8 Search Results for "Heinrich, Irene"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.89
Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification

Authors: Georg Schindling

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph classes, two structures agree on all homomorphism counts from the class if and only if they satisfy the same sentences in a corresponding logic. This perspective often reveals connections between the combinatorial properties of graph classes and the syntactic structure of logical fragments. In this work, we extend this perspective to logics with restricted requantification, refining the stratification of logical resources in finite-variable counting logics. Specifically, we generalize Lovász-type theorems for these logics with either restricted conjunction or bounded quantifier-rank and present new combinatorial proofs of existing results. To this end, we introduce novel path and tree decompositions that incorporate the concept of reusability and develop characterizations based on pursuit-evasion games. Leveraging this framework, we establish that classes of bounded pathwidth and treewidth with reusability constraints are homomorphism distinguishing closed. Finally, we develop a comonadic perspective on requantification by constructing new comonads that encapsulate restricted-reusability pebble games. We show a tight correspondence between their coalgebras and path/tree decompositions, yielding categorical characterizations of reusability in graph decompositions. This unifies logical, combinatorial, and categorical perspectives on the notion of reusability.
Cite as

Georg Schindling. Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schindling:LIPIcs.MFCS.2025.89,
  author =	{Schindling, Georg},
  title =	{{Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{89:1--89:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.89},
  URN =		{urn:nbn:de:0030-drops-241962},
  doi =		{10.4230/LIPIcs.MFCS.2025.89},
  annote =	{Keywords: homomorphism indistinguishability, game comonads, finite variable counting logic, restricted conjunction, restricted requantification, tree decomposition, path decomposition}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.39
The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators

Authors: Tianwei Zhang and Stefan Szeider

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
We investigate the 3-decomposition conjecture, which states that every connected cubic graph can be decomposed into a spanning tree, a collection of cycles, and a matching. Using a SAT-based approach enhanced with specialized propagators, we verify the conjecture for all relevant graphs up to 28 vertices. Our method extends the Satisfiability Modulo Symmetries (SMS) framework with specialized propagators that exploit theoretical properties of minimal counterexamples (counterexamples with the minimal number of vertices), enabling efficient pruning. We demonstrate that graphs containing certain substructures cannot be minimal counterexamples to the conjecture, allowing us to exclude these patterns during the search dynamically. Our experimental results quantify the impact of different propagator configurations and forbidden subgraph constraints on solving efficiency, showing significant performance improvements when leveraging these techniques. The approach scales effectively to graphs of 28 vertices. Our work illustrates how combining SAT solving with specialized constraint propagation techniques can successfully address challenging combinatorial problems in contemporary graph theory.
Cite as

Tianwei Zhang and Stefan Szeider. The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang_et_al:LIPIcs.CP.2025.39,
  author =	{Zhang, Tianwei and Szeider, Stefan},
  title =	{{The 3-Decomposition Conjecture: A SAT-Based Approach with Specialized Propagators}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.39},
  URN =		{urn:nbn:de:0030-drops-239005},
  doi =		{10.4230/LIPIcs.CP.2025.39},
  annote =	{Keywords: SAT, Symmetry Breaking, Subgraphs, Propagators, Combinatorics}
}
Document
Resource Paper
DOI: 10.4230/TGDK.2.2.5
The Reasonable Ontology Templates Framework

Authors: Martin Georg Skjæveland and Leif Harald Karlsen

Published in: TGDK, Volume 2, Issue 2 (2024): Special Issue on Resources for Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 2, Issue 2

Abstract
Reasonable Ontology Templates (OTTR) is a templating language for representing and instantiating patterns. It is based on simple and generic, but powerful, mechanisms such as recursive macro expansion, term substitution and type systems, and is designed particularly for building and maintaining RDF knowledge graphs and OWL ontologies. In this resource paper, we present the formal specifications that define the OTTR framework. This includes the fundamentals of the OTTR language and the adaptions to make it fit with standard semantic web languages, and two serialization formats developed for semantic web practitioners. We also present the OTTR framework’s support for documenting, publishing and managing template libraries, and for tools for practical bulk instantiation of templates from tabular data and queryable data sources. The functionality of the OTTR framework is available for use through Lutra, an open-source reference implementation, and other independent implementations. We report on the use and impact of OTTR by presenting selected industrial use cases. Finally, we reflect on some design considerations of the language and framework and present ideas for future work.
Cite as

Martin Georg Skjæveland and Leif Harald Karlsen. The Reasonable Ontology Templates Framework. In Special Issue on Resources for Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 2, pp. 5:1-5:54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{skjaeveland_et_al:TGDK.2.2.5,
  author =	{Skj{\ae}veland, Martin Georg and Karlsen, Leif Harald},
  title =	{{The Reasonable Ontology Templates Framework}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:54},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.2.5},
  URN =		{urn:nbn:de:0030-drops-225896},
  doi =		{10.4230/TGDK.2.2.5},
  annote =	{Keywords: Ontology engineering, Ontology design patterns, Template mechanism, Macros}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2023.25
Twin-Width of Graphs with Tree-Structured Decompositions

Authors: Irene Heinrich and Simon Raßmann

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

Abstract
The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 [Édouard Bonnet et al., 2022; Édouard Bonnet et al., 2020], a mass of new results has appeared relating twin width to group theory, model theory, combinatorial optimization, and structural graph theory. We take a detailed look at the interplay between the twin-width of a graph and the twin-width of its components under tree-structured decompositions: We prove that the twin-width of a graph is at most twice its strong tree-width, contrasting nicely with the result of [Édouard Bonnet and Hugues Déprés, 2023; Édouard Bonnet and Hugues Déprés, 2022], which states that twin-width can be exponential in tree-width. Further, we employ the fundamental concept from structural graph theory of decomposing a graph into highly connected components, in order to obtain optimal linear bounds on the twin-width of a graph given the widths of its biconnected components. For triconnected components we obtain a linear upper bound if we add red edges to the components indicating the splits which led to the components. Extending this approach to quasi-4-connectivity, we obtain a quadratic upper bound. Finally, we investigate how the adhesion of a tree decomposition influences the twin-width of the decomposed graph.
Cite as

Irene Heinrich and Simon Raßmann. Twin-Width of Graphs with Tree-Structured Decompositions. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{heinrich_et_al:LIPIcs.IPEC.2023.25,
  author =	{Heinrich, Irene and Ra{\ss}mann, Simon},
  title =	{{Twin-Width of Graphs with Tree-Structured Decompositions}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{25:1--25:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.25},
  URN =		{urn:nbn:de:0030-drops-194449},
  doi =		{10.4230/LIPIcs.IPEC.2023.25},
  annote =	{Keywords: twin-width, quasi-4 connected components, strong tree-width}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2023.2
Using Light Spanning Graphs for Passenger Assignment in Public Transport

Authors: Irene Heinrich, Olli Herrala, Philine Schiewe, and Topias Terho

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
In a public transport network a passenger’s preferred route from a point x to another point y is usually the shortest path from x to y. However, it is simply impossible to provide all the shortest paths of a network via public transport. Hence, it is a natural question how a lighter sub-network should be designed in order to satisfy both the operator as well as the passengers. We provide a detailed analysis of the interplay of the following three quality measures of lighter public transport networks: - building cost: the sum of the costs of all edges remaining in the lighter network, - routing costs: the sum of all shortest paths costs weighted by the demands, - fairness: compared to the original network, for each two points the shortest path in the new network should cost at most a given multiple of the shortest path in the original network. We study the problem by generalizing the concepts of optimum communication spanning trees (Hu, 1974) and optimum requirement graphs (Wu, Chao, and Tang, 2002) to generalized optimum requirement graphs (GORGs), which are graphs achieving the social optimum amongst all subgraphs satisfying a given upper bound on the building cost. We prove that the corresponding decision problem is NP-complete, even on orb-webs, a variant of grids which serves as an important model of cities with a center. For the case that the given network is a parametric city (cf. Fielbaum et. al., 2017) with a heavy vertex we provide a polynomial-time algorithm solving the GORG-problem. Concerning the fairness-aspect, we prove that light spanners are a strong concept for public transport optimization. We underpin our theoretical considerations with integer programming-based experiments that allow us to compare the fairness-approach with the routing cost-approach as well as passenger assignment approaches from the literature.
Cite as

Irene Heinrich, Olli Herrala, Philine Schiewe, and Topias Terho. Using Light Spanning Graphs for Passenger Assignment in Public Transport. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{heinrich_et_al:OASIcs.ATMOS.2023.2,
  author =	{Heinrich, Irene and Herrala, Olli and Schiewe, Philine and Terho, Topias},
  title =	{{Using Light Spanning Graphs for Passenger Assignment in Public Transport}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{2:1--2:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.2},
  URN =		{urn:nbn:de:0030-drops-187637},
  doi =		{10.4230/OASIcs.ATMOS.2023.2},
  annote =	{Keywords: passenger assignment, line planning, public transport, discrete optimization, complexity, algorithm design}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2023.4
Non-Pool-Based Line Planning on Graphs of Bounded Treewidth

Authors: Irene Heinrich, Philine Schiewe, and Constantin Seebach

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
Line planning, i.e. choosing routes which are to be serviced by vehicles in order to satisfy network demands, is an important aspect of public transport planning. While there exist heuristic procedures for generating lines from scratch, most theoretical investigations consider the problem of choosing lines only from a predefined line pool. We consider the line planning problem when all simple paths can be used as lines and present an algorithm which is fixed-parameter tractable, i.e. it is efficient on instances with small parameter. As a parameter we consider the treewidth of the public transport network, along with its maximum degree as well as the maximum allowed frequency.
Cite as

Irene Heinrich, Philine Schiewe, and Constantin Seebach. Non-Pool-Based Line Planning on Graphs of Bounded Treewidth. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{heinrich_et_al:OASIcs.ATMOS.2023.4,
  author =	{Heinrich, Irene and Schiewe, Philine and Seebach, Constantin},
  title =	{{Non-Pool-Based Line Planning on Graphs of Bounded Treewidth}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{4:1--4:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.4},
  URN =		{urn:nbn:de:0030-drops-187656},
  doi =		{10.4230/OASIcs.ATMOS.2023.4},
  annote =	{Keywords: line planning, public transport, treewidth, integer programming, fixed parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.11
Exploration of Graphs with Excluded Minors

Authors: Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the online graph exploration problem proposed by Kalyanasundaram and Pruhs (1994) and prove a constant competitive ratio on minor-free graphs. This result encompasses and significantly extends the graph classes that were previously known to admit a constant competitive ratio. The main ingredient of our proof is that we find a connection between the performance of the particular exploration algorithm Blocking and the existence of light spanners. Conversely, we exploit this connection to construct light spanners of bounded genus graphs. In particular, we achieve a lightness that improves on the best known upper bound for genus g ≥ 1 and recovers the known tight bound for the planar case (g = 0).
Cite as

Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer. Exploration of Graphs with Excluded Minors. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baligacs_et_al:LIPIcs.ESA.2023.11,
  author =	{Balig\'{a}cs, J\'{u}lia and Disser, Yann and Heinrich, Irene and Schweitzer, Pascal},
  title =	{{Exploration of Graphs with Excluded Minors}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.11},
  URN =		{urn:nbn:de:0030-drops-186644},
  doi =		{10.4230/LIPIcs.ESA.2023.11},
  annote =	{Keywords: online algorithms, competitive analysis, graph exploration, graph spanners, minor-free graphs, bounded genus graphs}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.8
Algorithms and Hardness for Non-Pool-Based Line Planning

Authors: Irene Heinrich, Philine Schiewe, and Constantin Seebach

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

Abstract
Line planning, i.e. choosing paths which are operated by one vehicle end-to-end, is an important aspect of public transport planning. While there exist heuristic procedures for generating lines from scratch, most theoretical observations consider the problem of choosing lines from a predefined line pool. In this paper, we consider the complexity of the line planning problem when all simple paths can be used as lines. Depending on the cost structure, we show that the problem can be NP-hard even for paths and stars, and that no polynomial time approximation of sub-linear performance is possible. Additionally, we identify polynomially solvable cases and present a pseudo-polynomial solution approach for trees.
Cite as

Irene Heinrich, Philine Schiewe, and Constantin Seebach. Algorithms and Hardness for Non-Pool-Based Line Planning. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{heinrich_et_al:OASIcs.ATMOS.2022.8,
  author =	{Heinrich, Irene and Schiewe, Philine and Seebach, Constantin},
  title =	{{Algorithms and Hardness for Non-Pool-Based Line Planning}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{8:1--8:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.8},
  URN =		{urn:nbn:de:0030-drops-171124},
  doi =		{10.4230/OASIcs.ATMOS.2022.8},
  annote =	{Keywords: line planning, public transport, discrete optimization, complexity, algorithm design}
}
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