• Publications
  • Influence
Some results on fixed points
  • 734
  • 83
On clusterings-good, bad and spectral
TLDR
We propose a new measure for assessing the quality of clustering. Expand
  • 956
  • 74
Quick Approximation to Matrices and Applications
TLDR
We draw on two lines of research to develop the algorithms: one is built around the fundamental Regularity Lemma of Szemerédi in Graph Theory and the constructive version of Alon, Duke, Leffman, Rödl and Yuster. Expand
  • 445
  • 70
Minkowski's Convex Body Theorem and Integer Programming
  • R. Kannan
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1 August 1987
TLDR
The paper presents an algorithm for solving Integer Programming problems whose running time depends on the number n of variables as nOn. Expand
  • 658
  • 58
Isoperimetric problems for convex bodies and a localization lemma
TLDR
Our main tool is a general “Localization Lemma” that reduces integral inequalities over then-dimensional space to integral inequalities in a single variable. Expand
  • 366
  • 54
  • PDF
Computing a nonnegative matrix factorization -- provably
TLDR
The Nonnegative Matrix Factorization (NMF) problem has a rich history spanning quantum mechanics, probability theory, data analysis, polyhedral combinatorics, communication complexity, demography, chemometrics, etc. Expand
  • 335
  • 53
  • PDF
Some Results on Fixed Points—II
(1969). Some Results on Fixed Points—II. The American Mathematical Monthly: Vol. 76, No. 4, pp. 405-408.
  • 416
  • 40
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
TLDR
In many applications, the data consist of (or may be naturally formulated as) an $m \times n$ matrix $A$. Expand
  • 481
  • 38
  • PDF
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
TLDR
In this paper, we devise two algorithms for the matrix multiplication problem. Expand
  • 378
  • 37
  • PDF
Chvátal closures for mixed integer programming problems
TLDR
We show that for a given polyhedronP and integral vectorw, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again apolyhedron, analogous to the process of repeatedly taking Chvátal closures in integer programming. Expand
  • 265
  • 37
  • PDF
...
1
2
3
4
5
...