R
Ravi Kannan
Researcher at Microsoft
Publications - 150
Citations - 15973
Ravi Kannan is an academic researcher from Microsoft. The author has contributed to research in topics: Matrix (mathematics) & Time complexity. The author has an hindex of 57, co-authored 148 publications receiving 14886 citations. Previous affiliations of Ravi Kannan include Madras Medical College & Massachusetts Institute of Technology.
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Proceedings ArticleDOI
On clusterings-good, bad and spectral
TL;DR: 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.
Journal ArticleDOI
Minkowski's convex body theorem and integer programming
TL;DR: 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.
Journal ArticleDOI
On clusterings: Good, bad and spectral
TL;DR: A natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures is motivated and a simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure.
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A random polynomial-time algorithm for approximating the volume of convex bodies
TL;DR: The proof of correctness of the algorithm relies on recent theory of rapidly mixing Markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within K within Euclidean space.
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Fast monte-carlo algorithms for finding low-rank approximations
TL;DR: An algorithm is developed that is qualitatively faster, provided the authors may sample the entries of the matrix in accordance with a natural probability distribution, and implies that in constant time, it can be determined if a given matrix of arbitrary size has a good low-rank approximation.