8 Search Results for "Schulz, André"

Document
DOI: 10.4230/LIPIcs.SEA.2023.10
Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover

Authors: Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ⊆ V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.
Cite as

Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 10:1-10:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{angrick_et_al:LIPIcs.SEA.2023.10,
  author =	{Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Ki{\ss}ig, Otto and Schmidt, Jonas and Wendt, Leo},
  title =	{{Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.10},
  URN =		{urn:nbn:de:0030-drops-183602},
  doi =		{10.4230/LIPIcs.SEA.2023.10},
  annote =	{Keywords: directed feedback vertex set, vertex cover, reduction rules}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.44
On the Geometric Thickness of 2-Degenerate Graphs

Authors: Rahul Jain, Marco Ricci, Jonathan Rollin, and André Schulz

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

Abstract
A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric arboricity, and hence the geometric thickness, of 2-degenerate graphs is at most 4. On the other hand, we show that there are 2-degenerate graphs that do not admit any straight-line drawing with a decomposition of the edge set into 2 plane graphs. That is, there are 2-degenerate graphs with geometric thickness, and hence geometric arboricity, at least 3. This answers two questions posed by Eppstein [Separating thickness from geometric thickness. In Towards a Theory of Geometric Graphs, vol. 342 of Contemp. Math., AMS, 2004].
Cite as

Rahul Jain, Marco Ricci, Jonathan Rollin, and André Schulz. On the Geometric Thickness of 2-Degenerate Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 44:1-44:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jain_et_al:LIPIcs.SoCG.2023.44,
  author =	{Jain, Rahul and Ricci, Marco and Rollin, Jonathan and Schulz, Andr\'{e}},
  title =	{{On the Geometric Thickness of 2-Degenerate Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{44:1--44:15},
  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.2023.44},
  URN =		{urn:nbn:de:0030-drops-178946},
  doi =		{10.4230/LIPIcs.SoCG.2023.44},
  annote =	{Keywords: Degeneracy, geometric thickness, geometric arboricity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.25
Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time

Authors: Hjalmar Schulz, André Nichterlein, Rolf Niedermeier, and Christopher Weyand

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
Given an undirected graph, the task in Cluster Editing is to insert and delete a minimum number of edges to obtain a cluster graph, that is, a disjoint union of cliques. In the weighted variant each vertex pair comes with a weight and the edge modifications have to be of minimum overall weight. In this work, we provide the first polynomial-time algorithm to apply the following data reduction rule of Böcker et al. [Algorithmica, 2011] for Weighted Cluster Editing: For a graph G = (V,E), merge a vertex set S ⊆ V into a single vertex if the minimum cut of G[S] is at least the combined cost of inserting all missing edges within G[S] plus the cost of cutting all edges from S to the rest of the graph. Complementing our theoretical findings, we experimentally demonstrate the effectiveness of the data reduction rule, shrinking real-world test instances from the PACE Challenge 2021 by around 24% while previous heuristic implementations of the data reduction rule only achieve 8%.
Cite as

Hjalmar Schulz, André Nichterlein, Rolf Niedermeier, and Christopher Weyand. Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 25:1-25:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schulz_et_al:LIPIcs.IPEC.2022.25,
  author =	{Schulz, Hjalmar and Nichterlein, Andr\'{e} and Niedermeier, Rolf and Weyand, Christopher},
  title =	{{Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.25},
  URN =		{urn:nbn:de:0030-drops-173816},
  doi =		{10.4230/LIPIcs.IPEC.2022.25},
  annote =	{Keywords: Correlation Clustering, Minimum Cut, Maximum s-t-Flow}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.11
Adjacency Graphs of Polyhedral Surfaces

Authors: Elena Arseneva, Linda Kleist, Boris Klemz, Maarten Löffler, André Schulz, Birgit Vogtenhuber, and Alexander Wolff

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

Abstract
We study whether a given graph can be realized as an adjacency graph of the polygonal cells of a polyhedral surface in ℝ³. We show that every graph is realizable as a polyhedral surface with arbitrary polygonal cells, and that this is not true if we require the cells to be convex. In particular, if the given graph contains K_5, K_{5,81}, or any nonplanar 3-tree as a subgraph, no such realization exists. On the other hand, all planar graphs, K_{4,4}, and K_{3,5} can be realized with convex cells. The same holds for any subdivision of any graph where each edge is subdivided at least once, and, by a result from McMullen et al. (1983), for any hypercube. Our results have implications on the maximum density of graphs describing polyhedral surfaces with convex cells: The realizability of hypercubes shows that the maximum number of edges over all realizable n-vertex graphs is in Ω(n log n). From the non-realizability of K_{5,81}, we obtain that any realizable n-vertex graph has 𝒪(n^{9/5}) edges. As such, these graphs can be considerably denser than planar graphs, but not arbitrarily dense.
Cite as

Elena Arseneva, Linda Kleist, Boris Klemz, Maarten Löffler, André Schulz, Birgit Vogtenhuber, and Alexander Wolff. Adjacency Graphs of Polyhedral Surfaces. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 11:1-11:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arseneva_et_al:LIPIcs.SoCG.2021.11,
  author =	{Arseneva, Elena and Kleist, Linda and Klemz, Boris and L\"{o}ffler, Maarten and Schulz, Andr\'{e} and Vogtenhuber, Birgit and Wolff, Alexander},
  title =	{{Adjacency Graphs of Polyhedral Surfaces}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{11:1--11:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.11},
  URN =		{urn:nbn:de:0030-drops-138107},
  doi =		{10.4230/LIPIcs.SoCG.2021.11},
  annote =	{Keywords: polyhedral complexes, realizability, contact representation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.79
Recognizing Planar Laman Graphs

Authors: Jonathan Rollin, Lena Schlipf, and André Schulz

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Laman graphs are the minimally rigid graphs in the plane. We present two algorithms for recognizing planar Laman graphs. A simple algorithm with running time O(n^(3/2)) and a more complicated algorithm with running time O(n log^3 n) based on involved planar network flow algorithms. Both improve upon the previously fastest algorithm for general graphs by Gabow and Westermann [Algorithmica, 7(5-6):465 - 497, 1992] with running time O(n sqrt{n log n}). To solve this problem we introduce two algorithms (with the running times stated above) that check whether for a directed planar graph G, disjoint sets S, T subseteq V(G), and a fixed k the following connectivity condition holds: for each vertex s in S there are k directed paths from s to T pairwise having only vertex s in common. This variant of connectivity seems interesting on its own.
Cite as

Jonathan Rollin, Lena Schlipf, and André Schulz. Recognizing Planar Laman Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 79:1-79:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rollin_et_al:LIPIcs.ESA.2019.79,
  author =	{Rollin, Jonathan and Schlipf, Lena and Schulz, Andr\'{e}},
  title =	{{Recognizing Planar Laman Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{79:1--79:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.79},
  URN =		{urn:nbn:de:0030-drops-112001},
  doi =		{10.4230/LIPIcs.ESA.2019.79},
  annote =	{Keywords: planar graphs, Laman graphs, network flow, connectivity}
}
Document
Multimedia Exposition
DOI: 10.4230/LIPIcs.SoCG.2019.66
Fréchet View - A Tool for Exploring Fréchet Distance Algorithms (Multimedia Exposition)

Authors: Peter Schäfer

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

Abstract
The Fréchet-distance is a similarity measure for geometric shapes. Alt and Godau presented the first algorithm for computing the Fréchet-distance and introduced a key concept, the free-space diagram. Since then, numerous variants of the Fréchet-distance have been studied. We present here an interactive, graphical tool for exploring some Fréchet-distance algorithms. Given two curves, users can experiment with the free-space diagram and compute the Fréchet-distance. The Fréchet-distance can be computed for two important classes of shapes: for polygonal curves in the plane, and for simple polygonal surfaces. Finally, we demonstrate an implementation of a very recent concept, the k-Fréchet-distance.
Cite as

Peter Schäfer. Fréchet View - A Tool for Exploring Fréchet Distance Algorithms (Multimedia Exposition). In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 66:1-66:5, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{schafer:LIPIcs.SoCG.2019.66,
  author =	{Sch\"{a}fer, Peter},
  title =	{{Fr\'{e}chet View - A Tool for Exploring Fr\'{e}chet Distance Algorithms}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{66:1--66:5},
  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.2019.66},
  URN =		{urn:nbn:de:0030-drops-104703},
  doi =		{10.4230/LIPIcs.SoCG.2019.66},
  annote =	{Keywords: Fr\'{e}chet distance, free-space diagram, polygonal curves, simple polygons}
}
Document
DOI: 10.4230/LIPIcs.STACS.2013.269
Algorithms for Designing Pop-Up Cards

Authors: Zachary Abel, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, André Schulz, Diane L. Souvaine, Giovanni Viglietta, and Andrew Winslow

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

Abstract
We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360°. More precisely, given a simple polygon attached to the two walls of the open pop-up, our polynomial-time algorithm subdivides the polygon into a single-degree-of-freedom linkage structure, such that closing the pop-up flattens the linkage without collision. This result solves an open problem of Hara and Sugihara from 2009. We also show how to obtain a more efficient construction for the special case of orthogonal polygons, and how to make 3D orthogonal polyhedra, from pop-ups that open to 90°, 180°, 270°, or 360°.
Cite as

Zachary Abel, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Anna Lubiw, André Schulz, Diane L. Souvaine, Giovanni Viglietta, and Andrew Winslow. Algorithms for Designing Pop-Up Cards. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 269-280, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{abel_et_al:LIPIcs.STACS.2013.269,
  author =	{Abel, Zachary and Demaine, Erik D. and Demaine, Martin L. and Eisenstat, Sarah and Lubiw, Anna and Schulz, Andr\'{e} and Souvaine, Diane L. and Viglietta, Giovanni and Winslow, Andrew},
  title =	{{Algorithms for Designing Pop-Up Cards}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{269--280},
  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.2013.269},
  URN =		{urn:nbn:de:0030-drops-39407},
  doi =		{10.4230/LIPIcs.STACS.2013.269},
  annote =	{Keywords: geometric folding, linkages, universality}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.637
Bounds on the maximum multiplicity of some common geometric graphs

Authors: Adrian Dumitrescu, Andre Schulz, Adam Sheffer, and Csaba D. Toth

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
We obtain new lower and upper bounds for the maximum multiplicity of some weighted, and respectively non-weighted, common geometric graphs drawn on $n$ points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of $n$ points in general position can have. In particular, we show that a generalized double chain formed by two almost convex chains admits Omega (8.65^n) different triangulations. This improves the bound Omega (8.48^n) achieved by the previous best construction, the double zig-zag chain studied by Aichholzer et al. (ii) We present a new lower bound of Omega(11.97^n) for the number of non-crossing spanning trees of the double chain composed of two convex chains. The previous bound, Omega(10.42^n), stood unchanged for more than 10 years. (iii) Using a recent upper bound of 30^n for the number of triangulations, due to Sharir and Sheffer, we show that n points in the plane in general position admit at most O(68.664^n) non-crossing spanning cycles. (iv) We derive exponential lower bounds for the number of maximum and minimum weighted geometric graphs (matchings, spanning trees, and tours). It was known that the number of longest non-crossing spanning trees of a point set can be exponentially large, and here we show that this can be also realized with points in convex position. For points in convex position we obtain tight bounds for the number of longest and shortest tours. We give a combinatorial characterization of the longest tours, which leads to an O(n log n) time algorithm for computing them.
Cite as

Adrian Dumitrescu, Andre Schulz, Adam Sheffer, and Csaba D. Toth. Bounds on the maximum multiplicity of some common geometric graphs. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 637-648, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

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@InProceedings{dumitrescu_et_al:LIPIcs.STACS.2011.637,
  author =	{Dumitrescu, Adrian and Schulz, Andre and Sheffer, Adam and Toth, Csaba D.},
  title =	{{Bounds on the maximum multiplicity of some common geometric graphs}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{637--648},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.637},
  URN =		{urn:nbn:de:0030-drops-30505},
  doi =		{10.4230/LIPIcs.STACS.2011.637},
  annote =	{Keywords: combinatorial geometry, matching, triangulation, spanning tree, spanning cycle, weighted structure, non-crossing condition}
}
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