15 Search Results for "Gärtner, Bernd"

Document
Short Paper
DOI: 10.4230/LIPIcs.COSIT.2024.15
Exploring the Relation Between Sense of Direction and Spatial Anxiety in Everyday Mobile Map App Use (Short Paper)

Authors: Donatella Zingaro, Tumasch Reichenbacher, Mona Bartling, and Sara Irina Fabrikant

Published in: LIPIcs, Volume 315, 16th International Conference on Spatial Information Theory (COSIT 2024)

Abstract
Many studies have examined the effect of GPS reliance on individual spatial abilities and emotional disposition. Yet, how those individual differences relate to everyday mobile map interactions in the wild is poorly understood. Hence, we empirically studied the effect of users' sense of direction and spatial anxiety using mobile map apps in their everyday lives by deploying an ecologically valid approach to recording phone-based touchscreen interaction. We operationalised touchscreen interactions as switching patterns for mobile maps and other app categories. We hypothesised that users with a better sense of direction would spend less time on mobile map apps and show increased switching patterns between mobile map apps and other apps compared to users with a worse sense of direction. Conversely, users with higher levels of spatial anxiety would spend more time on mobile map apps and show decreased switching patterns. Our results contradicted our hypotheses. We did, however, find gender-specific trends: Women with higher spatial anxiety switch more often from different categories of apps (for all apps, not specifically map apps) in a phone session. Contrary to our hypothesis, men with a better sense of direction tend to spend more time on mobile map apps. This research reveals insights into the effect of users' spatial abilities and emotional dispositions on everyday users' touchscreen interactions with mobile map apps. It provides ground for mobile map app interaction design on accounting for individual-related differences.
Cite as

Donatella Zingaro, Tumasch Reichenbacher, Mona Bartling, and Sara Irina Fabrikant. Exploring the Relation Between Sense of Direction and Spatial Anxiety in Everyday Mobile Map App Use (Short Paper). In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 15:1-15:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zingaro_et_al:LIPIcs.COSIT.2024.15,
  author =	{Zingaro, Donatella and Reichenbacher, Tumasch and Bartling, Mona and Fabrikant, Sara Irina},
  title =	{{Exploring the Relation Between Sense of Direction and Spatial Anxiety in Everyday Mobile Map App Use}},
  booktitle =	{16th International Conference on Spatial Information Theory (COSIT 2024)},
  pages =	{15:1--15:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-330-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{315},
  editor =	{Adams, Benjamin and Griffin, Amy L. and Scheider, Simon and McKenzie, Grant},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2024.15},
  URN =		{urn:nbn:de:0030-drops-208300},
  doi =		{10.4230/LIPIcs.COSIT.2024.15},
  annote =	{Keywords: mobile map apps, sense of direction, spatial anxiety, app-switching, navigation, touchscreen interactions}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.18
Experimental Analysis of LP Scaling Methods Based on Circuit Imbalance Minimization

Authors: Jakub Komárek and Martin Koutecký

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Linear programming (LP) is a fundamental problem with rich theory and wide applications. A ubiquitous technique in LP is scaling, where the input instance is transformed in some way to make its solution easier. Dadush et al. [STOC '20] have recently devised an algorithm which scales the columns of the constraint matrix of a linear program in a way that aims to minimize the circuit imbalance measure, a matrix condition number of growing theoretical interest. They show that this rescaling achieves favorable theoretical guarantees for certain LP algorithms. We follow up on their work in an experimental manner. First, we have implemented their algorithm, overcoming several engineering obstacles. Next, we have used our implementation to obtain a rescaling of 142 publicly available instances. Finally, we have performed experiments evaluating the effects of the obtained rescalings on the runtime of real-world LP solvers, and we have evaluated their quality with regard to the circuit imbalance measure.
Cite as

Jakub Komárek and Martin Koutecký. Experimental Analysis of LP Scaling Methods Based on Circuit Imbalance Minimization. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{komarek_et_al:LIPIcs.SEA.2024.18,
  author =	{Kom\'{a}rek, Jakub and Kouteck\'{y}, Martin},
  title =	{{Experimental Analysis of LP Scaling Methods Based on Circuit Imbalance Minimization}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.18},
  URN =		{urn:nbn:de:0030-drops-203832},
  doi =		{10.4230/LIPIcs.SEA.2024.18},
  annote =	{Keywords: Linear programming, scaling, circuit imbalance measure}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.15
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.
Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.112
Testing Spreading Behavior in Networks with Arbitrary Topologies

Authors: Augusto Modanese and Yuichi Yoshida

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given the full topology of a network, how hard is it to test if it is evolving according to a local rule or is far from doing so? Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron (ICALP, 2021), we initiate the study of property testing in dynamic environments with arbitrary topologies. Our focus is on the simplest non-trivial rule that can be tested, which corresponds to the 1-BP rule of bootstrap percolation and models a simple spreading behavior: Every "infected" node stays infected forever, and each "healthy" node becomes infected if and only if it has at least one infected neighbor. Our results are subdivided into two main groups: - If we are testing a single time step of evolution, then the query complexity is O(Δ/ε) or Õ(√n/ε) (whichever is smaller), where Δ and n are the maximum degree of a node and the number of vertices in the underlying graph, respectively. We also give lower bounds for both one- and two-sided error testers that match our upper bounds up to Δ = o(√n) and Δ = O(n^{1/3}), respectively. If ε is constant, then the first of these also holds against adaptive testers. - When testing the environment over T time steps, we have two algorithms that need O(Δ^{T-1}/εT) and Õ(|E|/εT) queries, respectively, where E is the set of edges of the underlying graph. All of our algorithms are one-sided error, and all of them are also non-adaptive, with the single exception of the more complex Õ(√n/ε)-query tester for the case T = 2.
Cite as

Augusto Modanese and Yuichi Yoshida. Testing Spreading Behavior in Networks with Arbitrary Topologies. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 112:1-112:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{modanese_et_al:LIPIcs.ICALP.2024.112,
  author =	{Modanese, Augusto and Yoshida, Yuichi},
  title =	{{Testing Spreading Behavior in Networks with Arbitrary Topologies}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{112:1--112:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.112},
  URN =		{urn:nbn:de:0030-drops-202554},
  doi =		{10.4230/LIPIcs.ICALP.2024.112},
  annote =	{Keywords: Property testing, bootstrap percolation, local phenomena, expander graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.32
Two Choices Are Enough for P-LCPs, USOs, and Colorful Tangents

Authors: Michaela Borzechowski, John Fearnley, Spencer Gordon, Rahul Savani, Patrick Schnider, and Simon Weber

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We provide polynomial-time reductions between three search problems from three distinct areas: the P-matrix linear complementarity problem (P-LCP), finding the sink of a unique sink orientation (USO), and a variant of the α-Ham Sandwich problem. For all three settings, we show that "two choices are enough", meaning that the general non-binary version of the problem can be reduced in polynomial time to the binary version. This specifically means that generalized P-LCPs are equivalent to P-LCPs, and grid USOs are equivalent to cube USOs. These results are obtained by showing that both the P-LCP and our α-Ham Sandwich variant are equivalent to a new problem we introduce, P-Lin-Bellman. This problem can be seen as a new tool for formulating problems as P-LCPs.
Cite as

Michaela Borzechowski, John Fearnley, Spencer Gordon, Rahul Savani, Patrick Schnider, and Simon Weber. Two Choices Are Enough for P-LCPs, USOs, and Colorful Tangents. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{borzechowski_et_al:LIPIcs.ICALP.2024.32,
  author =	{Borzechowski, Michaela and Fearnley, John and Gordon, Spencer and Savani, Rahul and Schnider, Patrick and Weber, Simon},
  title =	{{Two Choices Are Enough for P-LCPs, USOs, and Colorful Tangents}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.32},
  URN =		{urn:nbn:de:0030-drops-201751},
  doi =		{10.4230/LIPIcs.ICALP.2024.32},
  annote =	{Keywords: P-LCP, Unique Sink Orientation, \alpha-Ham Sandwich, search complexity, TFNP, UEOPL}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.24
Optimizing Symbol Visibility Through Displacement

Authors: Bernd Gärtner, Vishwas Kalani, Meghana M. Reddy, Wouter Meulemans, Bettina Speckmann, and Miloš Stojaković

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This flexibility can be exploited to reduce symbol overlap, and thereby increase legibility. In this paper we initialize the algorithmic study of optimizing symbol legibility via a limited displacement of the symbols. Specifically, we consider unit square symbols that need to be placed at specified y-coordinates. We optimize the drawing order of the symbols as well as their x-displacement, constrained within a rectangular container, to maximize the minimum visible perimeter over all squares. If the container has width and height at most 2, there is a point that stabs all squares. In this case, we prove that a staircase layout is arbitrarily close to optimality and can be computed in O(nlog n) time. If the width is at most 2, there is a vertical line that stabs all squares, and in this case, we give a 2-approximation algorithm (assuming fixed container height) that runs in O(nlog n) time. As a minimum visible perimeter of 2 is always trivially achievable, we measure this approximation with respect to the visible perimeter exceeding 2. We show that, despite its simplicity, the algorithm gives asymptotically optimal results for certain instances.
Cite as

Bernd Gärtner, Vishwas Kalani, Meghana M. Reddy, Wouter Meulemans, Bettina Speckmann, and Miloš Stojaković. Optimizing Symbol Visibility Through Displacement. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gartner_et_al:LIPIcs.SWAT.2024.24,
  author =	{G\"{a}rtner, Bernd and Kalani, Vishwas and M. Reddy, Meghana and Meulemans, Wouter and Speckmann, Bettina and Stojakovi\'{c}, Milo\v{s}},
  title =	{{Optimizing Symbol Visibility Through Displacement}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.24},
  URN =		{urn:nbn:de:0030-drops-200643},
  doi =		{10.4230/LIPIcs.SWAT.2024.24},
  annote =	{Keywords: symbol placement, visibility, jittering, stacking order}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.69
A Subexponential Algorithm for ARRIVAL

Authors: Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
The ARRIVAL problem is to decide the fate of a train moving along the edges of a directed graph, according to a simple (deterministic) pseudorandom walk. The problem is in NP∩coNP but not known to be in 𝖯. The currently best algorithms have runtime 2^Θ(n) where n is the number of vertices. This is not much better than just performing the pseudorandom walk. We develop a subexponential algorithm with runtime 2^O(√nlog n). We also give a polynomial-time algorithm if the graph is almost acyclic. Both results are derived from a new general approach to solve ARRIVAL instances.
Cite as

Bernd Gärtner, Sebastian Haslebacher, and Hung P. Hoang. A Subexponential Algorithm for ARRIVAL. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gartner_et_al:LIPIcs.ICALP.2021.69,
  author =	{G\"{a}rtner, Bernd and Haslebacher, Sebastian and Hoang, Hung P.},
  title =	{{A Subexponential Algorithm for ARRIVAL}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.69},
  URN =		{urn:nbn:de:0030-drops-141387},
  doi =		{10.4230/LIPIcs.ICALP.2021.69},
  annote =	{Keywords: Pseudorandom walks, reachability, graph games, switching systems}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.5
Two Phase Transitions in Two-Way Bootstrap Percolation

Authors: Ahad N. Zehmakan

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
Consider a graph G and an initial random configuration, where each node is black with probability p and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least r black neighbors and white otherwise. We prove that this basic process exhibits a threshold behavior with two phase transitions when the underlying graph is a d-dimensional torus and identify the threshold values.
Cite as

Ahad N. Zehmakan. Two Phase Transitions in Two-Way Bootstrap Percolation. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{zehmakan:LIPIcs.ISAAC.2019.5,
  author =	{Zehmakan, Ahad N.},
  title =	{{Two Phase Transitions in Two-Way Bootstrap Percolation}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.5},
  URN =		{urn:nbn:de:0030-drops-115017},
  doi =		{10.4230/LIPIcs.ISAAC.2019.5},
  annote =	{Keywords: bootstrap percolation, cellular automata, phase transition, d-dimensional torus, r-threshold model, biased majority}
}
Document
Vision Paper
DOI: 10.4230/LIPIcs.COSIT.2019.19
The Future of Geographic Information Displays from GIScience, Cartographic, and Cognitive Science Perspectives (Vision Paper)

Authors: Tyler Thrash, Sara Lanini-Maggi, Sara I. Fabrikant, Sven Bertel, Annina Brügger, Sascha Credé, Cao Tri Do, Georg Gartner, Haosheng Huang, Stefan Münzer, and Kai-Florian Richter

Published in: LIPIcs, Volume 142, 14th International Conference on Spatial Information Theory (COSIT 2019)

Abstract
With the development of modern geovisual analytics tools, several researchers have emphasized the importance of understanding users' cognitive, perceptual, and affective tendencies for supporting spatial decisions with geographic information displays (GIDs). However, most recent technological developments have focused on support for navigation in terms of efficiency and effectiveness while neglecting the importance of spatial learning. In the present paper, we will envision the future of GIDs that also support spatial learning in the context of large-scale navigation. Specifically, we will illustrate the manner in which GIDs have been (in the past) and might be (in the future) designed to be context-responsive, personalized, and supportive for active spatial learning from three different perspectives (i.e., GIScience, cartography, and cognitive science). We will also explain why this approach is essential for preventing the technological infantilizing of society (i.e., the reduction of our capacity to make decisions without technological assistance). Although these issues are common to nearly all emerging digital technologies, we argue that these issues become especially relevant in consideration of a person’s current and future locations.
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Tyler Thrash, Sara Lanini-Maggi, Sara I. Fabrikant, Sven Bertel, Annina Brügger, Sascha Credé, Cao Tri Do, Georg Gartner, Haosheng Huang, Stefan Münzer, and Kai-Florian Richter. The Future of Geographic Information Displays from GIScience, Cartographic, and Cognitive Science Perspectives (Vision Paper). In 14th International Conference on Spatial Information Theory (COSIT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 142, pp. 19:1-19:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{thrash_et_al:LIPIcs.COSIT.2019.19,
  author =	{Thrash, Tyler and Lanini-Maggi, Sara and Fabrikant, Sara I. and Bertel, Sven and Br\"{u}gger, Annina and Cred\'{e}, Sascha and Do, Cao Tri and Gartner, Georg and Huang, Haosheng and M\"{u}nzer, Stefan and Richter, Kai-Florian},
  title =	{{The Future of Geographic Information Displays from GIScience, Cartographic, and Cognitive Science Perspectives}},
  booktitle =	{14th International Conference on Spatial Information Theory (COSIT 2019)},
  pages =	{19:1--19:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-115-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{142},
  editor =	{Timpf, Sabine and Schlieder, Christoph and Kattenbeck, Markus and Ludwig, Bernd and Stewart, Kathleen},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2019.19},
  URN =		{urn:nbn:de:0030-drops-111113},
  doi =		{10.4230/LIPIcs.COSIT.2019.19},
  annote =	{Keywords: visual displays, geographic information, cartography, cognitive science}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.38
The Crossing Tverberg Theorem

Authors: Radoslav Fulek, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner

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

Abstract
The Tverberg theorem is one of the cornerstones of discrete geometry. It states that, given a set X of at least (d+1)(r-1)+1 points in R^d, one can find a partition X=X_1 cup ... cup X_r of X, such that the convex hulls of the X_i, i=1,...,r, all share a common point. In this paper, we prove a strengthening of this theorem that guarantees a partition which, in addition to the above, has the property that the boundaries of full-dimensional convex hulls have pairwise nonempty intersections. Possible generalizations and algorithmic aspects are also discussed. As a concrete application, we show that any n points in the plane in general position span floor[n/3] vertex-disjoint triangles that are pairwise crossing, meaning that their boundaries have pairwise nonempty intersections; this number is clearly best possible. A previous result of Alvarez-Rebollar et al. guarantees floor[n/6] pairwise crossing triangles. Our result generalizes to a result about simplices in R^d,d >=2.
Cite as

Radoslav Fulek, Bernd Gärtner, Andrey Kupavskii, Pavel Valtr, and Uli Wagner. The Crossing Tverberg Theorem. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 38:1-38:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{fulek_et_al:LIPIcs.SoCG.2019.38,
  author =	{Fulek, Radoslav and G\"{a}rtner, Bernd and Kupavskii, Andrey and Valtr, Pavel and Wagner, Uli},
  title =	{{The Crossing Tverberg Theorem}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{38:1--38:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.38},
  URN =		{urn:nbn:de:0030-drops-104423},
  doi =		{10.4230/LIPIcs.SoCG.2019.38},
  annote =	{Keywords: Discrete geometry, Tverberg theorem, Crossing Tverberg theorem}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.60
ARRIVAL: Next Stop in CLS

Authors: Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study the computational complexity of Arrival, a zero-player game on n-vertex switch graphs introduced by Dohrau, Gärtner, Kohler, Matousek, and Welzl. They showed that the problem of deciding termination of this game is contained in NP n coNP. Karthik C. S. recently introduced a search variant of Arrival and showed that it is in the complexity class PLS. In this work, we significantly improve the known upper bounds for both the decision and the search variants of Arrival. First, we resolve a question suggested by Dohrau et al. and show that the decision variant of Arrival is in UP n coUP. Second, we prove that the search variant of Arrival is contained in CLS. Third, we give a randomized O(1.4143^n)-time algorithm to solve both variants. Our main technical contributions are (a) an efficiently verifiable characterization of the unique witness for termination of the Arrival game, and (b) an efficient way of sampling from the state space of the game. We show that the problem of finding the unique witness is contained in CLS, whereas it was previously conjectured to be FPSPACE-complete. The efficient sampling procedure yields the first algorithm for the problem that has expected runtime O(c^n) with c<2.
Cite as

Bernd Gärtner, Thomas Dueholm Hansen, Pavel Hubácek, Karel Král, Hagar Mosaad, and Veronika Slívová. ARRIVAL: Next Stop in CLS. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 60:1-60:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gartner_et_al:LIPIcs.ICALP.2018.60,
  author =	{G\"{a}rtner, Bernd and Hansen, Thomas Dueholm and Hub\'{a}cek, Pavel and Kr\'{a}l, Karel and Mosaad, Hagar and Sl{\'\i}vov\'{a}, Veronika},
  title =	{{ARRIVAL: Next Stop in CLS}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{60:1--60:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.60},
  URN =		{urn:nbn:de:0030-drops-90641},
  doi =		{10.4230/LIPIcs.ICALP.2018.60},
  annote =	{Keywords: CLS, switch graphs, zero-player game, UP n coUP}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.30
The Niceness of Unique Sink Orientations

Authors: Bernd Gärtner and Antonis Thomas

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
Random Edge is the most natural randomized pivot rule for the simplex algorithm. Considerable progress has been made recently towards fully understanding its behavior. Back in 2001, Welzl introduced the concepts of reachmaps and niceness of Unique Sink Orientations (USO), in an effort to better understand the behavior of Random Edge. In this paper, we initiate the systematic study of these concepts. We settle the questions that were asked by Welzl about the niceness of (acyclic) USO. Niceness implies natural upper bounds for Random Edge and we provide evidence that these are tight or almost tight in many interesting cases. Moreover, we show that Random Edge is polynomial on at least n^{Omega(2^n)} many (possibly cyclic) USO. As a bonus, we describe a derandomization of Random Edge which achieves the same asymptotic upper bounds with respect to niceness.
Cite as

Bernd Gärtner and Antonis Thomas. The Niceness of Unique Sink Orientations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{gartner_et_al:LIPIcs.APPROX-RANDOM.2016.30,
  author =	{G\"{a}rtner, Bernd and Thomas, Antonis},
  title =	{{The Niceness of Unique Sink Orientations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.30},
  URN =		{urn:nbn:de:0030-drops-66538},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.30},
  annote =	{Keywords: random edge, unique sink orientation, random walk, reachmap, niceness}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.40
Random Sampling with Removal

Authors: Bernd Gärtner, Johannes Lengler, and May Szedlák

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
Random sampling is a classical tool in constrained optimization. Under favorable conditions, the optimal solution subject to a small subset of randomly chosen constraints violates only a small subset of the remaining constraints. Here we study the following variant that we call random sampling with removal: suppose that after sampling the subset, we remove a fixed number of constraints from the sample, according to an arbitrary rule. Is it still true that the optimal solution of the reduced sample violates only a small subset of the constraints? The question naturally comes up in situations where the solution subject to the sampled constraints is used as an approximate solution to the original problem. In this case, it makes sense to improve cost and volatility of the sample solution by removing some of the constraints that appear most restricting. At the same time, the approximation quality (measured in terms of violated constraints) should remain high. We study random sampling with removal in a generalized, completely abstract setting where we assign to each subset R of the constraints an arbitrary set V(R) of constraints disjoint from R; in applications, V(R) corresponds to the constraints violated by the optimal solution subject to only the constraints in R. Furthermore, our results are parametrized by the dimension d, i.e., we assume that every set R has a subset B of size at most d with the same set of violated constraints. This is the first time this generalized setting is studied. In this setting, we prove matching upper and lower bounds for the expected number of constraints violated by a random sample, after the removal of k elements. For a large range of values of k, the new upper bounds improve the previously best bounds for LP-type problems, which moreover had only been known in special cases. We show that this bound on special LP-type problems, can be derived in the much more general setting of violator spaces, and with very elementary proofs.
Cite as

Bernd Gärtner, Johannes Lengler, and May Szedlák. Random Sampling with Removal. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{gartner_et_al:LIPIcs.SoCG.2016.40,
  author =	{G\"{a}rtner, Bernd and Lengler, Johannes and Szedl\'{a}k, May},
  title =	{{Random Sampling with Removal}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.40},
  URN =		{urn:nbn:de:0030-drops-59328},
  doi =		{10.4230/LIPIcs.SoCG.2016.40},
  annote =	{Keywords: LP-type problem, violator space, random sampling, sampling with removal}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.315
Combinatorial Redundancy Detection

Authors: Komei Fukuda, Bernd Gärtner, and May Szedlák

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs) in dictionary form, given by n equality constraints in n+d variables, where the variables are constrained to be nonnegative. A variable x_r is called redundant, if after removing its nonnegativity constraint the LP still has the same feasible region. The time needed to solve such an LP is denoted by LP(n,d). It is easy to see that solving n+d LPs of the above size is sufficient to detect all redundancies. The currently fastest practical method is the one by Clarkson: it solves n+d linear programs, but each of them has at most s variables, where s is the number of nonredundant constraints. In the first part we show that knowing all of the finitely many dictionaries of the LP is sufficient for the purpose of redundancy detection. A dictionary is a matrix that can be thought of as an enriched encoding of a vertex in the LP. Moreover - and this is the combinatorial aspect - it is enough to know only the signs of the entries, the actual values do not matter. Concretely we show that for any variable x_r one can find a dictionary, such that its sign pattern is either a redundancy or nonredundancy certificate for x_r. In the second part we show that considering only the sign patterns of the dictionary, there is an output sensitive algorithm of running time of order d (n+d) s^{d-1} LP(s,d) + d s^{d} LP(n,d) to detect all redundancies. In the case where all constraints are in general position, the running time is of order s LP(n,d) + (n+d) LP(s,d), which is essentially the running time of the Clarkson method. Our algorithm extends naturally to a more general setting of arrangements of oriented topological hyperplane arrangements.
Cite as

Komei Fukuda, Bernd Gärtner, and May Szedlák. Combinatorial Redundancy Detection. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 315-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{fukuda_et_al:LIPIcs.SOCG.2015.315,
  author =	{Fukuda, Komei and G\"{a}rtner, Bernd and Szedl\'{a}k, May},
  title =	{{Combinatorial Redundancy Detection}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{315--328},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.315},
  URN =		{urn:nbn:de:0030-drops-51434},
  doi =		{10.4230/LIPIcs.SOCG.2015.315},
  annote =	{Keywords: system of linear inequalities, redundancy removal, linear programming, output sensitive algorithm, Clarkson’s method}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.341
The Complexity of Recognizing Unique Sink Orientations

Authors: Bernd Gärtner and Antonis Thomas

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
Given a Boolean Circuit with n inputs and n outputs, we want to decide if it represents a Unique Sink Orientation (USO). USOs are useful combinatorial objects that serve as abstraction of many relevant optimization problems. We prove that recognizing a USO is coNP-complete. However, the situation appears to be more complicated for recognizing acyclic USOs. Firstly, we give a construction to prove that there exist cyclic USOs where the smallest cycle is of superpolynomial size. This implies that the straightforward representation of a cycle (i.e. by a list of vertices) does not make up for a coNP certificate. Inspired by this fact, we investigate the connection of recognizing an acyclic USO to PSPACE and we prove that the problem is PSPACE-complete.
Cite as

Bernd Gärtner and Antonis Thomas. The Complexity of Recognizing Unique Sink Orientations. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 341-353, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{gartner_et_al:LIPIcs.STACS.2015.341,
  author =	{G\"{a}rtner, Bernd and Thomas, Antonis},
  title =	{{The Complexity of Recognizing Unique Sink Orientations}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{341--353},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.341},
  URN =		{urn:nbn:de:0030-drops-49252},
  doi =		{10.4230/LIPIcs.STACS.2015.341},
  annote =	{Keywords: complexity, recognizing, unique sink orientations, coNP, PSPACE}
}
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