2 Search Results for "Møller, Mikael H."

Document
DOI: 10.4230/LIPIcs.STACS.2023.31
Barriers for Faster Dimensionality Reduction

Authors: Ora Nova Fandina, Mikael Møller Høgsgaard, and Kasper Green Larsen

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
The Johnson-Lindenstrauss transform allows one to embed a dataset of n points in ℝ^d into ℝ^m, while preserving the pairwise distance between any pair of points up to a factor (1 ± ε), provided that m = Ω(ε^{-2} lg n). The transform has found an overwhelming number of algorithmic applications, allowing to speed up algorithms and reducing memory consumption at the price of a small loss in accuracy. A central line of research on such transforms, focus on developing fast embedding algorithms, with the classic example being the Fast JL transform by Ailon and Chazelle. All known such algorithms have an embedding time of Ω(d lg d), but no lower bounds rule out a clean O(d) embedding time. In this work, we establish the first non-trivial lower bounds (of magnitude Ω(m lg m)) for a large class of embedding algorithms, including in particular most known upper bounds.
Cite as

Ora Nova Fandina, Mikael Møller Høgsgaard, and Kasper Green Larsen. Barriers for Faster Dimensionality Reduction. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{novafandina_et_al:LIPIcs.STACS.2023.31,
  author =	{Nova Fandina, Ora and M{\o}ller H{\o}gsgaard, Mikael and Green Larsen, Kasper},
  title =	{{Barriers for Faster Dimensionality Reduction}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.31},
  URN =		{urn:nbn:de:0030-drops-176838},
  doi =		{10.4230/LIPIcs.STACS.2023.31},
  annote =	{Keywords: Dimensional reduction, Lower bound, Linear Circuits}
}
Document
DOI: 10.4230/DROPS.MEMICS.2009.2346
Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants

Authors: Lasse Jacobsen, Morten Jacobsen, and Mikael H. Møller

Published in: OASIcs, Volume 13, Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09) (2009)

Abstract
Timed-Arc Petri Nets (TAPN) is a well studied extension of the classical Petri net model where tokens are decorated with real numbers that represent their age. Unlike reachability, which is known to be undecidable for TAPN, boundedness and coverability remain decidable. The model is supported by a recent tool called TAPAAL which, among others, further extends TAPN with invariants on places in order to model urgency. The decidability of boundedness and coverability for this extended model has not yet been considered. We present a reduction from two-counter Minsky machines to TAPN with invariants to show that both the boundedness and coverability problems are undecidable.
Cite as

Lasse Jacobsen, Morten Jacobsen, and Mikael H. Møller. Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants. In Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09). Open Access Series in Informatics (OASIcs), Volume 13, pp. 106-113, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{jacobsen_et_al:OASIcs:2009:DROPS.MEMICS.2009.2346,
  author =	{Jacobsen, Lasse and Jacobsen, Morten and M{\o}ller, Mikael H.},
  title =	{{Undecidability of Coverability and Boundedness for Timed-Arc Petri Nets with Invariants}},
  booktitle =	{Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09)},
  pages =	{106--113},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-15-6},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{13},
  editor =	{Hlinen\'{y}, Petr and Maty\'{a}\v{s}, V\'{a}clav and Vojnar, Tom\'{a}\v{s}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DROPS.MEMICS.2009.2346},
  URN =		{urn:nbn:de:0030-drops-23461},
  doi =		{10.4230/DROPS.MEMICS.2009.2346},
  annote =	{Keywords: Timed-Arc Petri Nets, Undecidability, Coverability, Boundedness}
}
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