2 Search Results for "Kohonen, Jukka"

Document
DOI: 10.4230/LIPIcs.ESA.2025.95
The Planted Orthogonal Vectors Problem

Authors: David Kühnemann, Adam Polak, and Alon Rosen

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
In the k-Orthogonal Vectors (k-OV) problem we are given k sets, each containing n binary vectors of dimension d = n^o(1), and our goal is to pick one vector from each set so that at each coordinate at least one vector has a zero. It is a central problem in fine-grained complexity, conjectured to require n^{k-o(1)} time in the worst case. We propose a way to plant a solution among vectors with i.i.d. p-biased entries, for appropriately chosen p, so that the planted solution is the unique one. Our conjecture is that the resulting k-OV instances still require time n^{k-o(1)} to solve, on average. Our planted distribution has the property that any subset of strictly less than k vectors has the same marginal distribution as in the model distribution, consisting of i.i.d. p-biased random vectors. We use this property to give average-case search-to-decision reductions for k-OV.
Cite as

David Kühnemann, Adam Polak, and Alon Rosen. The Planted Orthogonal Vectors Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kuhnemann_et_al:LIPIcs.ESA.2025.95,
  author =	{K\"{u}hnemann, David and Polak, Adam and Rosen, Alon},
  title =	{{The Planted Orthogonal Vectors Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{95:1--95:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.95},
  URN =		{urn:nbn:de:0030-drops-245640},
  doi =		{10.4230/LIPIcs.ESA.2025.95},
  annote =	{Keywords: Average-case complexity, fine-grained complexity, orthogonal vectors}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.52
Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time

Authors: Matti Karppa, Petteri Kaski, Jukka Kohonen, and Padraig Ó Catháin

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We derandomize G. Valiant's [J.ACM 62(2015) Art.13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant's randomized algorithm, but the precise constants we save over quadratic scaling are more modest. Our main technical tool for derandomization is an explicit family of correlation amplifiers built via a family of zigzag-product expanders in Reingold, Vadhan, and Wigderson [Ann. of Math 155(2002), 157-187]. We say that a function f:{-1,1}^d ->{-1,1}^D is a correlation amplifier with threshold 0 <= tau <= 1, error gamma >= 1, and strength p an even positive integer if for all pairs of vectors x,y in {-1,1}^d it holds that (i) |<x,y>|<tau d implies |<f(x),f(y)>| <= (tau*gamma)^p*D; and (ii) |<x,y>| >= tau*d implies (<x,y>/gamma^d})^p*D <= <f(x),f(y)> <= (gamma*<x,y>/d)^p*D.
Cite as

Matti Karppa, Petteri Kaski, Jukka Kohonen, and Padraig Ó Catháin. Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{karppa_et_al:LIPIcs.ESA.2016.52,
  author =	{Karppa, Matti and Kaski, Petteri and Kohonen, Jukka and \'{O} Cath\'{a}in, Padraig},
  title =	{{Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{52:1--52:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.52},
  URN =		{urn:nbn:de:0030-drops-63944},
  doi =		{10.4230/LIPIcs.ESA.2016.52},
  annote =	{Keywords: correlation, derandomization, outlier, similarity search, expander graph}
}
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