5 Search Results for "Kulik, Lars"

Document
DOI: 10.4230/LIPIcs.ESA.2024.104
Solving Directed Multiway Cut Faster Than 2ⁿ

Authors: Mingyu Xiao

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
In the Directed Multiway Cut problem, we are given a directed graph G = (V,E) and a subset T ⊆ V, called the terminal set. The aim is to find a minimum sized set S ⊆ V⧵ T, such that after deleting S, no directed path exists from one terminal to another terminal in the remaining graph. It has been an open question whether Directed Multiway Cut can be solved faster than the trivial running-time bound O^*(2^{|V|}). In this paper, we provide a positive answer to this question, presenting an algorithm with a running-time bound O(1.9967^{|V|}).
Cite as

Mingyu Xiao. Solving Directed Multiway Cut Faster Than 2ⁿ. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 104:1-104:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{xiao:LIPIcs.ESA.2024.104,
  author =	{Xiao, Mingyu},
  title =	{{Solving Directed Multiway Cut Faster Than 2ⁿ}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{104:1--104:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.104},
  URN =		{urn:nbn:de:0030-drops-211758},
  doi =		{10.4230/LIPIcs.ESA.2024.104},
  annote =	{Keywords: Exact Algorithms, Parameterized Algorithms, Directed Multiway Cut, Directed Multicut, Directed Graphs}
}
Document
DOI: 10.4230/LIPIcs.COSIT.2024.4
Qualitative Formalization of a Curve on a Two-Dimensional Plane

Authors: Kazuko Takahashi

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

Abstract
We propose a theoretical framework for qualitative spatial representation and reasoning about curves on a two-dimensional plane. We regard a curve as a sequence of segments, each of which has its own direction and convexity, and give a symbolic expression to it. We propose a reasoning method on this symbolic expression; when only a few segments of a curve are visible, we find missing segments by connecting them to create a global smooth continuous curve. In addition, we discuss whether the shape of the created curve can represent that of a real object; if the curve forms a spiral, such a curve is sometimes not appropriate as a border of an object. We show a method that judges the appropriateness of a curve, by considering the orientations of the segments.
Cite as

Kazuko Takahashi. Qualitative Formalization of a Curve on a Two-Dimensional Plane. In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{takahashi:LIPIcs.COSIT.2024.4,
  author =	{Takahashi, Kazuko},
  title =	{{Qualitative Formalization of a Curve on a Two-Dimensional Plane}},
  booktitle =	{16th International Conference on Spatial Information Theory (COSIT 2024)},
  pages =	{4:1--4:19},
  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.2024.4},
  URN =		{urn:nbn:de:0030-drops-208193},
  doi =		{10.4230/LIPIcs.COSIT.2024.4},
  annote =	{Keywords: qualitative spatial reasoning, knowledge representation, logical reasoning, shape information}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.26
Capturing the Shape of a Point Set with a Line Segment

Authors: Nathan van Beusekom, Marc van Kreveld, Max van Mulken, Marcel Roeloffzen, Bettina Speckmann, and Jules Wulms

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Detecting location-correlated groups in point sets is an important task in a wide variety of applications areas. In addition to merely detecting such groups, the group’s shape carries meaning as well. In this paper, we represent a group’s shape using a simple geometric object, a line segment. Specifically, given a radius r, we say a line segment is representative of a point set P of n points if it is within distance r of each point p ∈ P. We aim to find the shortest such line segment. This problem is equivalent to stabbing a set of circles of radius r using the shortest line segment. We describe an algorithm to find the shortest representative segment in O(n log h + h log³h) time, where h is the size of the convex hull of P. Additionally, we show how to maintain a stable approximation of the shortest representative segment when the points in P move.
Cite as

Nathan van Beusekom, Marc van Kreveld, Max van Mulken, Marcel Roeloffzen, Bettina Speckmann, and Jules Wulms. Capturing the Shape of a Point Set with a Line Segment. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{vanbeusekom_et_al:LIPIcs.MFCS.2024.26,
  author =	{van Beusekom, Nathan and van Kreveld, Marc and van Mulken, Max and Roeloffzen, Marcel and Speckmann, Bettina and Wulms, Jules},
  title =	{{Capturing the Shape of a Point Set with a Line Segment}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.26},
  URN =		{urn:nbn:de:0030-drops-205820},
  doi =		{10.4230/LIPIcs.MFCS.2024.26},
  annote =	{Keywords: Shape descriptor, Stabbing, Rotating calipers}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.19
Algorithms for Gradual Polyline Simplification

Authors: Nick Krumbholz, Stefan Funke, Peter Schäfer, and Sabine Storandt

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

Abstract
Displaying line data is important in many visualization applications, and especially in the context of interactive geographical and cartographic visualization. When rendering linear features as roads, rivers or movement data on zoomable maps, the challenge is to display the data in an appropriate level of detail. A too detailed representation results in slow rendering and cluttered maps, while a too coarse representation might miss important data aspects. In this paper, we propose the gradual line simplification (GLS) problem, which aims to compute a fine-grained succession of consistent simplifications of a given input polyline with certain quality guarantees. The core concept of gradual simplification is to iteratively remove points from the polyline to obtain increasingly coarser representations. We devise two objective functions to guide this simplification process and present dynamic programs that compute the optimal solutions in 𝒪(n³) for an input line with n points. For practical application to large inputs, we also devise significantly faster greedy algorithms that provide constant factor guarantees for both problem variants at once. In an extensive experimental study on real-world data, we demonstrate that our algorithms are capable of producing simplification sequences of high quality within milliseconds on polylines consisting of over half a million points.
Cite as

Nick Krumbholz, Stefan Funke, Peter Schäfer, and Sabine Storandt. Algorithms for Gradual Polyline Simplification. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{krumbholz_et_al:LIPIcs.SEA.2024.19,
  author =	{Krumbholz, Nick and Funke, Stefan and Sch\"{a}fer, Peter and Storandt, Sabine},
  title =	{{Algorithms for Gradual Polyline Simplification}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{19:1--19:18},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-203847},
  doi =		{10.4230/LIPIcs.SEA.2024.19},
  annote =	{Keywords: Polyline simplification, Progressive simplification, Fr\'{e}chet distance}
}
Document
DOI: 10.4230/LIPIcs.GISCIENCE.2018.14
Continuous Obstructed Detour Queries

Authors: Rudra Ranajee Saha, Tanzima Hashem, Tasmia Shahriar, and Lars Kulik

Published in: LIPIcs, Volume 114, 10th International Conference on Geographic Information Science (GIScience 2018)

Abstract
In this paper, we introduce Continuous Obstructed Detour (COD) Queries, a novel query type in spatial databases. COD queries continuously return the nearest point of interests (POIs) such as a restaurant, an ATM machine and a pharmacy with respect to the current location and the fixed destination of a moving pedestrian in presence of obstacles like a fence, a lake or a private building. The path towards a destination is typically not predetermined and the nearest POIs can change over time with the change of a pedestrian's current location towards a fixed destination. The distance to a POI is measured as the summation of the obstructed distance from the pedestrian's current location to the POI and the obstructed distance from the POI to the pedestrian's destination. Evaluating the query for every change of a pedestrian's location would incur extremely high processing overhead. We develop an efficient solution for COD queries and verify the effectiveness and efficiency of our solution in experiments.
Cite as

Rudra Ranajee Saha, Tanzima Hashem, Tasmia Shahriar, and Lars Kulik. Continuous Obstructed Detour Queries. In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{saha_et_al:LIPIcs.GISCIENCE.2018.14,
  author =	{Saha, Rudra Ranajee and Hashem, Tanzima and Shahriar, Tasmia and Kulik, Lars},
  title =	{{Continuous Obstructed Detour Queries}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-083-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{114},
  editor =	{Winter, Stephan and Griffin, Amy and Sester, Monika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.14},
  URN =		{urn:nbn:de:0030-drops-93426},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.14},
  annote =	{Keywords: Obstacles Continuous Detour Queries Spatial Databases}
}
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