16 Search Results for "Gr�be, Mathias"

Document
DOI: 10.4230/LIPIcs.IPEC.2023.19
Finding Degree-Constrained Acyclic Orientations

Authors: Jaroslav Garvardt, Malte Renken, Jannik Schestag, and Mathias Weller

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
We consider the problem of orienting a given, undirected graph into a (directed) acyclic graph such that the in-degree of each vertex v is in a prescribed list λ(v). Variants of this problem have been studied for a long time and with various applications, but mostly without the requirement for acyclicity. Without this requirement, the problem is closely related to the classical General Factor problem, which is known to be NP-hard in general, but polynomial-time solvable if no list λ(v) contains large "gaps" [Cornuéjols, J. Comb. Theory B, 1988]. In contrast, we show that deciding if an acyclic orientation exists is NP-hard even in the absence of such "gaps". On the positive side, we design parameterized algorithms for various, natural parameterizations of the acyclic orientation problem. A special case of the orientation problem with degree constraints recently came up in the context of reconstructing evolutionary histories (that is, phylogenetic networks). This phylogenetic setting imposes additional structure onto the problem that can be exploited algorithmically, allowing us to show fixed-parameter tractability when parameterized by either the treewidth of G (a smaller parameter than the frequently employed "level"), by the number of vertices v for which |λ(v)| ≥ 2, by the number of vertices v for which the highest value in λ(v) is at least 2. While the latter result can be extended to the general degree-constraint acyclic orientation problem, we show that the former cannot unless FPT=W[1].
Cite as

Jaroslav Garvardt, Malte Renken, Jannik Schestag, and Mathias Weller. Finding Degree-Constrained Acyclic Orientations. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{garvardt_et_al:LIPIcs.IPEC.2023.19,
  author =	{Garvardt, Jaroslav and Renken, Malte and Schestag, Jannik and Weller, Mathias},
  title =	{{Finding Degree-Constrained Acyclic Orientations}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.19},
  URN =		{urn:nbn:de:0030-drops-194383},
  doi =		{10.4230/LIPIcs.IPEC.2023.19},
  annote =	{Keywords: Graph Orientation, Phylogenetic Networks, General Factor, NP-hardness, Parameterized Algorithms, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.20
Graph Clustering Problems Under the Lens of Parameterized Local Search

Authors: Jaroslav Garvardt, Nils Morawietz, André Nichterlein, and Mathias Weller

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract
Cluster Editing is the problem of finding the minimum number of edge-modifications that transform a given graph G into a cluster graph G', that is, each connected component of G' is a clique. Similarly, in the Cluster Deletion problem, we further restrict the sought cluster graph G' to contain only edges that are also present in G. In this work, we consider the parameterized complexity of a local search variant for both problems: LS Cluster Deletion and LS Cluster Editing. Herein, the input also comprises an integer k and a partition 𝒞 of the vertex set of G that describes an initial cluster graph G^*, and we are to decide whether the "k-move-neighborhood" of G^* contains a cluster graph G' that is "better" (uses less modifications) than G^*. Roughly speaking, two cluster graphs G₁ and G₂ are k-move-neighbors if G₁ can be obtained from G₂ by moving at most k vertices to different connected components. We consider parameterizations by k + 𝓁 for some natural parameters 𝓁, such as the number of clusters in 𝒞, the size of a largest cluster in 𝒞, or the cluster-vertex-deletion number (cvd) of G. Our main lower-bound results are that LS Cluster Editing is W[1]-hard when parameterized by k even if 𝒞 has size two and that both LS Cluster Deletion and LS Cluster Editing are W[1]-hard when parameterized by k + 𝓁, where 𝓁 is the size of the largest cluster of 𝒞. On the positive side, we show that both problems admit an algorithm that runs in k^{𝒪(k)}⋅ cvd^{3k} ⋅ n^{𝒪(1)} time and either finds a better cluster graph or correctly outputs that there is no better cluster graph in the k-move-neighborhood of the initial cluster graph. As an intermediate result, we also obtain an algorithm that solves Cluster Deletion in cvd^{cvd} ⋅ n^{𝒪(1)} time.
Cite as

Jaroslav Garvardt, Nils Morawietz, André Nichterlein, and Mathias Weller. Graph Clustering Problems Under the Lens of Parameterized Local Search. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{garvardt_et_al:LIPIcs.IPEC.2023.20,
  author =	{Garvardt, Jaroslav and Morawietz, Nils and Nichterlein, Andr\'{e} and Weller, Mathias},
  title =	{{Graph Clustering Problems Under the Lens of Parameterized Local Search}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.20},
  URN =		{urn:nbn:de:0030-drops-194391},
  doi =		{10.4230/LIPIcs.IPEC.2023.20},
  annote =	{Keywords: parameterized local search, permissive local search, FPT, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.8
IPASIR-UP: User Propagators for CDCL

Authors: Katalin Fazekas, Aina Niemetz, Mathias Preiner, Markus Kirchweger, Stefan Szeider, and Armin Biere

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
Modern SAT solvers are frequently embedded as sub-reasoning engines into more complex tools for addressing problems beyond the Boolean satisfiability problem. Examples include solvers for Satisfiability Modulo Theories (SMT), combinatorial optimization, model enumeration and counting. In such use cases, the SAT solver is often able to provide relevant information beyond the satisfiability answer. Further, domain knowledge of the embedding system (e.g., symmetry properties or theory axioms) can be beneficial for the CDCL search, but cannot be efficiently represented in clausal form. In this paper, we propose a general interface to inspect and influence the internal behaviour of CDCL SAT solvers. Our goal is to capture the most essential functionalities that are sufficient to simplify and improve use cases that require a more fine-grained interaction with the SAT solver than provided via the standard IPASIR interface. For our experiments, we extend CaDiCaL with our interface and evaluate it on two representative use cases: enumerating graphs within the SAT modulo Symmetries framework (SMS), and as the main CDCL(T) SAT engine of the SMT solver cvc5.
Cite as

Katalin Fazekas, Aina Niemetz, Mathias Preiner, Markus Kirchweger, Stefan Szeider, and Armin Biere. IPASIR-UP: User Propagators for CDCL. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fazekas_et_al:LIPIcs.SAT.2023.8,
  author =	{Fazekas, Katalin and Niemetz, Aina and Preiner, Mathias and Kirchweger, Markus and Szeider, Stefan and Biere, Armin},
  title =	{{IPASIR-UP: User Propagators for CDCL}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.8},
  URN =		{urn:nbn:de:0030-drops-184709},
  doi =		{10.4230/LIPIcs.SAT.2023.8},
  annote =	{Keywords: SAT, CDCL, Satisfiability Modulo Theories, Satisfiability Modulo Symmetries}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.69
Embedding Phylogenetic Trees in Networks of Low Treewidth

Authors: Leo van Iersel, Mark Jones, and Mathias Weller

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

Abstract
Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called Tree Containment, arises when validating networks constructed by phylogenetic inference methods. We present the first algorithm for (rooted) Tree Containment using the treewidth t of the input network N as parameter, showing that the problem can be solved in 2^O(t²)⋅|N| time and space.
Cite as

Leo van Iersel, Mark Jones, and Mathias Weller. Embedding Phylogenetic Trees in Networks of Low Treewidth. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{vaniersel_et_al:LIPIcs.ESA.2022.69,
  author =	{van Iersel, Leo and Jones, Mark and Weller, Mathias},
  title =	{{Embedding Phylogenetic Trees in Networks of Low Treewidth}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{69:1--69:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.69},
  URN =		{urn:nbn:de:0030-drops-170070},
  doi =		{10.4230/LIPIcs.ESA.2022.69},
  annote =	{Keywords: fixed-parameter tractability, treewidth, phylogenetic tree, phylogenetic network, display graph, tree containment, embedding}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.6
Sea-Rise Flooding on Massive Dynamic Terrains

Authors: Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Predicting floods caused by storm surges is a crucial task. Since the rise of ocean water can create floods that extend far onto land, the flood damage can be severe. By developing efficient flood prediction algorithms that use very detailed terrain models and accurate sea-level forecasts, users can plan mitigations such as flood walls and gates to minimize the damage from storm surge flooding. In this paper we present a data structure for predicting floods from dynamic sea-level forecast data on dynamic massive terrains. The forecast data is dynamic in the sense that new forecasts are released several times per day; the terrain is dynamic in the sense that the terrain model may be updated to plan flood mitigations. Since accurate flood risk computations require using very detailed terrain models, and such terrain models can easily exceed the size of the main memory in a regular computer, our data structure is I/O-efficient, that is, it minimizes the number of I/Os (i.e. block transfers) between main memory and disk. For a terrain represented as a raster of N cells, it can be constructed using O(N/B log_M/B N/B) I/Os, it can compute the flood risk in a given small region using O(log_B N) I/Os, and it can handle updating the terrain elevation in a given small region using O(log²_B N) I/Os, where B is the block size and M is the capacity of main memory.
Cite as

Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang. Sea-Rise Flooding on Massive Dynamic Terrains. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arge_et_al:LIPIcs.SWAT.2020.6,
  author =	{Arge, Lars and Rav, Mathias and Revsb{\ae}k, Morten and Shin, Yujin and Yang, Jungwoo},
  title =	{{Sea-Rise Flooding on Massive Dynamic Terrains}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.6},
  URN =		{urn:nbn:de:0030-drops-122539},
  doi =		{10.4230/LIPIcs.SWAT.2020.6},
  annote =	{Keywords: Computational geometry, I/O-algorithms, merge tree, dynamic terrain}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GISCIENCE.2018.63
Towards the Statistical Analysis and Visualization of Places (Short Paper)

Authors: René Westerholt, Mathias Gröbe, Alexander Zipf, and Dirk Burghardt

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

Abstract
The concept of place recently gains momentum in GIScience. In some fields like human geography, spatial cognition or information theory, this topic already has a longer scholarly tradition. This is however not yet completely the case with statistical spatial analysis and cartography. Despite that, taking full advantage of the plethora of user-generated information that we have available these days requires mature place-based statistical and visualization concepts. This paper contributes to these developments: We integrate existing place definitions into an understanding of places as a system of interlinked, constituent characteristics. Based on this, challenges and first promising conceptual ideas are discussed from statistical and visualization viewpoints.
Cite as

René Westerholt, Mathias Gröbe, Alexander Zipf, and Dirk Burghardt. Towards the Statistical Analysis and Visualization of Places (Short Paper). In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 63:1-63:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{westerholt_et_al:LIPIcs.GISCIENCE.2018.63,
  author =	{Westerholt, Ren\'{e} and Gr\"{o}be, Mathias and Zipf, Alexander and Burghardt, Dirk},
  title =	{{Towards the Statistical Analysis and Visualization of Places}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{63:1--63:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-083-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{114},
  editor =	{Winter, Stephan and Griffin, Amy and Sester, Monika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.63},
  URN =		{urn:nbn:de:0030-drops-93914},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.63},
  annote =	{Keywords: Platial Analysis, Visualization, Statistics, Geosocial Media}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.5
Power of d Choices with Simple Tabulation

Authors: Anders Aamand, Mathias Bæk Tejs Knudsen, and Mikkel Thorup

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We consider the classic d-choice paradigm of Azar et al. [STOC'94] in which m balls are put into n bins sequentially as follows: For each ball we are given a choice of d bins chosen according to d hash functions and the ball is placed in the least loaded of these bins, breaking ties arbitrarily. The interest is in the number of balls in the fullest bin after all balls have been placed. In this paper we suppose that the d hash functions are simple tabulation hash functions which are easy to implement and can be evaluated in constant time. Generalising a result by Dahlgaard et al. [SODA'16] we show that for an arbitrary constant d >= 2 the expected maximum load is at most (lg lg n)/(lg d) + O(1). We further show that by using a simple tie-breaking algorithm introduced by Vöcking [J.ACM'03] the expected maximum load is reduced to (lg lg n)/(d lg phi_d) + O(1) where phi_d is the rate of growth of the d-ary Fibonacci numbers. Both of these expected bounds match those known from the fully random setting. The analysis by Dahlgaard et al. relies on a proof by Patrascu and Thorup [J.ACM'11] concerning the use of simple tabulation for cuckoo hashing. We require a generalisation to d>2 hash functions, but the original proof is an 8-page tour de force of ad-hoc arguments that do not appear to generalise. Our main technical contribution is a shorter, simpler and more accessible proof of the result by Patrascu and Thorup, where the relevant parts generalise nicely to the analysis of d choices.
Cite as

Anders Aamand, Mathias Bæk Tejs Knudsen, and Mikkel Thorup. Power of d Choices with Simple Tabulation. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{aamand_et_al:LIPIcs.ICALP.2018.5,
  author =	{Aamand, Anders and B{\ae}k Tejs Knudsen, Mathias and Thorup, Mikkel},
  title =	{{Power of d Choices with Simple Tabulation}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.5},
  URN =		{urn:nbn:de:0030-drops-90096},
  doi =		{10.4230/LIPIcs.ICALP.2018.5},
  annote =	{Keywords: Hashing, Load Balancing, Balls and Bins, Simple Tabulation}
}
Document
DOI: 10.4230/LIPIcs.TIME.2017.12
Time Expressions Recognition with Word Vectors and Neural Networks

Authors: Mathias Etcheverry and Dina Wonsever

Published in: LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

Abstract
This work re-examines the widely addressed problem of the recognition and interpretation of time expressions, and suggests an approach based on distributed representations and artificial neural networks. Artificial neural networks allow us to build highly generic models, but the large variety of hyperparameters makes it difficult to determine the best configuration. In this work we study the behavior of different models by varying the number of layers, sizes and normalization techniques. We also analyze the behavior of distributed representations in the temporal domain, where we find interesting properties regarding order and granularity. The experiments were conducted mainly for Spanish, although this does not affect the approach, given its generic nature. This work aims to be a starting point towards processing temporality in texts via word vectors and neural networks, without the need of any kind of feature engineering.
Cite as

Mathias Etcheverry and Dina Wonsever. Time Expressions Recognition with Word Vectors and Neural Networks. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{etcheverry_et_al:LIPIcs.TIME.2017.12,
  author =	{Etcheverry, Mathias and Wonsever, Dina},
  title =	{{Time Expressions Recognition with Word Vectors and Neural Networks}},
  booktitle =	{24th International Symposium on Temporal Representation and Reasoning (TIME 2017)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-052-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{90},
  editor =	{Schewe, Sven and Schneider, Thomas and Wijsen, Jef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.12},
  URN =		{urn:nbn:de:0030-drops-79253},
  doi =		{10.4230/LIPIcs.TIME.2017.12},
  annote =	{Keywords: Natural Language Processing, Time Expressions, Word Embeddings, Neural Networks}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.11
Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

Authors: Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below epsilon-0. In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes. Our formal library also provides, somewhat nonstandardly, multisets with negative multiplicities and syntactic ordinals with negative coefficients. We present applications of the library to formalizations of Goodstein's theorem and the decidability of unary PCF (programming computable functions).
Cite as

Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel. Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{blanchette_et_al:LIPIcs.FSCD.2017.11,
  author =	{Blanchette, Jasmin Christian and Fleury, Mathias and Traytel, Dmitriy},
  title =	{{Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.11},
  URN =		{urn:nbn:de:0030-drops-77155},
  doi =		{10.4230/LIPIcs.FSCD.2017.11},
  annote =	{Keywords: Multisets, ordinals, proof assistants}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.64
Additive Spanners and Distance Oracles in Quadratic Time

Authors: Mathias Bæk Tejs Knudsen

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

Abstract
Let G be an unweighted, undirected graph. An additive k-spanner of G is a subgraph H that approximates all distances between pairs of nodes up to an additive error of +k, that is, it satisfies d_H(u,v) <= d_G(u,v)+k for all nodes u,v, where d is the shortest path distance. We give a deterministic algorithm that constructs an additive O(1)-spanner with O(n^(4/3)) edges in O(n^2) time. This should be compared with the randomized Monte Carlo algorithm by Woodruff [ICALP 2010] giving an additive 6-spanner with O(n^(4/3)log^3 n) edges in expected time O(n^2 log^2 n). An (alpha,beta)-approximate distance oracle for G is a data structure that supports the following distance queries between pairs of nodes in G. Given two nodes u, v it can in constant time compute a distance estimate d' that satisfies d <= d' <= alpha d + beta where d is the distance between u and v in G. Sommer [ICALP 2016] gave a randomized Monte Carlo (2,1)-distance oracle of size O(n^(5/3) polylog n) in expected time O(n^2 polylog n). As an application of the additive O(1)-spanner we improve the construction by Sommer [ICALP 2016] and give a Las Vegas (2,1)-distance oracle of size O(n^(5/3)) in time O(n^2). This also implies an algorithm that in O(n^2) time gives approximate distance for all pairs of nodes in G improving on the O(n^2 log n) algorithm by Baswana and Kavitha [SICOMP 2010].
Cite as

Mathias Bæk Tejs Knudsen. Additive Spanners and Distance Oracles in Quadratic Time. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 64:1-64:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{knudsen:LIPIcs.ICALP.2017.64,
  author =	{Knudsen, Mathias B{\ae}k Tejs},
  title =	{{Additive Spanners and Distance Oracles in Quadratic Time}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{64:1--64:12},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.64},
  URN =		{urn:nbn:de:0030-drops-73924},
  doi =		{10.4230/LIPIcs.ICALP.2017.64},
  annote =	{Keywords: graph algorithms, data structures, additive spanners, distance oracles}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2012.35
Reliability and Delay Distributions of Train Connections

Authors: Mohammad H. Keyhani, Mathias Schnee, Karsten Weihe, and Hans-Peter Zorn

Published in: OASIcs, Volume 25, 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2012)

Abstract
Finding reliable train connections is a considerable issue in timetable information since train delays perturb the timetable daily. We present an effective probabilistic approach for estimating the reliability of connections in a large train network. Experiments on real customer queries and real timetables for all trains in Germany show that our approach can be implemented to deliver good results at the expense of only little processing time. Based on probability distributions for train events in connections, we estimate the reliability of connections. We have analyzed our computed reliability ratings by validating our predictions against real delay data from German Railways. This study shows that we are able to predict the feasibility of connections very well. In essence, our predictions are slightly optimistic for connections with a high rating and pretty accurate for connections with a medium rating. Only for the rare cases of a very low rating, we are too pessimistic. Our probabilistic approach already delivers good results, still has improvement potential, and offers a new perspective in the search for more reliable connections in order to bring passengers safely to their destinations even in case of delays.
Cite as

Mohammad H. Keyhani, Mathias Schnee, Karsten Weihe, and Hans-Peter Zorn. Reliability and Delay Distributions of Train Connections. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 35-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{keyhani_et_al:OASIcs.ATMOS.2012.35,
  author =	{Keyhani, Mohammad H. and Schnee, Mathias and Weihe, Karsten and Zorn, Hans-Peter},
  title =	{{Reliability and Delay Distributions of Train Connections}},
  booktitle =	{12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{35--46},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-45-3},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{25},
  editor =	{Delling, Daniel and Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2012.35},
  URN =		{urn:nbn:de:0030-drops-37014},
  doi =		{10.4230/OASIcs.ATMOS.2012.35},
  annote =	{Keywords: Stochastic Delay Propagation, Timetable Information, Connection Reliability}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2011.191
Conditional Reactive Systems

Authors: H. J. Sander Bruggink, Raphaël Cauderlier, Mathias Hülsbusch, and Barbara König

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Abstract
We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; second, it turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done very elegantly in the more general setting.
Cite as

H. J. Sander Bruggink, Raphaël Cauderlier, Mathias Hülsbusch, and Barbara König. Conditional Reactive Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 191-203, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bruggink_et_al:LIPIcs.FSTTCS.2011.191,
  author =	{Bruggink, H. J. Sander and Cauderlier, Rapha\"{e}l and H\"{u}lsbusch, Mathias and K\"{o}nig, Barbara},
  title =	{{Conditional Reactive Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{191--203},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.191},
  URN =		{urn:nbn:de:0030-drops-33257},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.191},
  annote =	{Keywords: reactive systems, graph transformation, graph logic, Hoare triples, critical pair analysis}
}
Document
DOI: 10.4230/DFU.SciViz.2010.78
CSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Casting

Authors: Younis Hijazi, Aaron Knoll, Mathias Schott, Andrew Kensler, and Charles Hansen

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
We apply Knoll et al.'s algorithm [Knoll et al., "Fast ray tracing of arbitrary implicit surfaces with interval and affine arithmetic.", Comput. Graph. Forum, 28(1):26–40, 2009] to interactively ray-cast constructive solid geometry (CSG) objects of arbitrary primitives represented as implicit functions. Whereas modeling globally with implicit surfaces suffers from a lack of control, implicits are well-suited for arbitrary primitives and can be combined through various operations. The conventional way to represent union and intersection with interval arithmetic (IA) is simply using min and max but other operations such as the product of two forms can be useful in modeling joints between multiple objects. Typical primitives are objects of simple shape, e.g. cubes, cylinders, spheres, etc. Our method handles arbitrary primitives, e.g. superquadrics or non-algebraic implicits. Subdivision and interval arithmetic guarantee robustness whereas GPU ray casting allows for fast and aesthetic rendering. Indeed, ray casting parallelizes efficiently and trivially and thus takes advantage of the continuous increasing computational power of hardware (CPUs and GPUs); moreover it lends itself to multi-bounce effects, such as shadows and transparency, which help for the visualization of complicated objects. With our system, we are able to render multi-material CSG trees of implicits robustly, in interactive time and with good visual quality.
Cite as

Younis Hijazi, Aaron Knoll, Mathias Schott, Andrew Kensler, and Charles Hansen. CSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Casting. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 78-89, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{hijazi_et_al:DFU.SciViz.2010.78,
  author =	{Hijazi, Younis and Knoll, Aaron and Schott, Mathias and Kensler, Andrew and Hansen, Charles},
  title =	{{CSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Casting}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{78--89},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.78},
  URN =		{urn:nbn:de:0030-drops-26986},
  doi =		{10.4230/DFU.SciViz.2010.78},
  annote =	{Keywords: Implicit Surface, Constructive Solid Geometry, Interval Arithmetic, Ray Casting}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2008.1584
Efficient On-Trip Timetable Information in the Presence of Delays

Authors: Lennart Frede, Matthias Müller-Hannemann, and Mathias Schnee

Published in: OASIcs, Volume 9, 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) (2008)

Abstract
The search for train connections in state-of-the-art commercial timetable information systems is based on a static schedule. Unfortunately, public transportation systems suffer from delays for various reasons. Thus, dynamic changes of the planned schedule have to be taken into account. A system that has access to delay information of trains (and uses this information within search queries) can provide valid alternatives in case a train change breaks. Additionally, it can be used to actively guide passengers as these alternatives may be presented before the passenger is already stranded at a station due to a broken transfer. In this work we present an approach which takes a stream of delay information and schedule changes on short notice (partial train cancellations, extra trains) into account. Primary delays of trains may cause a cascade of so-called secondary delays of other trains which have to wait according to certain waiting policies between connecting trains. We introduce the concept of a dependency graph to efficiently calculate and update all primary and secondary delays. This delay information is then incorporated into a time-expanded search graph which has to be updated dynamically. These update operations are quite complex, but turn out to be not time-critical in a fully realistic scenario. We finally present a case study with data provided by Deutsche Bahn AG showing that this approach has been successfully integrated into our multi-criteria timetable information system MOTIS and can handle massive delay data streams instantly.
Cite as

Lennart Frede, Matthias Müller-Hannemann, and Mathias Schnee. Efficient On-Trip Timetable Information in the Presence of Delays. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Open Access Series in Informatics (OASIcs), Volume 9, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{frede_et_al:OASIcs.ATMOS.2008.1584,
  author =	{Frede, Lennart and M\"{u}ller-Hannemann, Matthias and Schnee, Mathias},
  title =	{{Efficient On-Trip Timetable Information in the Presence of Delays}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)},
  pages =	{1--16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Fischetti, Matteo and Widmayer, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2008.1584},
  URN =		{urn:nbn:de:0030-drops-15843},
  doi =		{10.4230/OASIcs.ATMOS.2008.1584},
  annote =	{Keywords: Timetable information system, primary and secondary delays dependency graph, dynamic graph update}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2007.1178
16. Improved Search for Night Train Connections

Authors: Thorsten Gunkel, Matthias Müller-Hannemann, and Mathias Schnee

Published in: OASIcs, Volume 7, 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07) (2007)

Abstract
The search for attractive night train connections is fundamentally different from ordinary search: the primary objective of a costumer of a night train is to have a reasonably long sleeping period without interruptions due to train changes. For most passenger it is also undesired to reach the final destination too early in the morning. These objectives are in sharp contrast to standard information systems which focus on minimizing the total travel time. In this paper we present and compare two new approaches to support queries for night train connections. These approaches have been integrated into the Multi-Objective Traffic Information System (MOTIS) which is currently developed by our group. Its purpose is to find all train connections which are attractive from a costumer point of view. With a computational study we demonstrate that our specialized algorithms for night train connections are able to satisfy costumer queries much better than standard methods. This can be achieved with reasonable computational costs: a specialized night train search requires only a few seconds of CPU time.
Cite as

Thorsten Gunkel, Matthias Müller-Hannemann, and Mathias Schnee. 16. Improved Search for Night Train Connections. In 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07). Open Access Series in Informatics (OASIcs), Volume 7, pp. 243-258, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{gunkel_et_al:OASIcs.ATMOS.2007.1178,
  author =	{Gunkel, Thorsten and M\"{u}ller-Hannemann, Matthias and Schnee, Mathias},
  title =	{{16. Improved Search for Night Train Connections}},
  booktitle =	{7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07)},
  pages =	{243--258},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-04-0},
  ISSN =	{2190-6807},
  year =	{2007},
  volume =	{7},
  editor =	{Ahuja, Ravindra K. and Liebchen, Christian and Mesa, Juan A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2007.1178},
  URN =		{urn:nbn:de:0030-drops-11781},
  doi =		{10.4230/OASIcs.ATMOS.2007.1178},
  annote =	{Keywords: Timetable information system, multi-criteria optimization, night trains, computational study}
}
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