2 Search Results for "Schneider, Petra"


Document
Parallel Computation of Combinatorial Symmetries

Authors: Markus Anders and Pascal Schweitzer

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)


Abstract
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the automorphism group of the constructed graph. Such solvers have been developed for over 50 years, and highly efficient sequential, single core tools are available. However no competitive parallel tools are available for the task. We introduce a new parallel randomized algorithm that is based on a modification of the individualization-refinement paradigm used by sequential solvers. The use of randomization crucially enables parallelization. We report extensive benchmark results that show that our solver is competitive to state-of-the-art solvers on a single thread, while scaling remarkably well with the use of more threads. This results in order-of-magnitude improvements on many graph classes over state-of-the-art solvers. In fact, our tool is the first parallel graph automorphism tool that outperforms current sequential tools.

Cite as

Markus Anders and Pascal Schweitzer. Parallel Computation of Combinatorial Symmetries. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{anders_et_al:LIPIcs.ESA.2021.6,
  author =	{Anders, Markus and Schweitzer, Pascal},
  title =	{{Parallel Computation of Combinatorial Symmetries}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.6},
  URN =		{urn:nbn:de:0030-drops-145875},
  doi =		{10.4230/LIPIcs.ESA.2021.6},
  annote =	{Keywords: graph isomorphism, automorphism groups, algorithm engineering, parallel algorithms}
}
Document
Relevance Matrices in LVQ

Authors: Petra Schneider

Published in: Dagstuhl Seminar Proceedings, Volume 7131, Similarity-based Clustering and its Application to Medicine and Biology (2007)


Abstract
LVQ-networks belong to the class of distance-based classifiers. The underlying distance measure is of special importance for their performance, because it defines how the data items are compared and how they are grouped in clusters. Relevance Learning techniques try to adapt the distance measure to the specific data used for training. I will present a new adaptive distance measure in Learning Vector Quantization which is an extension of previously proposed Relevance Learning schemes. In comparison to the already existing techniques for Relevance Learning, this distance measure is more powerful to represent the internal structure of the data appropriately. Two applications will be used to demonstrate the behavior of the new algorithm (artificial and real life).

Cite as

Petra Schneider. Relevance Matrices in LVQ. In Similarity-based Clustering and its Application to Medicine and Biology. Dagstuhl Seminar Proceedings, Volume 7131, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)


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@InProceedings{schneider:DagSemProc.07131.7,
  author =	{Schneider, Petra},
  title =	{{Relevance Matrices in LVQ}},
  booktitle =	{Similarity-based Clustering and its Application to Medicine and Biology},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7131},
  editor =	{Michael Biehl and Barbara Hammer and Michel Verleysen and Thomas Villmann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07131.7},
  URN =		{urn:nbn:de:0030-drops-11332},
  doi =		{10.4230/DagSemProc.07131.7},
  annote =	{Keywords: Learning Vector Quantization, Relevance Learning, adaptive distance measure}
}
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