19 Search Results for "Hoffmann, Michael"

Document
DOI: 10.4230/OASIcs.WCET.2024.2
The Platin Multi-Target Worst-Case Analysis Tool

Authors: Emad Jacob Maroun, Eva Dengler, Christian Dietrich, Stefan Hepp, Henriette Herzog, Benedikt Huber, Jens Knoop, Daniel Wiltsche-Prokesch, Peter Puschner, Phillip Raffeck, Martin Schoeberl, Simon Schuster, and Peter Wägemann

Published in: OASIcs, Volume 121, 22nd International Workshop on Worst-Case Execution Time Analysis (WCET 2024)

Abstract
With the increasing number of applications that require reliable runtime guarantees, the relevance of static worst-case analysis tools that can provide such guarantees increases. These analysis tools determine resource-consumption bounds of application tasks, with a model of the underlying hardware, to meet given resource budgets during runtime, such as deadlines of real-time tasks. This paper presents enhancements to the Platin worst-case analysis tool developed since its original release more than ten years ago. These novelties comprise Platin’s support for new architectures (i.e., ARMv6-M, RISC-V, and AVR) in addition to the previous backends for Patmos and ARMv7-M. Further, Platin now features system-wide analysis methods and annotation support to express system-level constraints. Besides an overview of these enhancements, we evaluate Platin’s accuracy for the two supported architecture implementations, Patmos and RISC-V.
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Emad Jacob Maroun, Eva Dengler, Christian Dietrich, Stefan Hepp, Henriette Herzog, Benedikt Huber, Jens Knoop, Daniel Wiltsche-Prokesch, Peter Puschner, Phillip Raffeck, Martin Schoeberl, Simon Schuster, and Peter Wägemann. The Platin Multi-Target Worst-Case Analysis Tool. In 22nd International Workshop on Worst-Case Execution Time Analysis (WCET 2024). Open Access Series in Informatics (OASIcs), Volume 121, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{maroun_et_al:OASIcs.WCET.2024.2,
  author =	{Maroun, Emad Jacob and Dengler, Eva and Dietrich, Christian and Hepp, Stefan and Herzog, Henriette and Huber, Benedikt and Knoop, Jens and Wiltsche-Prokesch, Daniel and Puschner, Peter and Raffeck, Phillip and Schoeberl, Martin and Schuster, Simon and W\"{a}gemann, Peter},
  title =	{{The Platin Multi-Target Worst-Case Analysis Tool}},
  booktitle =	{22nd International Workshop on Worst-Case Execution Time Analysis (WCET 2024)},
  pages =	{2:1--2:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-346-1},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{121},
  editor =	{Carle, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2024.2},
  URN =		{urn:nbn:de:0030-drops-204704},
  doi =		{10.4230/OASIcs.WCET.2024.2},
  annote =	{Keywords: worst-case resource consumption, WCET, static analysis tool}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.55
Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous

Authors: Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.

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

Abstract
Temporal graphs are dynamic graphs where the edge set can change in each time step, while the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been widely studied. In this paper, we extend the concept of graph automorphisms from static graphs to temporal graphs and show for the first time that symmetries enable faster exploration: We prove that a connected temporal graph with n vertices and orbit number r (i.e., r is the number of automorphism orbits) can be explored in O(r n^{1+ε}) time steps, for any fixed ε > 0. For r = O(n^c) for constant c < 1, this is a significant improvement over the known tight worst-case bound of Θ(n²) time steps for arbitrary connected temporal graphs. We also give two lower bounds for temporal exploration, showing that Ω(n log n) time steps are required for some inputs with r = O(1) and that Ω(rn) time steps are required for some inputs for any r with 1 ≤ r ≤ n. Moreover, we show that the techniques we develop for fast exploration can be used to derive the following result for rendezvous: Two agents with different programs and without communication ability are placed by an adversary at arbitrary vertices and given full information about the connected temporal graph, except that they do not have consistent vertex labels. Then the two agents can meet at a common vertex after O(n^{1+ε}) time steps, for any constant ε > 0. For some connected temporal graphs with the orbit number being a constant, we also present a complementary lower bound of Ω(nlog n) time steps.
Cite as

Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.. Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dogeas_et_al:LIPIcs.ICALP.2024.55,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Kammer, Frank and Meintrup, Johannes and Moses Jr., William K.},
  title =	{{Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{55:1--55:18},
  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.2024.55},
  URN =		{urn:nbn:de:0030-drops-201989},
  doi =		{10.4230/LIPIcs.ICALP.2024.55},
  annote =	{Keywords: dynamic graphs, parameterized algorithms, algorithmic graph theory, graph automorphism, orbit number}
}
Document
DOI: 10.4230/DagMan.10.1.1
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.6
Drawings of Complete Multipartite Graphs up to Triangle Flips

Authors: Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang, Michael Hoffmann, Jan Kynčl, Yannic Maus, Birgit Vogtenhuber, and Alexandra Weinberger

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

Abstract
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan’s Theorem states that for any two simple drawings of the complete graph K_n with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation. We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on n vertices is bounded by O(n^{16}). The latter proof uses a Carathéodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest. Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the following sense: For the complete bipartite graph K_{m,n} minus two edges and K_{m,n} plus one edge for any m,n ≥ 4, as well as K_n minus a 4-cycle for any n ≥ 5, there exist two simple drawings with the same ERS that cannot be transformed into each other using triangle flips. So having the same ERS does not remain sufficient when removing or adding very few edges.
Cite as

Oswin Aichholzer, Man-Kwun Chiu, Hung P. Hoang, Michael Hoffmann, Jan Kynčl, Yannic Maus, Birgit Vogtenhuber, and Alexandra Weinberger. Drawings of Complete Multipartite Graphs up to Triangle Flips. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{aichholzer_et_al:LIPIcs.SoCG.2023.6,
  author =	{Aichholzer, Oswin and Chiu, Man-Kwun and Hoang, Hung P. and Hoffmann, Michael and Kyn\v{c}l, Jan and Maus, Yannic and Vogtenhuber, Birgit and Weinberger, Alexandra},
  title =	{{Drawings of Complete Multipartite Graphs up to Triangle Flips}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{6:1--6:16},
  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.2023.6},
  URN =		{urn:nbn:de:0030-drops-178563},
  doi =		{10.4230/LIPIcs.SoCG.2023.6},
  annote =	{Keywords: Simple drawings, simple topological graphs, complete graphs, multipartite graphs, k-partite graphs, bipartite graphs, Gioan’s Theorem, triangle flips, Reidemeister moves}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2023.39
The Number of Edges in Maximal 2-Planar Graphs

Authors: Michael Hoffmann and Meghana M. Reddy

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

Abstract
A graph is 2-planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal 2-planar if no edge can be added such that the resulting graph remains 2-planar. A 2-planar graph on n vertices has at most 5n-10 edges, and some (maximal) 2-planar graphs - referred to as optimal 2-planar - achieve this bound. However, in strong contrast to maximal planar graphs, a maximal 2-planar graph may have fewer than the maximum possible number of edges. In this paper, we determine the minimum edge density of maximal 2-planar graphs by proving that every maximal 2-planar graph on n ≥ 5 vertices has at least 2n edges. We also show that this bound is tight, up to an additive constant. The lower bound is based on an analysis of the degree distribution in specific classes of drawings of the graph. The upper bound construction is verified by carefully exploring the space of admissible drawings using computer support.
Cite as

Michael Hoffmann and Meghana M. Reddy. The Number of Edges in Maximal 2-Planar Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hoffmann_et_al:LIPIcs.SoCG.2023.39,
  author =	{Hoffmann, Michael and M. Reddy, Meghana},
  title =	{{The Number of Edges in Maximal 2-Planar Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{39:1--39:15},
  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.2023.39},
  URN =		{urn:nbn:de:0030-drops-178894},
  doi =		{10.4230/LIPIcs.SoCG.2023.39},
  annote =	{Keywords: k-planar graphs, local crossing number, saturated graphs, beyond-planar graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.11
Bounding and Computing Obstacle Numbers of Graphs

Authors: Martin Balko, Steven Chaplick, Robert Ganian, Siddharth Gupta, Michael Hoffmann, Pavel Valtr, and Alexander Wolff

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

Abstract
An obstacle representation of a graph G consists of a set of pairwise disjoint simply-connected closed regions and a one-to-one mapping of the vertices of G to points such that two vertices are adjacent in G if and only if the line segment connecting the two corresponding points does not intersect any obstacle. The obstacle number of a graph is the smallest number of obstacles in an obstacle representation of the graph in the plane such that all obstacles are simple polygons. It is known that the obstacle number of each n-vertex graph is O(n log n) [Balko, Cibulka, and Valtr, 2018] and that there are n-vertex graphs whose obstacle number is Ω(n/(log log n)²) [Dujmović and Morin, 2015]. We improve this lower bound to Ω(n/log log n) for simple polygons and to Ω(n) for convex polygons. To obtain these stronger bounds, we improve known estimates on the number of n-vertex graphs with bounded obstacle number, solving a conjecture by Dujmović and Morin. We also show that if the drawing of some n-vertex graph is given as part of the input, then for some drawings Ω(n²) obstacles are required to turn them into an obstacle representation of the graph. Our bounds are asymptotically tight in several instances. We complement these combinatorial bounds by two complexity results. First, we show that computing the obstacle number of a graph G is fixed-parameter tractable in the vertex cover number of G. Second, we show that, given a graph G and a simple polygon P, it is NP-hard to decide whether G admits an obstacle representation using P as the only obstacle.
Cite as

Martin Balko, Steven Chaplick, Robert Ganian, Siddharth Gupta, Michael Hoffmann, Pavel Valtr, and Alexander Wolff. Bounding and Computing Obstacle Numbers of Graphs. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{balko_et_al:LIPIcs.ESA.2022.11,
  author =	{Balko, Martin and Chaplick, Steven and Ganian, Robert and Gupta, Siddharth and Hoffmann, Michael and Valtr, Pavel and Wolff, Alexander},
  title =	{{Bounding and Computing Obstacle Numbers of Graphs}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{11:1--11:13},
  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.2022.11},
  URN =		{urn:nbn:de:0030-drops-169495},
  doi =		{10.4230/LIPIcs.ESA.2022.11},
  annote =	{Keywords: Obstacle representation, Obstacle number, Visibility, NP-hardness, FPT}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.23
Long Plane Trees

Authors: Sergio Cabello, Michael Hoffmann, Katharina Klost, Wolfgang Mulzer, and Josef Tkadlec

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
In the longest plane spanning tree problem, we are given a finite planar point set 𝒫, and our task is to find a plane (i.e., noncrossing) spanning tree T_OPT for 𝒫 with maximum total Euclidean edge length |T_OPT|. Despite more than two decades of research, it remains open if this problem is NP-hard. Thus, previous efforts have focused on polynomial-time algorithms that produce plane trees whose total edge length approximates |T_OPT|. The approximate trees in these algorithms all have small unweighted diameter, typically three or four. It is natural to ask whether this is a common feature of longest plane spanning trees, or an artifact of the specific approximation algorithms. We provide three results to elucidate the interplay between the approximation guarantee and the unweighted diameter of the approximate trees. First, we describe a polynomial-time algorithm to construct a plane tree T_ALG with diameter at most four and |T_ALG| ≥ 0.546 ⋅ |T_OPT|. This constitutes a substantial improvement over the state of the art. Second, we show that a longest plane tree among those with diameter at most three can be found in polynomial time. Third, for any candidate diameter d ≥ 3, we provide upper bounds on the approximation factor that can be achieved by a longest plane tree with diameter at most d (compared to a longest plane tree without constraints).
Cite as

Sergio Cabello, Michael Hoffmann, Katharina Klost, Wolfgang Mulzer, and Josef Tkadlec. Long Plane Trees. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cabello_et_al:LIPIcs.SoCG.2022.23,
  author =	{Cabello, Sergio and Hoffmann, Michael and Klost, Katharina and Mulzer, Wolfgang and Tkadlec, Josef},
  title =	{{Long Plane Trees}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.23},
  URN =		{urn:nbn:de:0030-drops-160311},
  doi =		{10.4230/LIPIcs.SoCG.2022.23},
  annote =	{Keywords: geometric network design, spanning trees, plane straight-line graphs, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.45
Hardness and Approximation of Minimum Convex Partition

Authors: Nicolas Grelier

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show that Minimum Convex Partition is NP-hard, and we give several approximation algorithms, from an 𝒪(log OPT)-approximation running in 𝒪(n⁸)-time, where OPT denotes the minimum number of convex faces needed, to an 𝒪(√nlog n)-approximation algorithm running in 𝒪(n²)-time. We say that a point set is k-directed if the (straight) lines containing at least three points have up to k directions. We present an 𝒪(k)-approximation algorithm running in n^{𝒪(k)}-time. Those hardness and approximation results also holds for the Minimum Convex Tiling problem, defined similarly but allowing the use of Steiner points. The approximation results are obtained by relating the problem to the Covering Points with Non-Crossing Segments problem. We show that this problem is NP-hard, and present an FPT algorithm. This allows us to obtain a constant-approximation FPT algorithm for the Minimum Convex Partition Problem where the parameter is the number of faces.
Cite as

Nicolas Grelier. Hardness and Approximation of Minimum Convex Partition. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{grelier:LIPIcs.SoCG.2022.45,
  author =	{Grelier, Nicolas},
  title =	{{Hardness and Approximation of Minimum Convex Partition}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{45:1--45:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.45},
  URN =		{urn:nbn:de:0030-drops-160530},
  doi =		{10.4230/LIPIcs.SoCG.2022.45},
  annote =	{Keywords: degenerate point sets, point cover, non-crossing segments, approximation algorithm, complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.34
On the Complexity of Intersection Non-emptiness for Star-Free Language Classes

Authors: Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.
Cite as

Emmanuel Arrighi, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismaël Jecker, Mateus de Oliveira Oliveira, and Petra Wolf. On the Complexity of Intersection Non-emptiness for Star-Free Language Classes. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arrighi_et_al:LIPIcs.FSTTCS.2021.34,
  author =	{Arrighi, Emmanuel and Fernau, Henning and Hoffmann, Stefan and Holzer, Markus and Jecker, Isma\"{e}l and de Oliveira Oliveira, Mateus and Wolf, Petra},
  title =	{{On the Complexity of Intersection Non-emptiness for Star-Free Language Classes}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.34},
  URN =		{urn:nbn:de:0030-drops-155456},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.34},
  annote =	{Keywords: Intersection Non-emptiness Problem, Star-Free Languages, Straubing-Th\'{e}rien Hierarchy, dot-depth Hierarchy, Commutative Languages, Complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.55
Polygon-Universal Graphs

Authors: Tim Ophelders, Ignaz Rutter, Bettina Speckmann, and Kevin Verbeek

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

Abstract
We study a fundamental question from graph drawing: given a pair (G,C) of a graph G and a cycle C in G together with a simple polygon P, is there a straight-line drawing of G inside P which maps C to P? We say that such a drawing of (G,C) respects P. We fully characterize those instances (G,C) which are polygon-universal, that is, they have a drawing that respects P for any simple (not necessarily convex) polygon P. Specifically, we identify two necessary conditions for an instance to be polygon-universal. Both conditions are based purely on graph and cycle distances and are easy to check. We show that these two conditions are also sufficient. Furthermore, if an instance (G,C) is planar, that is, if there exists a planar drawing of G with C on the outer face, we show that the same conditions guarantee for every simple polygon P the existence of a planar drawing of (G,C) that respects P. If (G,C) is polygon-universal, then our proofs directly imply a linear-time algorithm to construct a drawing that respects a given polygon P.
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Tim Ophelders, Ignaz Rutter, Bettina Speckmann, and Kevin Verbeek. Polygon-Universal Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ophelders_et_al:LIPIcs.SoCG.2021.55,
  author =	{Ophelders, Tim and Rutter, Ignaz and Speckmann, Bettina and Verbeek, Kevin},
  title =	{{Polygon-Universal Graphs}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{55:1--55:15},
  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.2021.55},
  URN =		{urn:nbn:de:0030-drops-138540},
  doi =		{10.4230/LIPIcs.SoCG.2021.55},
  annote =	{Keywords: Graph drawing, partial drawing extension, simple polygon}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.27
Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Authors: Thomas Erlebach, Michael Hoffmann, and Murilo Santos de Lima

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds. Given a set of uncertain elements and a family of m subsets of that set, we present an algorithm for determining the value of the minimum of each of the subsets that requires at most (2+ε) ⋅ opt_k+O(1/(ε) ⋅ lg m) rounds for every 0 < ε < 1, where opt_k is the optimal number of rounds, as well as nearly matching lower bounds. For the problem of determining the i-th smallest value and identifying all elements with that value in a set of uncertain elements, we give a 2-round-competitive algorithm. We also show that the problem of sorting a family of sets of uncertain elements admits a 2-round-competitive algorithm and this is the best possible.
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Thomas Erlebach, Michael Hoffmann, and Murilo Santos de Lima. Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{erlebach_et_al:LIPIcs.STACS.2021.27,
  author =	{Erlebach, Thomas and Hoffmann, Michael and de Lima, Murilo Santos},
  title =	{{Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.27},
  URN =		{urn:nbn:de:0030-drops-136728},
  doi =		{10.4230/LIPIcs.STACS.2021.27},
  annote =	{Keywords: online algorithms, competitive analysis, explorable uncertainty, parallel algorithms, minimum problem, selection problem}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.58
Triconnected Planar Graphs of Maximum Degree Five are Subhamiltonian

Authors: Michael Hoffmann and Boris Klemz

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

Abstract
We show that every triconnected planar graph of maximum degree five is subhamiltonian planar. A graph is subhamiltonian planar if it is a subgraph of a Hamiltonian planar graph or, equivalently, if it admits a 2-page book embedding. In fact, our result is stronger because we only require vertices of a separating triangle to have degree at most five, all other vertices may have arbitrary degree. This degree bound is tight: We describe a family of triconnected planar graphs that are not subhamiltonian planar and where every vertex of a separating triangle has degree at most six. Our results improve earlier work by Heath and by Bauernöppel and, independently, Bekos, Gronemann, and Raftopoulou, who showed that planar graphs of maximum degree three and four, respectively, are subhamiltonian planar. The proof is constructive and yields a quadratic time algorithm to obtain a subhamiltonian plane cycle for a given graph. As one of our main tools, which might be of independent interest, we devise an algorithm that, in a given 3-connected plane graph satisfying the above degree bounds, collapses each maximal separating triangle into a single edge such that the resulting graph is biconnected, contains no separating triangle, and no separation pair whose vertices are adjacent.
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Michael Hoffmann and Boris Klemz. Triconnected Planar Graphs of Maximum Degree Five are Subhamiltonian. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hoffmann_et_al:LIPIcs.ESA.2019.58,
  author =	{Hoffmann, Michael and Klemz, Boris},
  title =	{{Triconnected Planar Graphs of Maximum Degree Five are Subhamiltonian}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{58:1--58:14},
  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.2019.58},
  URN =		{urn:nbn:de:0030-drops-111797},
  doi =		{10.4230/LIPIcs.ESA.2019.58},
  annote =	{Keywords: Graph drawing, book embedding, Hamiltonian graph, planar graph, bounded degree graph, graph augmentation, computational geometry, SPQR decomposition}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.9
Geometric Multicut

Authors: Mikkel Abrahamsen, Panos Giannopoulos, Maarten Löffler, and Günter Rote

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" F, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, where k is the number of different colors, as it can be seen as a geometric analogue to the well-studied multicut problem on graphs. We first give an O(n^4 log^3 n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colors and n corners in total. We then show that the problem is NP-hard for the case of three colors. Finally, we give a (2-4/3k)-approximation algorithm.
Cite as

Mikkel Abrahamsen, Panos Giannopoulos, Maarten Löffler, and Günter Rote. Geometric Multicut. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{abrahamsen_et_al:LIPIcs.ICALP.2019.9,
  author =	{Abrahamsen, Mikkel and Giannopoulos, Panos and L\"{o}ffler, Maarten and Rote, G\"{u}nter},
  title =	{{Geometric Multicut}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.9},
  URN =		{urn:nbn:de:0030-drops-105850},
  doi =		{10.4230/LIPIcs.ICALP.2019.9},
  annote =	{Keywords: multicut, clustering, Steiner tree}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2018.8
Convex Hulls in Polygonal Domains

Authors: Luis Barba, Michael Hoffmann, Matias Korman, and Alexander Pilz

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

Abstract
We study generalizations of convex hulls to polygonal domains with holes. Convexity in Euclidean space is based on the notion of shortest paths, which are straight-line segments. In a polygonal domain, shortest paths are polygonal paths called geodesics. One possible generalization of convex hulls is based on the "rubber band" conception of the convex hull boundary as a shortest curve that encloses a given set of sites. However, it is NP-hard to compute such a curve in a general polygonal domain. Hence, we focus on a different, more direct generalization of convexity, where a set X is geodesically convex if it contains all geodesics between every pair of points x,y in X. The corresponding geodesic convex hull presents a few surprises, and turns out to behave quite differently compared to the classic Euclidean setting or to the geodesic hull inside a simple polygon. We describe a class of geometric objects that suffice to represent geodesic convex hulls of sets of sites, and characterize which such domains are geodesically convex. Using such a representation we present an algorithm to construct the geodesic convex hull of a set of O(n) sites in a polygonal domain with a total of n vertices and h holes in O(n^3h^{3+epsilon}) time, for any constant epsilon > 0.
Cite as

Luis Barba, Michael Hoffmann, Matias Korman, and Alexander Pilz. Convex Hulls in Polygonal Domains. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{barba_et_al:LIPIcs.SWAT.2018.8,
  author =	{Barba, Luis and Hoffmann, Michael and Korman, Matias and Pilz, Alexander},
  title =	{{Convex Hulls in Polygonal Domains}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{8:1--8:13},
  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.2018.8},
  URN =		{urn:nbn:de:0030-drops-88343},
  doi =		{10.4230/LIPIcs.SWAT.2018.8},
  annote =	{Keywords: geometric graph, polygonal domain, geodesic hull, shortest path}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.47
Two-Planar Graphs Are Quasiplanar

Authors: Michael Hoffmann and Csaba D. Tóth

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.
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Michael Hoffmann and Csaba D. Tóth. Two-Planar Graphs Are Quasiplanar. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{hoffmann_et_al:LIPIcs.MFCS.2017.47,
  author =	{Hoffmann, Michael and T\'{o}th, Csaba D.},
  title =	{{Two-Planar Graphs Are Quasiplanar}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.47},
  URN =		{urn:nbn:de:0030-drops-80811},
  doi =		{10.4230/LIPIcs.MFCS.2017.47},
  annote =	{Keywords: graph drawing, near-planar graph, simple topological plane graph}
}
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