2 Search Results for "Krishnan, Aditya"


Document
Track A: Algorithms, Complexity and Games
Lower Bounds for Pseudo-Deterministic Counting in a Stream

Authors: Vladimir Braverman, Robert Krauthgamer, Aditya Krishnan, and Shay Sapir

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary - for many streaming problems, both relaxations must be employed simultaneously, to avoid an exponentially larger (and often trivial) space complexity. A common drawback of these randomized approximate algorithms is that independent executions on the same input have different outputs, that depend on their random coins. Pseudo-deterministic algorithms combat this issue, and for every input, they output with high probability the same "canonical" solution. We consider perhaps the most basic problem in data streams, of counting the number of items in a stream of length at most n. Morris’s counter [CACM, 1978] is a randomized approximation algorithm for this problem that uses O(log log n) bits of space, for every fixed approximation factor (greater than 1). Goldwasser, Grossman, Mohanty and Woodruff [ITCS 2020] asked whether pseudo-deterministic approximation algorithms can match this space complexity. Our main result answers their question negatively, and shows that such algorithms must use Ω(√{log n / log log n}) bits of space. Our approach is based on a problem that we call Shift Finding, and may be of independent interest. In this problem, one has query access to a shifted version of a known string F ∈ {0,1}^{3n}, which is guaranteed to start with n zeros and end with n ones, and the goal is to find the unknown shift using a small number of queries. We provide for this problem an algorithm that uses O(√n) queries. It remains open whether poly(log n) queries suffice; if true, then our techniques immediately imply a nearly-tight Ω(log n/log log n) space bound for pseudo-deterministic approximate counting.

Cite as

Vladimir Braverman, Robert Krauthgamer, Aditya Krishnan, and Shay Sapir. Lower Bounds for Pseudo-Deterministic Counting in a Stream. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{braverman_et_al:LIPIcs.ICALP.2023.30,
  author =	{Braverman, Vladimir and Krauthgamer, Robert and Krishnan, Aditya and Sapir, Shay},
  title =	{{Lower Bounds for Pseudo-Deterministic Counting in a Stream}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.30},
  URN =		{urn:nbn:de:0030-drops-180827},
  doi =		{10.4230/LIPIcs.ICALP.2023.30},
  annote =	{Keywords: streaming algorithms, pseudo-deterministic, approximate counting}
}
Document
On Sketching the q to p Norms

Authors: Aditya Krishnan, Sidhanth Mohanty, and David P. Woodruff

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)


Abstract
We initiate the study of data dimensionality reduction, or sketching, for the q -> p norms. Given an n x d matrix A, the q -> p norm, denoted |A |_{q -> p} = sup_{x in R^d \ 0} |Ax |_p / |x |_q, is a natural generalization of several matrix and vector norms studied in the data stream and sketching models, with applications to datamining, hardness of approximation, and oblivious routing. We say a distribution S on random matrices L in R^{nd} - > R^k is a (k,alpha)-sketching family if from L(A), one can approximate |A |_{q -> p} up to a factor alpha with constant probability. We provide upper and lower bounds on the sketching dimension k for every p, q in [1, infty], and in a number of cases our bounds are tight. While we mostly focus on constant alpha, we also consider large approximation factors alpha, as well as other variants of the problem such as when A has low rank.

Cite as

Aditya Krishnan, Sidhanth Mohanty, and David P. Woodruff. On Sketching the q to p Norms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{krishnan_et_al:LIPIcs.APPROX-RANDOM.2018.15,
  author =	{Krishnan, Aditya and Mohanty, Sidhanth and Woodruff, David P.},
  title =	{{On Sketching the q to p Norms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.15},
  URN =		{urn:nbn:de:0030-drops-94192},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.15},
  annote =	{Keywords: Dimensionality Reduction, Norms, Sketching, Streaming}
}
  • Refine by Author
  • 2 Krishnan, Aditya
  • 1 Braverman, Vladimir
  • 1 Krauthgamer, Robert
  • 1 Mohanty, Sidhanth
  • 1 Sapir, Shay
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Lower bounds and information complexity
  • 1 Theory of computation → Numeric approximation algorithms
  • 1 Theory of computation → Pseudorandomness and derandomization
  • 1 Theory of computation → Streaming, sublinear and near linear time algorithms

  • Refine by Keyword
  • 1 Dimensionality Reduction
  • 1 Norms
  • 1 Sketching
  • 1 Streaming
  • 1 approximate counting
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2018
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail