8 Search Results for "Silveira, Rodrigo I."

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.SEA.2024.23
Engineering A* Search for the Flip Distance of Plane Triangulations

Authors: Philip Mayer and Petra Mutzel

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

Abstract
The flip distance for two triangulations of a point set is defined as the smallest number of edge flips needed to transform one triangulation into another, where an edge flip is the act of replacing an edge of a triangulation by a different edge such that the result remains a triangulation. We adapt and engineer a sophisticated A* search algorithm acting on the so-called flip graph. In particular, we prove that previously proposed lower bounds for the flip distance form consistent heuristics for A* and show that they can be computed efficiently using dynamic algorithms. As an alternative approach, we present an integer linear program (ILP) for the flip distance problem. We experimentally evaluate our approaches on a new real-world benchmark data set based on an application in geodesy, namely sea surface reconstruction. Our evaluation reveals that A* search consistently outperforms our ILP formulation as well as a naive baseline, which is bidirectional breadth-first search. In particular, the runtime of our approach improves upon the baseline by more than two orders of magnitude. Furthermore, our A* search successfully solves most of the considered sea surface instances with up to 41 points. This is a substantial improvement compared to the baseline, which struggles with subsets of the real-world data of size 25. Lastly, to allow the consideration of global sea level data, we developed a decomposition-based heuristic for the flip distance. In our experiments it yields optimal flip distance values for most of the considered sea level data and it can be applied to large data sets due to its fast runtime.
Cite as

Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mayer_et_al:LIPIcs.SEA.2024.23,
  author =	{Mayer, Philip and Mutzel, Petra},
  title =	{{Engineering A* Search for the Flip Distance of Plane Triangulations}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{23:1--23:20},
  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.2024.23},
  URN =		{urn:nbn:de:0030-drops-203887},
  doi =		{10.4230/LIPIcs.SEA.2024.23},
  annote =	{Keywords: Computational Geometry, Triangulations, Flip Distance, A-star Search, Integer Linear Programming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.22
Two-Sets Cut-Uncut on Planar Graphs

Authors: Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach, and Tuukka Korhonen

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

Abstract
We study Two-Sets Cut-Uncut on planar graphs. Therein, one is given an undirected planar graph G and two disjoint sets S and T of vertices as input. The question is, what is the minimum number of edges to remove from G, such that all vertices in S are separated from all vertices in T, while maintaining that every vertex in S, and respectively in T, stays in the same connected component. We show that this problem can be solved in 2^{|S|+|T|} n^𝒪(1) time with a one-sided-error randomized algorithm. Our algorithm implies a polynomial-time algorithm for the network diversion problem on planar graphs, which resolves an open question from the literature. More generally, we show that Two-Sets Cut-Uncut is fixed-parameter tractable when parameterized by the number r of faces in a planar embedding covering the terminals S ∪ T, by providing a 2^𝒪(r) n^𝒪(1)-time algorithm.
Cite as

Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach, and Tuukka Korhonen. Two-Sets Cut-Uncut on Planar Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bentert_et_al:LIPIcs.ICALP.2024.22,
  author =	{Bentert, Matthias and Drange, P\r{a}l Gr{\o}n\r{a}s and Fomin, Fedor V. and Golovach, Petr A. and Korhonen, Tuukka},
  title =	{{Two-Sets Cut-Uncut on Planar Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{22:1--22:18},
  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.2024.22},
  URN =		{urn:nbn:de:0030-drops-201654},
  doi =		{10.4230/LIPIcs.ICALP.2024.22},
  annote =	{Keywords: planar graphs, cut-uncut, group-constrained paths}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.48
Shortest Paths in Portalgons

Authors: Maarten Löffler, Tim Ophelders, Rodrigo I. Silveira, and Frank Staals

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
Any surface that is intrinsically polyhedral can be represented by a collection of simple polygons (fragments), glued along pairs of equally long oriented edges, where each fragment is endowed with the geodesic metric arising from its Euclidean metric. We refer to such a representation as a portalgon, and we call two portalgons equivalent if the surfaces they represent are isometric. We analyze the complexity of shortest paths. We call a fragment happy if any shortest path on the portalgon visits it at most a constant number of times. A portalgon is happy if all of its fragments are happy. We present an efficient algorithm to compute shortest paths on happy portalgons. The number of times that a shortest path visits a fragment is unbounded in general. We contrast this by showing that the intrinsic Delaunay triangulation of any polyhedral surface corresponds to a happy portalgon. Since computing the intrinsic Delaunay triangulation may be inefficient, we provide an efficient algorithm to compute happy portalgons for a restricted class of portalgons.
Cite as

Maarten Löffler, Tim Ophelders, Rodrigo I. Silveira, and Frank Staals. Shortest Paths in Portalgons. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{loffler_et_al:LIPIcs.SoCG.2023.48,
  author =	{L\"{o}ffler, Maarten and Ophelders, Tim and Silveira, Rodrigo I. and Staals, Frank},
  title =	{{Shortest Paths in Portalgons}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.48},
  URN =		{urn:nbn:de:0030-drops-178980},
  doi =		{10.4230/LIPIcs.SoCG.2023.48},
  annote =	{Keywords: Polyhedral surfaces, shortest paths, geodesic distance, Delaunay triangulation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.29
Efficient Fréchet Distance Queries for Segments

Authors: Maike Buchin, Ivor van der Hoog, Tim Ophelders, Lena Schlipf, Rodrigo I. Silveira, and Frank Staals

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study the problem of constructing a data structure that can store a two-dimensional polygonal curve P, such that for any query segment ab one can efficiently compute the Fréchet distance between P and ab. First we present a data structure of size O(n log n) that can compute the Fréchet distance between P and a horizontal query segment ab in O(log n) time, where n is the number of vertices of P. In comparison to prior work, this significantly reduces the required space. We extend the type of queries allowed, as we allow a query to be a horizontal segment ab together with two points s, t ∈ P (not necessarily vertices), and ask for the Fréchet distance between ab and the curve of P in between s and t. Using O(nlog²n) storage, such queries take O(log³ n) time, simplifying and significantly improving previous results. We then generalize our results to query segments of arbitrary orientation. We present an O(nk^{3+ε}+n²) size data structure, where k ∈ [1,n] is a parameter the user can choose, and ε > 0 is an arbitrarily small constant, such that given any segment ab and two points s, t ∈ P we can compute the Fréchet distance between ab and the curve of P in between s and t in O((n/k)log²n+log⁴ n) time. This is the first result that allows efficient exact Fréchet distance queries for arbitrarily oriented segments. We also present two applications of our data structure. First, we show that our data structure allows us to compute a local δ-simplification (with respect to the Fréchet distance) of a polygonal curve in O(n^{5/2+ε}) time, improving a previous O(n³) time algorithm. Second, we show that we can efficiently find a translation of an arbitrary query segment ab that minimizes the Fréchet distance with respect to a subcurve of P.
Cite as

Maike Buchin, Ivor van der Hoog, Tim Ophelders, Lena Schlipf, Rodrigo I. Silveira, and Frank Staals. Efficient Fréchet Distance Queries for Segments. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{buchin_et_al:LIPIcs.ESA.2022.29,
  author =	{Buchin, Maike and van der Hoog, Ivor and Ophelders, Tim and Schlipf, Lena and Silveira, Rodrigo I. and Staals, Frank},
  title =	{{Efficient Fr\'{e}chet Distance Queries for Segments}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.29},
  URN =		{urn:nbn:de:0030-drops-169671},
  doi =		{10.4230/LIPIcs.ESA.2022.29},
  annote =	{Keywords: Computational Geometry, Data Structures, Fr\'{e}chet distance}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2021.II.10
Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds

Authors: Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, and Frank Staals

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

Abstract
An important task in terrain analysis is computing viewsheds. A viewshed is the union of all the parts of the terrain that are visible from a given viewpoint or set of viewpoints. The complexity of a viewshed can vary significantly depending on the terrain topography and the viewpoint position. In this work we study a new topographic attribute, the prickliness, that measures the number of local maxima in a terrain from all possible angles of view. We show that the prickliness effectively captures the potential of terrains to have high complexity viewsheds. We present near-optimal algorithms to compute it for TIN terrains, and efficient approximate algorithms for raster DEMs. We validate the usefulness of the prickliness attribute with experiments in a large set of real terrains.
Cite as

Ankush Acharyya, Ramesh K. Jallu, Maarten Löffler, Gert G.T. Meijer, Maria Saumell, Rodrigo I. Silveira, and Frank Staals. Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part II. Leibniz International Proceedings in Informatics (LIPIcs), Volume 208, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{acharyya_et_al:LIPIcs.GIScience.2021.II.10,
  author =	{Acharyya, Ankush and Jallu, Ramesh K. and L\"{o}ffler, Maarten and Meijer, Gert G.T. and Saumell, Maria and Silveira, Rodrigo I. and Staals, Frank},
  title =	{{Terrain Prickliness: Theoretical Grounds for High Complexity Viewsheds}},
  booktitle =	{11th International Conference on Geographic Information Science (GIScience 2021) - Part II},
  pages =	{10:1--10:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.II.10},
  URN =		{urn:nbn:de:0030-drops-147697},
  doi =		{10.4230/LIPIcs.GIScience.2021.II.10},
  annote =	{Keywords: Digital elevation model, Triangulated irregular network, Viewshed complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.15
Computing Optimal Shortcuts for Networks

Authors: Delia Garijo, Alberto Márquez, Natalia Rodríguez, and Rodrigo I. Silveira

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable attention recently, mostly for discrete variants of the problem. We study a fully continuous setting, where all points on the network and the inserted segment must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model, together with several results for networks that are paths, restricted to two types of shortcuts: shortcuts with a fixed orientation and simple shortcuts.
Cite as

Delia Garijo, Alberto Márquez, Natalia Rodríguez, and Rodrigo I. Silveira. Computing Optimal Shortcuts for Networks. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 15:1-15:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{garijo_et_al:LIPIcs.ISAAC.2018.15,
  author =	{Garijo, Delia and M\'{a}rquez, Alberto and Rodr{\'\i}guez, Natalia and Silveira, Rodrigo I.},
  title =	{{Computing Optimal Shortcuts for Networks}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{15:1--15:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.15},
  URN =		{urn:nbn:de:0030-drops-99634},
  doi =		{10.4230/LIPIcs.ISAAC.2018.15},
  annote =	{Keywords: graph augmentation, shortcut, diameter, geometric graph}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.281
Space-Time Trade-offs for Stack-Based Algorithms

Authors: Luis Barba, Matias Korman, Stefan Langerman, Rodrigo I. Silveira, and Kunihiko Sadakane

Published in: LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

Abstract
In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space bottleneck is a stack into memory-constrained algorithms. Given an algorithm A that runs in O(n) time using a stack of length Theta(n), we can modify it so that it runs in O(n^2/2^s) time using a workspace of O(s) variables (for any s \in o(log n)) or O(n log n/log p)$ time using O(p log n/log p) variables (for any 2 <= p <= n). We also show how the technique can be applied to solve various geometric problems, namely computing the convex hull of a simple polygon, a triangulation of a monotone polygon, the shortest path between two points inside a monotone polygon, 1-dimensional pyramid approximation of a 1-dimensional vector, and the visibility profile of a point inside a simple polygon. Our approach exceeds or matches the best-known results for these problems in constant-workspace models (when they exist), and gives a trade-off between the size of the workspace and running time. To the best of our knowledge, this is the first general framework for obtaining memory-constrained algorithms.
Cite as

Luis Barba, Matias Korman, Stefan Langerman, Rodrigo I. Silveira, and Kunihiko Sadakane. Space-Time Trade-offs for Stack-Based Algorithms. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 281-292, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{barba_et_al:LIPIcs.STACS.2013.281,
  author =	{Barba, Luis and Korman, Matias and Langerman, Stefan and Silveira, Rodrigo I. and Sadakane, Kunihiko},
  title =	{{Space-Time Trade-offs for Stack-Based Algorithms}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{281--292},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Portier, Natacha and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.281},
  URN =		{urn:nbn:de:0030-drops-39411},
  doi =		{10.4230/LIPIcs.STACS.2013.281},
  annote =	{Keywords: space-time trade-off, constant workspace, stack algorithms}
}
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