• Publications
  • Influence
Quick Approximation to Matrices and Applications
TLDR
The matrix approximation is generalized to multi-dimensional arrays and from that derive approximation algorithms for all dense Max-SNP problems and the Regularity Lemma is derived.
On clusterings-good, bad and spectral
TLDR
Two results regarding the quality of the clustering found by a popular spectral algorithm are presented, one proffers worst case guarantees whilst the other shows that if there exists a "good" clustering then the spectral algorithm will find one close to it.
Some results on fixed points
Minkowski's Convex Body Theorem and Integer Programming
  • R. Kannan
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1 August 1987
TLDR
An algorithm for solving Integer Programming problems whose running time depends on the number n of variables as nOn by reducing an n variable problem to 2n5i/2 problems in n-i variables for some i greater than zero chosen by the algorithm.
Isoperimetric problems for convex bodies and a localization lemma
TLDR
This lemma is a general “Localization Lemma” that reduces integral inequalities over then-dimensional space to integral inequalities in a single variable and is illustrated by showing how a number of well-known results can be proved using it.
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
TLDR
A model (the pass-efficient model) is presented in which the efficiency of these and other approximate matrix algorithms may be studied and which is argued is well suited to many applications involving massive data sets.
Computing a nonnegative matrix factorization -- provably
TLDR
This work gives an algorithm that runs in time polynomial in n, m and r under the separablity condition identified by Donoho and Stodden in 2003, and is the firstPolynomial-time algorithm that provably works under a non-trivial condition on the input matrix.
Some Results on Fixed Points—II
(1969). Some Results on Fixed Points—II. The American Mathematical Monthly: Vol. 76, No. 4, pp. 405-408.
Fast Monte-Carlo algorithms for finding low-rank approximations
TLDR
This paper develops an algorithm which is qualitatively faster provided the entries of the matrix are sampled according to a natural probability distribution and the algorithm takes time polynomial in k, 1//spl epsiv/, log(1//spl delta/) only, independent of m, n.
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
TLDR
Two simple and intuitive algorithms are presented which compute a description of a low-rank approximation of a singular value decomposition (SVD) to an matrix of rank not greater than a specified rank, and which are qualitatively faster than the SVD.
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