functions, Using Connectivity Properties of Their Circuits
  • M. Tompa
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1980
TLDR
Time-space tradeoffs for pebbling superconcentrators and grates are developed for any set of expressions which compute given functions, including any straight-line program which computesPolynomial multiplication, polynomial convolution, the discrete Fourier transform,straight-line merging, and the computation of “most” sets of n linear functions in n indeterminates.
...
1
2
3
...