110 Search Results for "Speckmann, Bettina"


Volume

LIPIcs, Volume 99

34th International Symposium on Computational Geometry (SoCG 2018)

SoCG 2018, June 11-14, 2018, Budapest, Hungary

Editors: Bettina Speckmann and Csaba D. Tóth

Document
Fast Reconfiguration for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)


Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their actions can nevertheless result in the global change of the material’s physical properties and geometry. A fundamental algorithmic task for programmable matter is to achieve global shape reconfiguration by specifying local behavior of the particles. In this paper we describe a new approach for shape reconfiguration in the amoebot model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating the actions of particles to produce the desired behavior of the global system. Our reconfiguration algorithm is the first algorithm that does not use a canonical intermediate configuration when transforming between arbitrary shapes. We introduce new geometric primitives for amoebots and show how to reconfigure particle systems, using these primitives, in a linear number of activation rounds in the worst case. In practice, our method exploits the geometry of the symmetric difference between input and output shape: it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small. Furthermore, our reconfiguration algorithm moves the particles over as many parallel shortest paths as the problem instance allows.

Cite as

Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Fast Reconfiguration for Programmable Matter. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2023.27,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Fast Reconfiguration for Programmable Matter}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.27},
  URN =		{urn:nbn:de:0030-drops-191533},
  doi =		{10.4230/LIPIcs.DISC.2023.27},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
Document
Data-Spatial Layouts for Grid Maps

Authors: Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann, and Jo Wood

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)


Abstract
Grid maps are a well-known technique to visualize data associated with spatial regions. A grid map assigns each region to a tile in a grid (often orthogonal or hexagonal) and then represents the associated data values within this tile. Good grid maps represent the underlying geographic space well: regions that are geographically close are close in the grid map and vice versa. Though Tobler’s law suggests that spatial proximity relates to data similarity, local variations may obscure clusters and patterns in the data. For example, there are often clear differences between urban centers and adjacent rural areas with respect to socio-economic indicators. To get a better view of the data distribution, we propose grid-map layouts that take data values into account and place regions with similar data into close proximity. In the limit, such a data layout is essentially a chart and loses all spatial meaning. We present an algorithm to create hybrid layouts, allowing for trade-offs between data values and geographic space when assigning regions to tiles. Our algorithm also handles hierarchical grid maps and allows us to focus either on data or on geographic space on different levels of the hierarchy. Leveraging our algorithm we explore the design space of (hierarchical) grid maps with a hybrid layout and their semantics.

Cite as

Nathan van Beusekom, Wouter Meulemans, Bettina Speckmann, and Jo Wood. Data-Spatial Layouts for Grid Maps. In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{vanbeusekom_et_al:LIPIcs.GIScience.2023.10,
  author =	{van Beusekom, Nathan and Meulemans, Wouter and Speckmann, Bettina and Wood, Jo},
  title =	{{Data-Spatial Layouts for Grid Maps}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.10},
  URN =		{urn:nbn:de:0030-drops-189052},
  doi =		{10.4230/LIPIcs.GIScience.2023.10},
  annote =	{Keywords: Grid map, algorithms, trade-offs}
}
Document
Brief Announcement
Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)


Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material that can change its physical properties and shape based on the outcome of computation and movement performed by the individual particles in a concurrent manner. We use geometric insights to develop a new type of shortest path tree for programmable matter systems. Our feather trees utilize geometry to allow particles and information to traverse the programmable matter structure via shortest paths even in the presence of multiple overlapping trees.

Cite as

Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2022.47,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{47:1--47:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.47},
  URN =		{urn:nbn:de:0030-drops-172386},
  doi =		{10.4230/LIPIcs.DISC.2022.47},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
Document
Mobility Data Science (Dagstuhl Seminar 22021)

Authors: Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi

Published in: Dagstuhl Reports, Volume 12, Issue 1 (2022)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 22021 "Mobility Data Science". This seminar was held January 9-14, 2022, including 47 participants from industry and academia. The goal of this Dagstuhl Seminar was to create a new research community of mobility data science in which the whole is greater than the sum of its parts by bringing together established leaders as well as promising young researchers from all fields related to mobility data science. Specifically, this report summarizes the main results of the seminar by (1) defining Mobility Data Science as a research domain, (2) by sketching its agenda in the coming years, and by (3) building a mobility data science community. (1) Mobility data science is defined as spatiotemporal data that additionally captures the behavior of moving entities (human, vehicle, animal, etc.). To understand, explain, and predict behavior, we note that a strong collaboration with research in behavioral and social sciences is needed. (2) Future research directions for mobility data science described in this report include a) mobility data acquisition and privacy, b) mobility data management and analysis, and c) applications of mobility data science. (3) We identify opportunities towards building a mobility data science community, towards collaborations between academic and industry, and towards a mobility data science curriculum.

Cite as

Mohamed Mokbel, Mahmoud Sakr, Li Xiong, Andreas Züfle, Jussara Almeida, Taylor Anderson, Walid Aref, Gennady Andrienko, Natalia Andrienko, Yang Cao, Sanjay Chawla, Reynold Cheng, Panos Chrysanthis, Xiqi Fei, Gabriel Ghinita, Anita Graser, Dimitrios Gunopulos, Christian Jensen, Joon-Sook Kim, Kyoung-Sook Kim, Peer Kröger, John Krumm, Johannes Lauer, Amr Magdy, Mario Nascimento, Siva Ravada, Matthias Renz, Dimitris Sacharidis, Cyrus Shahabi, Flora Salim, Mohamed Sarwat, Maxime Schoemans, Bettina Speckmann, Egemen Tanin, Yannis Theodoridis, Kristian Torp, Goce Trajcevski, Marc van Kreveld, Carola Wenk, Martin Werner, Raymond Wong, Song Wu, Jianqiu Xu, Moustafa Youssef, Demetris Zeinalipour, Mengxuan Zhang, and Esteban Zimányi. Mobility Data Science (Dagstuhl Seminar 22021). In Dagstuhl Reports, Volume 12, Issue 1, pp. 1-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Article{mokbel_et_al:DagRep.12.1.1,
  author =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas and Almeida, Jussara and Anderson, Taylor and Aref, Walid and Andrienko, Gennady and Andrienko, Natalia and Cao, Yang and Chawla, Sanjay and Cheng, Reynold and Chrysanthis, Panos and Fei, Xiqi and Ghinita, Gabriel and Graser, Anita and Gunopulos, Dimitrios and Jensen, Christian and Kim, Joon-Sook and Kim, Kyoung-Sook and Kr\"{o}ger, Peer and Krumm, John and Lauer, Johannes and Magdy, Amr and Nascimento, Mario and Ravada, Siva and Renz, Matthias and Sacharidis, Dimitris and Shahabi, Cyrus and Salim, Flora and Sarwat, Mohamed and Schoemans, Maxime and Speckmann, Bettina and Tanin, Egemen and Theodoridis, Yannis and Torp, Kristian and Trajcevski, Goce and van Kreveld, Marc and Wenk, Carola and Werner, Martin and Wong, Raymond and Wu, Song and Xu, Jianqiu and Youssef, Moustafa and Zeinalipour, Demetris and Zhang, Mengxuan and Zim\'{a}nyi, Esteban},
  title =	{{Mobility Data Science (Dagstuhl Seminar 22021)}},
  pages =	{1--34},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{1},
  editor =	{Mokbel, Mohamed and Sakr, Mahmoud and Xiong, Li and Z\"{u}fle, Andreas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.12.1.1},
  URN =		{urn:nbn:de:0030-drops-169190},
  doi =		{10.4230/DagRep.12.1.1},
  annote =	{Keywords: Spatio-temporal, Tracking, Privacy, Behavior, Data cleaning, Data management, Analytics}
}
Document
Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares

Authors: Hugo A. Akitaya, Erik D. Demaine, Matias Korman, Irina Kostitsyna, Irene Parada, Willem Sonke, Bettina Speckmann, Ryuhei Uehara, and Jules Wulms

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)


Abstract
Edge-connected configurations of square modules, which can reconfigure through so-called sliding moves, are a well-established theoretical model for modular robots in two dimensions. Dumitrescu and Pach [Graphs and Combinatorics, 2006] proved that it is always possible to reconfigure one edge-connected configuration of n squares into any other using at most O(n²) sliding moves, while keeping the configuration connected at all times. For certain pairs of configurations, reconfiguration may require Ω(n²) sliding moves. However, significantly fewer moves may be sufficient. We prove that it is NP-hard to minimize the number of sliding moves for a given pair of edge-connected configurations. On the positive side we present Gather&Compact, an input-sensitive in-place algorithm that requires only O( ̄P n) sliding moves to transform one configuration into the other, where ̄P is the maximum perimeter of the two bounding boxes. The squares move within the bounding boxes only, with the exception of at most one square at a time which may move through the positions adjacent to the bounding boxes. The O( ̄P n) bound never exceeds O(n²), and is optimal (up to constant factors) among all bounds parameterized by just n and ̄P. Our algorithm is built on the basic principle that well-connected components of modular robots can be transformed efficiently. Hence we iteratively increase the connectivity within a configuration, to finally arrive at a single solid xy-monotone component. We implemented Gather&Compact and compared it experimentally to the in-place modification by Moreno and Sacristán [EuroCG 2020] of the Dumitrescu and Pach algorithm (MSDP). Our experiments show that Gather&Compact consistently outperforms MSDP by a significant margin, on all types of square configurations.

Cite as

Hugo A. Akitaya, Erik D. Demaine, Matias Korman, Irina Kostitsyna, Irene Parada, Willem Sonke, Bettina Speckmann, Ryuhei Uehara, and Jules Wulms. Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{a.akitaya_et_al:LIPIcs.SWAT.2022.4,
  author =	{A. Akitaya, Hugo and Demaine, Erik D. and Korman, Matias and Kostitsyna, Irina and Parada, Irene and Sonke, Willem and Speckmann, Bettina and Uehara, Ryuhei and Wulms, Jules},
  title =	{{Compacting Squares: Input-Sensitive In-Place Reconfiguration of Sliding Squares}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.4},
  URN =		{urn:nbn:de:0030-drops-161644},
  doi =		{10.4230/LIPIcs.SWAT.2022.4},
  annote =	{Keywords: Sliding cubes, Reconfiguration, Modular robots, NP-hardness}
}
Document
Media Exposition
An Interactive Framework for Reconfiguration in the Sliding Square Model (Media Exposition)

Authors: Willem Sonke and Jules Wulms

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)


Abstract
We describe SquareSlider, a software framework for visualizing reconfiguration algorithms of modular robots in the sliding square model. In this model, a robot consists of a configuration of squares in a rectangular grid, which can reconfigure through a fixed set of possible moves. SquareSlider is a web-based tool that implements an easy-to-use interface allowing the user to build a configuration, run a reconfiguration algorithm on it, and examine the results.

Cite as

Willem Sonke and Jules Wulms. An Interactive Framework for Reconfiguration in the Sliding Square Model (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 70:1-70:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{sonke_et_al:LIPIcs.SoCG.2022.70,
  author =	{Sonke, Willem and Wulms, Jules},
  title =	{{An Interactive Framework for Reconfiguration in the Sliding Square Model}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{70:1--70:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.70},
  URN =		{urn:nbn:de:0030-drops-160781},
  doi =		{10.4230/LIPIcs.SoCG.2022.70},
  annote =	{Keywords: Modular robots, Implementation, Visualization}
}
Document
Coordinated Schematization for Visualizing Mobility Patterns on Networks

Authors: Bram Custers, Wouter Meulemans, Bettina Speckmann, and Kevin Verbeek

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II


Abstract
GPS trajectories of vehicles moving on a road network are a valuable source of traffic information. However, the sheer volume of available data makes it challenging to identify and visualize salient patterns. Meaningful visual summaries of trajectory collections require that both the trajectories and the underlying network are aggregated and simplified in a coherent manner. In this paper we propose a coordinated fully-automated pipeline for computing a schematic overview of mobility patterns from a collection of trajectories on a street network. Our pipeline utilizes well-known building blocks from GIS, automated cartography, and trajectory analysis: map matching, road selection, schematization, movement patterns, and metro-map style rendering. We showcase the results of our pipeline on two real-world trajectory collections around The Hague and Beijing.

Cite as

Bram Custers, Wouter Meulemans, Bettina Speckmann, and Kevin Verbeek. Coordinated Schematization for Visualizing Mobility Patterns on Networks. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{custers_et_al:LIPIcs.GIScience.2021.II.7,
  author =	{Custers, Bram and Meulemans, Wouter and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Coordinated Schematization for Visualizing Mobility Patterns on Networks}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.7},
  URN =		{urn:nbn:de:0030-drops-147665},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.7},
  annote =	{Keywords: Trajectories, Visualization, Schematization}
}
Document
Harmonious Simplification of Isolines

Authors: Arthur van Goethem, Wouter Meulemans, Andreas Reimer, and Bettina Speckmann

Published in: LIPIcs, Volume 208, 11th International Conference on Geographic Information Science (GIScience 2021) - Part II


Abstract
Current techniques for simplification focus on reducing complexity while maintaining the geometric similarity to the input. For isolines that jointly describe a scalar field, however, we postulate that geometric similarity of each isoline separately is not sufficient. Rather, we need to maintain the harmony between these isolines to make them visually relate and describe the structures of the underlying terrain. Based on principles of manual cartography, we propose an algorithm for simplifying isolines while considering harmony explicitly. Our preliminary visual and quantitative results suggest that our algorithm is effective.

Cite as

Arthur van Goethem, Wouter Meulemans, Andreas Reimer, and Bettina Speckmann. Harmonious Simplification of Isolines. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{vangoethem_et_al:LIPIcs.GIScience.2021.II.8,
  author =	{van Goethem, Arthur and Meulemans, Wouter and Reimer, Andreas and Speckmann, Bettina},
  title =	{{Harmonious Simplification of Isolines}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-208-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{208},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.8},
  URN =		{urn:nbn:de:0030-drops-147675},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.8},
  annote =	{Keywords: Simplification, isolines, harmony}
}
Document
Obstructing Classification via Projection

Authors: Pantea Haghighatkhah, Wouter Meulemans, Bettina Speckmann, Jérôme Urhausen, and Kevin Verbeek

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
Machine learning and data mining techniques are effective tools to classify large amounts of data. But they tend to preserve any inherent bias in the data, for example, with regards to gender or race. Removing such bias from data or the learned representations is quite challenging. In this paper we study a geometric problem which models a possible approach for bias removal. Our input is a set of points P in Euclidean space ℝ^d and each point is labeled with k binary-valued properties. A priori we assume that it is "easy" to classify the data according to each property. Our goal is to obstruct the classification according to one property by a suitable projection to a lower-dimensional Euclidean space ℝ^m (m < d), while classification according to all other properties remains easy. What it means for classification to be easy depends on the classification model used. We first consider classification by linear separability as employed by support vector machines. We use Kirchberger’s Theorem to show that, under certain conditions, a simple projection to ℝ^{d-1} suffices to eliminate the linear separability of one of the properties whilst maintaining the linear separability of the other properties. We also study the problem of maximizing the linear "inseparability" of the chosen property. Second, we consider more complex forms of separability and prove a connection between the number of projections required to obstruct classification and the Helly-type properties of such separabilities.

Cite as

Pantea Haghighatkhah, Wouter Meulemans, Bettina Speckmann, Jérôme Urhausen, and Kevin Verbeek. Obstructing Classification via Projection. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 56:1-56:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{haghighatkhah_et_al:LIPIcs.MFCS.2021.56,
  author =	{Haghighatkhah, Pantea and Meulemans, Wouter and Speckmann, Bettina and Urhausen, J\'{e}r\^{o}me and Verbeek, Kevin},
  title =	{{Obstructing Classification via Projection}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{56:1--56:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.56},
  URN =		{urn:nbn:de:0030-drops-144965},
  doi =		{10.4230/LIPIcs.MFCS.2021.56},
  annote =	{Keywords: Projection, classification, models of learning}
}
Document
Restricted Constrained Delaunay Triangulations

Authors: Marc Khoury and Jonathan Richard Shewchuk

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


Abstract
We introduce the restricted constrained Delaunay triangulation (restricted CDT), a generalization of both the restricted Delaunay triangulation and the constrained Delaunay triangulation. The restricted CDT is a triangulation of a surface whose edges include a set of user-specified constraining segments. We define the restricted CDT to be the dual of a restricted Voronoi diagram defined on a surface that we have extended by topological surgery. We prove several properties of restricted CDTs, including sampling conditions under which the restricted CDT contains every constraining segment and is homeomorphic to the underlying surface.

Cite as

Marc Khoury and Jonathan Richard Shewchuk. Restricted Constrained Delaunay Triangulations. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 49:1-49:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{khoury_et_al:LIPIcs.SoCG.2021.49,
  author =	{Khoury, Marc and Shewchuk, Jonathan Richard},
  title =	{{Restricted Constrained Delaunay Triangulations}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{49:1--49:16},
  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.2021.49},
  URN =		{urn:nbn:de:0030-drops-138481},
  doi =		{10.4230/LIPIcs.SoCG.2021.49},
  annote =	{Keywords: restricted Delaunay triangulation, constrained Delaunay triangulation, surface meshing, surface reconstruction, topological surgery, portals}
}
Document
Polygon-Universal Graphs

Authors: Tim Ophelders, Ignaz Rutter, Bettina Speckmann, and Kevin Verbeek

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


Abstract
We study a fundamental question from graph drawing: given a pair (G,C) of a graph G and a cycle C in G together with a simple polygon P, is there a straight-line drawing of G inside P which maps C to P? We say that such a drawing of (G,C) respects P. We fully characterize those instances (G,C) which are polygon-universal, that is, they have a drawing that respects P for any simple (not necessarily convex) polygon P. Specifically, we identify two necessary conditions for an instance to be polygon-universal. Both conditions are based purely on graph and cycle distances and are easy to check. We show that these two conditions are also sufficient. Furthermore, if an instance (G,C) is planar, that is, if there exists a planar drawing of G with C on the outer face, we show that the same conditions guarantee for every simple polygon P the existence of a planar drawing of (G,C) that respects P. If (G,C) is polygon-universal, then our proofs directly imply a linear-time algorithm to construct a drawing that respects a given polygon P.

Cite as

Tim Ophelders, Ignaz Rutter, Bettina Speckmann, and Kevin Verbeek. Polygon-Universal Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{ophelders_et_al:LIPIcs.SoCG.2021.55,
  author =	{Ophelders, Tim and Rutter, Ignaz and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Polygon-Universal Graphs}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{55:1--55:15},
  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.2021.55},
  URN =		{urn:nbn:de:0030-drops-138540},
  doi =		{10.4230/LIPIcs.SoCG.2021.55},
  annote =	{Keywords: Graph drawing, partial drawing extension, simple polygon}
}
Document
Volume from Outlines on Terrains

Authors: Marc van Kreveld, Tim Ophelders, Willem Sonke, Bettina Speckmann, and Kevin Verbeek

Published in: LIPIcs, Volume 177, 11th International Conference on Geographic Information Science (GIScience 2021) - Part I (2020)


Abstract
Outlines (closed loops) delineate areas of interest on terrains, such as regions with a heightened risk of landslides. For various analysis tasks it is necessary to define and compute a volume of earth (soil) based on such an outline, capturing, for example, the possible volume of a landslide in a high-risk region. In this paper we discuss several options to define meaningful 2D surfaces induced by a 1D outline, which allow us to compute such volumes. We experimentally compare the proposed surface options for two applications: similarity of paths on terrains and landslide susceptibility analysis.

Cite as

Marc van Kreveld, Tim Ophelders, Willem Sonke, Bettina Speckmann, and Kevin Verbeek. Volume from Outlines on Terrains. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part I. Leibniz International Proceedings in Informatics (LIPIcs), Volume 177, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{vankreveld_et_al:LIPIcs.GIScience.2021.I.16,
  author =	{van Kreveld, Marc and Ophelders, Tim and Sonke, Willem and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Volume from Outlines on Terrains}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part I},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-166-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{177},
  editor =	{Janowicz, Krzysztof and Verstegen, Judith A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.I.16},
  URN =		{urn:nbn:de:0030-drops-130512},
  doi =		{10.4230/LIPIcs.GIScience.2021.I.16},
  annote =	{Keywords: Terrain model, similarity, volume, computation}
}
Document
Media Exposition
Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy (Media Exposition)

Authors: Tillmann Miltzow, Irene Parada, Willem Sonke, Bettina Speckmann, and Jules Wulms

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
Face-connected configurations of cubes are a common model for modular robots in three dimensions. In this abstract and the accompanying video we study reconfigurations of such modular robots using so-called sliding moves. Using sliding moves, it is always possible to reconfigure one face-connected configuration of n cubes into any other, while keeping the robot connected at all stages of the reconfiguration. For certain configurations Ω(n²) sliding moves are necessary. In contrast, the best current upper bound is O(n³). It has been conjectured that there is always a cube on the outside of any face-connected configuration of cubes which can be moved without breaking connectivity. The existence of such a cube would immediately imply a straight-forward O(n²) reconfiguration algorithm. However, we present a configuration of cubes such that no cube on the outside can move without breaking connectivity. In other words, we show that this particular avenue towards an O(n²) reconfiguration algorithm for face-connected cubes is blocked.

Cite as

Tillmann Miltzow, Irene Parada, Willem Sonke, Bettina Speckmann, and Jules Wulms. Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 78:1-78:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{miltzow_et_al:LIPIcs.SoCG.2020.78,
  author =	{Miltzow, Tillmann and Parada, Irene and Sonke, Willem and Speckmann, Bettina and Wulms, Jules},
  title =	{{Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{78:1--78:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.78},
  URN =		{urn:nbn:de:0030-drops-122363},
  doi =		{10.4230/LIPIcs.SoCG.2020.78},
  annote =	{Keywords: Sliding cubes, Reconfiguration, Modular robots}
}
Document
Preprocessing Ambiguous Imprecise Points

Authors: Ivor van der Hoog, Irina Kostitsyna, Maarten Löffler, and Bettina Speckmann

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


Abstract
Let R = {R_1, R_2, ..., R_n} be a set of regions and let X = {x_1, x_2, ..., x_n} be an (unknown) point set with x_i in R_i. Region R_i represents the uncertainty region of x_i. We consider the following question: how fast can we establish order if we are allowed to preprocess the regions in R? The preprocessing model of uncertainty uses two consecutive phases: a preprocessing phase which has access only to R followed by a reconstruction phase during which a desired structure on X is computed. Recent results in this model parametrize the reconstruction time by the ply of R, which is the maximum overlap between the regions in R. We introduce the ambiguity A(R) as a more fine-grained measure of the degree of overlap in R. We show how to preprocess a set of d-dimensional disks in O(n log n) time such that we can sort X (if d=1) and reconstruct a quadtree on X (if d >= 1 but constant) in O(A(R)) time. If A(R) is sub-linear, then reporting the result dominates the running time of the reconstruction phase. However, we can still return a suitable data structure representing the result in O(A(R)) time. In one dimension, {R} is a set of intervals and the ambiguity is linked to interval entropy, which in turn relates to the well-studied problem of sorting under partial information. The number of comparisons necessary to find the linear order underlying a poset P is lower-bounded by the graph entropy of P. We show that if P is an interval order, then the ambiguity provides a constant-factor approximation of the graph entropy. This gives a lower bound of Omega(A(R)) in all dimensions for the reconstruction phase (sorting or any proximity structure), independent of any preprocessing; hence our result is tight. Finally, our results imply that one can approximate the entropy of interval graphs in O(n log n) time, improving the O(n^{2.5}) bound by Cardinal et al.

Cite as

Ivor van der Hoog, Irina Kostitsyna, Maarten Löffler, and Bettina Speckmann. Preprocessing Ambiguous Imprecise Points. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 42:1-42:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{vanderhoog_et_al:LIPIcs.SoCG.2019.42,
  author =	{van der Hoog, Ivor and Kostitsyna, Irina and L\"{o}ffler, Maarten and Speckmann, Bettina},
  title =	{{Preprocessing Ambiguous Imprecise Points}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{42:1--42:16},
  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.2019.42},
  URN =		{urn:nbn:de:0030-drops-104460},
  doi =		{10.4230/LIPIcs.SoCG.2019.42},
  annote =	{Keywords: preprocessing, imprecise points, entropy, sorting, proximity structures}
}
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