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Documents authored by Morr, Sebastian

Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2021.62
Can You Walk This? Eulerian Tours and IDEA Instructions (Media Exposition)

Authors: Aaron T. Becker, Sándor P. Fekete, Matthias Konitzny, Sebastian Morr, and Arne Schmidt

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
We illustrate and animate the classic problem of deciding whether a given graph has an Eulerian path. Starting with a collection of instances of increasing difficulty, we present a set of pictorial instructions, and show how they can be used to solve all instances. These IDEA instructions ("A series of nonverbal algorithm assembly instructions") have proven to be both entertaining for experts and enlightening for novices. We (w)rap up with a song and dance to Euler’s original instance.
Cite as

Aaron T. Becker, Sándor P. Fekete, Matthias Konitzny, Sebastian Morr, and Arne Schmidt. Can You Walk This? Eulerian Tours and IDEA Instructions (Media Exposition). In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 62:1-62:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{becker_et_al:LIPIcs.SoCG.2021.62,
  author =	{Becker, Aaron T. and Fekete, S\'{a}ndor P. and Konitzny, Matthias and Morr, Sebastian and Schmidt, Arne},
  title =	{{Can You Walk This? Eulerian Tours and IDEA Instructions}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{62:1--62:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.62},
  URN =		{urn:nbn:de:0030-drops-138616},
  doi =		{10.4230/LIPIcs.SoCG.2021.62},
  annote =	{Keywords: Eulerian tours, algorithms, education, IDEA instructions}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2019.63
Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition)

Authors: Aaron T. Becker, Sándor P. Fekete, Phillip Keldenich, Sebastian Morr, and Christian Scheffer

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
We motivate and visualize problems and methods for packing a set of objects into a given container, in particular a set of {different-size} circles or squares into a square or circular container. Questions of this type have attracted a considerable amount of attention and are known to be notoriously hard. We focus on a particularly simple criterion for deciding whether a set can be packed: comparing the total area A of all objects to the area C of the container. The critical packing density delta^* is the largest value A/C for which any set of area A can be packed into a container of area C. We describe algorithms that establish the critical density of squares in a square (delta^*=0.5), of circles in a square (delta^*=0.5390 ...), regular octagons in a square (delta^*=0.5685 ...), and circles in a circle (delta^*=0.5).
Cite as

Aaron T. Becker, Sándor P. Fekete, Phillip Keldenich, Sebastian Morr, and Christian Scheffer. Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition). In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 63:1-63:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{becker_et_al:LIPIcs.SoCG.2019.63,
  author =	{Becker, Aaron T. and Fekete, S\'{a}ndor P. and Keldenich, Phillip and Morr, Sebastian and Scheffer, Christian},
  title =	{{Packing Geometric Objects with Optimal Worst-Case Density}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{63:1--63:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.63},
  URN =		{urn:nbn:de:0030-drops-104678},
  doi =		{10.4230/LIPIcs.SoCG.2019.63},
  annote =	{Keywords: Packing, complexity, bounds, packing density}
}
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