13 Search Results for "Schlipf, Lena"

Document
DOI: 10.4230/LIPIcs.STACS.2026.49
2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs

Authors: Rohit Gurjar, Kilian Rothmund, and Thomas Thierauf

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Minimally rigid graphs can be decided and embedded in the plane efficiently, i.e. in polynomial time. There is also an efficient randomized parallel algorithm, i.e. in RNC. We present an NC-algorithm to decide whether one-crossing-minor-free graphs are minimally rigid. In the special case of K_{3,3}-free graphs, we also compute an infinitesimally rigid embedding in NC.
Cite as

Rohit Gurjar, Kilian Rothmund, and Thomas Thierauf. 2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 49:1-49:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gurjar_et_al:LIPIcs.STACS.2026.49,
  author =	{Gurjar, Rohit and Rothmund, Kilian and Thierauf, Thomas},
  title =	{{2D Minimal Graph Rigidity is in NC for One-Crossing-Minor-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{49:1--49:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.49},
  URN =		{urn:nbn:de:0030-drops-255385},
  doi =		{10.4230/LIPIcs.STACS.2026.49},
  annote =	{Keywords: Graph Rigidity, Parallel Algorithms, Polynomial Identity Testing, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.36
Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces

Authors: Florestan Brunck, Hsien-Chih Chang, Maarten Löffler, Tim Ophelders, and Lena Schlipf

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We study reconfiguration in curve arrangements, where a subset of the crossings are marked as switches which have three possible states, and the goal is to set the switches such that the resulting curve arrangement has few self-intersections, or few faces that are incident to the same curve multiple times (a.k.a. popular faces). Our results are that these problems are NP-hard, but FPT in the number of switches. Minimizing self-intersections is also FPT in the number of non-switchable crossings; for minimizing popular faces this problem remains open. Our results can be applied to generating curved nonograms, a type of logic puzzle that has received some attention lately. Specifically, our results make it possible to efficiently convert expert puzzles into advanced puzzles (or determine that this is impossible).
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Florestan Brunck, Hsien-Chih Chang, Maarten Löffler, Tim Ophelders, and Lena Schlipf. Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brunck_et_al:LIPIcs.GD.2025.36,
  author =	{Brunck, Florestan and Chang, Hsien-Chih and L\"{o}ffler, Maarten and Ophelders, Tim and Schlipf, Lena},
  title =	{{Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.36},
  URN =		{urn:nbn:de:0030-drops-250220},
  doi =		{10.4230/LIPIcs.GD.2025.36},
  annote =	{Keywords: Curve Arrangements, Reconfiguration, Curve Arrangements, NP-hardness, Fixed-Parameter Tractability, Puzzle Generation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.21
A Unified FPT Framework for Crossing Number Problems

Authors: Éric Colin de Verdière and Petr Hliněný

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework that smoothly captures many generalized crossing number problems, and that yields fixed-parameter tractable (FPT) algorithms for them not only in the plane but also on surfaces. Our framework takes the following form. We fix a surface S, an integer r, and a map κ from the set of topological drawings of graphs in S to ℤ_+ ∪ {∞}, satisfying some natural monotonicity conditions, but essentially describing the allowed drawings and how we want to count the crossings in them. Then deciding whether an input graph G has an allowed drawing D on S with κ(D) ≤ r can be done in time quadratic in the size of G (and exponential in other parameters). More generally, we may take as input an edge-colored graph, and distinguish crossings by the colors of the involved edges; and we may allow to perform a bounded number of edge removals and vertex splits to G before drawing it. The proof is a reduction to the embeddability of a graph on a two-dimensional simplicial complex. This framework implies, in a unified way, quadratic FPT algorithms for many topological crossing number variants established in the graph drawing community. Some of these variants already had previously published FPT algorithms, mostly relying on Courcelle’s metatheorem, but for many of those, we obtain an algorithm with a better runtime. Moreover, our framework extends, at no cost, to these crossing number variants in any fixed surface.
Cite as

Éric Colin de Verdière and Petr Hliněný. A Unified FPT Framework for Crossing Number Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{colindeverdiere_et_al:LIPIcs.ESA.2025.21,
  author =	{Colin de Verdi\`{e}re, \'{E}ric and Hlin\v{e}n\'{y}, Petr},
  title =	{{A Unified FPT Framework for Crossing Number Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.21},
  URN =		{urn:nbn:de:0030-drops-244897},
  doi =		{10.4230/LIPIcs.ESA.2025.21},
  annote =	{Keywords: computational geometry, fixed-parameter tractability, graph drawing, graph embedding, crossing number, two-dimensional simplicial complex, surface}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.11
Crossing and Independent Families Among Polygons

Authors: Anna Brötzner, Robert Ganian, Thekla Hamm, Fabian Klute, and Irene Parada

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a set A of points in the plane, a family of line segments forming a matching in A is called crossing (or independent) if each pair of segments in the family intersects (or is non-intersecting, respectively). In past works, these notions have been generalized to polygons by identifying the points in A with the vertices of a given set of polygons and forbidding the line segments from intersecting or overlapping with polygon walls. In this work, we study the computational complexity of computing maximum crossing and independent families in this more general setting. As our first two results, we show that both problems are NP-hard already when the polygons are triangles. Motivated by this, we turn to parameterized algorithms. For our main algorithmic results, we consider the number of polygons on the input as the natural parameter and under this parameterization obtain a fixed-parameter algorithm for computing a largest crossing family among these polygons, and a separate XP-algorithm for computing a largest independent family that lies in one of the faces of the polygonal domain.
Cite as

Anna Brötzner, Robert Ganian, Thekla Hamm, Fabian Klute, and Irene Parada. Crossing and Independent Families Among Polygons. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brotzner_et_al:LIPIcs.WADS.2025.11,
  author =	{Br\"{o}tzner, Anna and Ganian, Robert and Hamm, Thekla and Klute, Fabian and Parada, Irene},
  title =	{{Crossing and Independent Families Among Polygons}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.11},
  URN =		{urn:nbn:de:0030-drops-242424},
  doi =		{10.4230/LIPIcs.WADS.2025.11},
  annote =	{Keywords: crossing families, crossing-free matchings, segment intersection graphs, computational geometry, parameterized algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.36
Faster Fréchet Distance Under Transformations

Authors: Kevin Buchin, Maike Buchin, Zijin Huang, André Nusser, and Sampson Wong

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the problem of computing the Fréchet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves π and σ of total complexity n and a threshold δ ≥ 0, we present an 𝒪̃(n^{7 + 1/3}) time algorithm to determine whether there exists a translation t ∈ ℝ² such that the Fréchet distance between π and σ + t is at most δ. This improves on the previous best result, which is an 𝒪(n⁸) time algorithm. We then generalize this result to any class of rationally parameterized transformations, which includes translation, rotation, scaling, and arbitrary affine transformations. For a class T of rationally parametrized transformations with k degrees of freedom, we show that one can determine whether there is a transformation τ ∈ T such that the Fréchet distance between π and τ(σ) is at most δ in 𝒪̃(n^{3k+4/3}) time.
Cite as

Kevin Buchin, Maike Buchin, Zijin Huang, André Nusser, and Sampson Wong. Faster Fréchet Distance Under Transformations. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{buchin_et_al:LIPIcs.ICALP.2025.36,
  author =	{Buchin, Kevin and Buchin, Maike and Huang, Zijin and Nusser, Andr\'{e} and Wong, Sampson},
  title =	{{Faster Fr\'{e}chet Distance Under Transformations}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.36},
  URN =		{urn:nbn:de:0030-drops-234137},
  doi =		{10.4230/LIPIcs.ICALP.2025.36},
  annote =	{Keywords: Fr\'{e}chet distance, curve similarity, shape matching}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.1
Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings

Authors: Mikkel Abrahamsen, Kevin Buchin, Maike Buchin, Linda Kleist, Maarten Löffler, Lena Schlipf, André Schulz, and Jack Stade

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study well-known reconfiguration problems. Given a start and a target configuration of geometric objects in a polygon, we wonder whether we can move the objects from the start configuration to the target configuration while avoiding collisions between the objects and staying within the polygon. Problems of this type have been considered since the early 80s by roboticists and computational geometers. In this paper, we study some of the simplest possible variants where the objects are labeled or unlabeled unit squares or unit disks. In unlabeled reconfiguration, the objects are identical, so that any object is allowed to end at any of the targets positions. In the labeled variant, each object has a designated target position. The results for the labeled variants are direct consequences from our insights on the unlabeled versions. We show that it is PSPACE-hard to decide whether there exists a reconfiguration of (unlabeled/labeled) unit squares even in a simple polygon. Previously, it was only known to be PSPACE-hard in a polygon with holes for both the unlabeled and labeled version [Solovey and Halperin, Int. J. Robotics Res. 2016]. Our proof is based on a result of independent interest, namely that reconfiguration between two satisfying assignments of a formula of Monotone-Planar-3-Sat is also PSPACE-complete. The reduction from reconfiguration of Monotone-Planar-3-Sat to reconfiguration of unit squares extends techniques recently developed to show NP-hardness of packing unit squares in a simple polygon [Abrahamsen and Stade, FOCS 2024]. We also show PSPACE-hardness of reconfiguration of (unlabeled/labeled) unit disks in a polygon with holes. Previously, it was known that unlabeled reconfiguration of disks of two different sizes was PSPACE-hard [Brocken, van der Heijden, Kostitsyna, Lo-Wong and Surtel, FUN 2021].
Cite as

Mikkel Abrahamsen, Kevin Buchin, Maike Buchin, Linda Kleist, Maarten Löffler, Lena Schlipf, André Schulz, and Jack Stade. Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abrahamsen_et_al:LIPIcs.SoCG.2025.1,
  author =	{Abrahamsen, Mikkel and Buchin, Kevin and Buchin, Maike and Kleist, Linda and L\"{o}ffler, Maarten and Schlipf, Lena and Schulz, Andr\'{e} and Stade, Jack},
  title =	{{Reconfiguration of Unit Squares and Disks: PSPACE-Hardness in Simple Settings}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.1},
  URN =		{urn:nbn:de:0030-drops-231539},
  doi =		{10.4230/LIPIcs.SoCG.2025.1},
  annote =	{Keywords: reconfiguration, unit square, unit disk, unlabeled, labeled, simple polygon, polygon}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.47
Shelling and Sinking Graphs on the Sphere

Authors: Jeff Erickson and Christian Howard

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We describe a promising approach to efficiently morph spherical graphs, extending earlier approaches of Awartani and Henderson [Trans. AMS 1987] and Kobourov and Landis [JGAA 2006]. Specifically, we describe two methods to morph shortest-path triangulations of the sphere by moving their vertices along longitudes into the southern hemisphere; we call a triangulation sinkable if such a morph exists. Our first method generalizes a longitudinal shelling construction of Awartani and Henderson; a triangulation is sinkable if a specific orientation of its dual graph is acyclic. We describe a simple polynomial-time algorithm to find a longitudinally shellable rotation of a given spherical triangulation, if one exists; we also construct a spherical triangulation that has no longitudinally shellable rotation. Our second method is based on a linear-programming characterization of sinkability. By identifying its optimal basis, we show that this linear program can be solved in O(n^{ω/2}) time, where ω is the matrix-multiplication exponent, assuming the underlying linear system is non-singular. Finally, we pose several conjectures and describe experimental results that support them.
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Jeff Erickson and Christian Howard. Shelling and Sinking Graphs on the Sphere. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erickson_et_al:LIPIcs.SoCG.2025.47,
  author =	{Erickson, Jeff and Howard, Christian},
  title =	{{Shelling and Sinking Graphs on the Sphere}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{47:1--47:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.47},
  URN =		{urn:nbn:de:0030-drops-231996},
  doi =		{10.4230/LIPIcs.SoCG.2025.47},
  annote =	{Keywords: morphing, planar graphs, spherical graph drawing, longitudinal shelling}
}
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.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.
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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.SWAT.2018.6
On Romeo and Juliet Problems: Minimizing Distance-to-Sight

Authors: Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, and Darren Strash

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Abstract
We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points s and t in a simple polygon P with no holes, we want to minimize the distance these persons travel in order to see each other in P. We solve two variants of this problem, one minimizing the longer distance the two persons travel (min-max) and one minimizing the total travel distance (min-sum), optimally in linear time. We also consider a query version of this problem for the min-max variant. We can preprocess a simple n-gon in linear time so that the minimum of the longer distance the two persons travel can be computed in O(log^2 n) time for any two query positions where the two persons lie.
Cite as

Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, and Darren Strash. On Romeo and Juliet Problems: Minimizing Distance-to-Sight. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ahn_et_al:LIPIcs.SWAT.2018.6,
  author =	{Ahn, Hee-Kap and Oh, Eunjin and Schlipf, Lena and Stehn, Fabian and Strash, Darren},
  title =	{{On Romeo and Juliet Problems: Minimizing Distance-to-Sight}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.6},
  URN =		{urn:nbn:de:0030-drops-88322},
  doi =		{10.4230/LIPIcs.SWAT.2018.6},
  annote =	{Keywords: Visibility polygon, shortest-path, watchman problems}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.75
Edge-Orders

Authors: Lena Schlipf and Jens M. Schmidt

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying link behind all these orders has been shown that links them to well-known graph decompositions into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs in linear time, respectively. While the former can be seen as the edge-variants of st-numberings, the latter are the edge-variants of Mondshein sequences and non-separating ear decompositions. The methods that we use for obtaining such edge-orders differ considerably in almost all details from the ones used for their vertex-counterparts, as different graph-theoretic constructions are used in the inductive proof and standard reductions from edge- to vertex-connectivity are bound to fail. As a first application, we consider the famous Edge-Independent Spanning Tree Conjecture, which asserts that every k-edge-connected graph contains k rooted spanning trees that are pairwise edge-independent. We illustrate the impact of the above edge-orders by deducing algorithms that construct 2- and 3-edge independent spanning trees of 2- and 3-edge-connected graphs, the latter of which improves the best known running time from O(n^2) to linear time.
Cite as

Lena Schlipf and Jens M. Schmidt. Edge-Orders. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{schlipf_et_al:LIPIcs.ICALP.2017.75,
  author =	{Schlipf, Lena and Schmidt, Jens M.},
  title =	{{Edge-Orders}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{75:1--75:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.75},
  URN =		{urn:nbn:de:0030-drops-74078},
  doi =		{10.4230/LIPIcs.ICALP.2017.75},
  annote =	{Keywords: edge-order, st-edge-order, canonical ordering, edge-independent spanning tree, Mondshein sequence, linear time}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.658
Shortest Path to a Segment and Quickest Visibility Queries

Authors: Esther M. Arkin, Alon Efrat, Christian Knauer, Joseph S. B. Mitchell, Valentin Polishchuk, Günter Rote, Lena Schlipf, and Topi Talvitie

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

Abstract
We show how to preprocess a polygonal domain with a fixed starting point s in order to answer efficiently the following queries: Given a point q, how should one move from s in order to see q as soon as possible? This query resembles the well-known shortest-path-to-a-point query, except that the latter asks for the fastest way to reach q, instead of seeing it. Our solution methods include a data structure for a different generalization of shortest-path-to-a-point queries, which may be of independent interest: to report efficiently a shortest path from s to a query segment in the domain.
Cite as

Esther M. Arkin, Alon Efrat, Christian Knauer, Joseph S. B. Mitchell, Valentin Polishchuk, Günter Rote, Lena Schlipf, and Topi Talvitie. Shortest Path to a Segment and Quickest Visibility Queries. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 658-673, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{arkin_et_al:LIPIcs.SOCG.2015.658,
  author =	{Arkin, Esther M. and Efrat, Alon and Knauer, Christian and Mitchell, Joseph S. B. and Polishchuk, Valentin and Rote, G\"{u}nter and Schlipf, Lena and Talvitie, Topi},
  title =	{{Shortest Path to a Segment and Quickest Visibility Queries}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{658--673},
  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.2015.658},
  URN =		{urn:nbn:de:0030-drops-51474},
  doi =		{10.4230/LIPIcs.SOCG.2015.658},
  annote =	{Keywords: path planning, visibility, query structures and complexity, persistent data structures, continuous Dijkstra}
}
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