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Documents authored by Kannan, Ravi

Document
DOI: 10.4230/LIPIcs.ITCS.2023.42
Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization

Authors: Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
We study the bit complexity of two related fundamental computational problems in linear algebra and control theory. Our results are: (1) An Õ(n^{ω+3}a+n⁴a²+n^ωlog(1/ε)) time algorithm for finding an ε-approximation to the Jordan Normal form of an integer matrix with a-bit entries, where ω is the exponent of matrix multiplication. (2) An Õ(n⁶d⁶a+n⁴d⁴a²+n³d³log(1/ε)) time algorithm for ε-approximately computing the spectral factorization P(x) = Q^*(x)Q(x) of a given monic n× n rational matrix polynomial of degree 2d with rational a-bit coefficients having a-bit common denominators, which satisfies P(x)⪰0 for all real x. The first algorithm is used as a subroutine in the second one. Despite its being of central importance, polynomial complexity bounds were not previously known for spectral factorization, and for Jordan form the best previous best running time was an unspecified polynomial in n of degree at least twelve [Cai, 1994]. Our algorithms are simple and judiciously combine techniques from numerical and symbolic computation, yielding significant advantages over either approach by itself.
Cite as

Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava. Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dey_et_al:LIPIcs.ITCS.2023.42,
  author =	{Dey, Papri and Kannan, Ravi and Ryder, Nick and Srivastava, Nikhil},
  title =	{{Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.42},
  URN =		{urn:nbn:de:0030-drops-175450},
  doi =		{10.4230/LIPIcs.ITCS.2023.42},
  annote =	{Keywords: Symbolic algorithms, numerical algorithms, linear algebra}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2009
LIPIcs, Volume 4, FSTTCS'09, Complete Volume

Authors: Ravi Kannan and K. Narayan Kumar

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
LIPIcs, Volume 4, FSTTCS'09, Complete Volume
Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Proceedings{kannan_et_al:LIPIcs.FSTTCS.2009,
  title =	{{LIPIcs, Volume 4, FSTTCS'09, Complete Volume}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009},
  URN =		{urn:nbn:de:0030-drops-40987},
  doi =		{10.4230/LIPIcs.FSTTCS.2009},
  annote =	{Keywords: LIPIcs, Volume 4, FSTTCS'09, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2009.2341
Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Authors: Ravi Kannan and K. Narayan Kumar

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract
This volume contains the proceedings of the 29th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009), organized under the auspices of the Indian Association for Research in Computing Science (IARCS) at the Indian Institute of Technology, Kanpur, India.
Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. i-vii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kannan_et_al:LIPIcs.FSTTCS.2009.2341,
  author =	{Kannan, Ravi and Narayan Kumar, K.},
  title =	{{Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{i--vii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2341},
  URN =		{urn:nbn:de:0030-drops-23415},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2341},
  annote =	{Keywords: Preface, proceedings, FSTTCS, referees, programme committee, organising committee}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2008.1752
A new approach to the planted clique problem

Authors: Alan Frieze and Ravi Kannan

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

Abstract
We study the problem of finding a large planted clique in the random graph $G_{n,1/2}$. We reduce the problem to that of maximising a three dimensional tensor over the unit ball in $n$ dimensions. This latter problem has not been well studied and so we hope that this reduction will eventually lead to an improved solution to the planted clique problem.
Cite as

Alan Frieze and Ravi Kannan. A new approach to the planted clique problem. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 187-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{frieze_et_al:LIPIcs.FSTTCS.2008.1752,
  author =	{Frieze, Alan and Kannan, Ravi},
  title =	{{A new approach to the planted clique problem}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{187--198},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1752},
  URN =		{urn:nbn:de:0030-drops-17521},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1752},
  annote =	{Keywords: Planted Clique, Tensor, Random Graph}
}
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