7 Search Results for "G�rg, Carsten"


Document
A Natural Intuitionistic Modal Logic: Axiomatization and Bi-Nested Calculus

Authors: Philippe Balbiani, Han Gao, Çiğdem Gencer, and Nicola Olivetti

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)


Abstract
We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The calculus provides a decision procedure as well as a countermodel extraction: from any failed derivation of a given formula, we obtain by the calculus a finite countermodel of it directly.

Cite as

Philippe Balbiani, Han Gao, Çiğdem Gencer, and Nicola Olivetti. A Natural Intuitionistic Modal Logic: Axiomatization and Bi-Nested Calculus. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 13:1-13:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{balbiani_et_al:LIPIcs.CSL.2024.13,
  author =	{Balbiani, Philippe and Gao, Han and Gencer, \c{C}i\u{g}dem and Olivetti, Nicola},
  title =	{{A Natural Intuitionistic Modal Logic: Axiomatization and Bi-Nested Calculus}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{13:1--13:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.13},
  URN =		{urn:nbn:de:0030-drops-196565},
  doi =		{10.4230/LIPIcs.CSL.2024.13},
  annote =	{Keywords: Intuitionistic Modal Logic, Axiomatization, Completeness, Sequent Calculus}
}
Document
On Dynamic α + 1 Arboricity Decomposition and Out-Orientation

Authors: Aleksander B. G. Christiansen, Jacob Holm, Eva Rotenberg, and Carsten Thomassen

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
A graph has arboricity α if its edges can be partitioned into α forests. The dynamic arboricity decomposition problem is to update a partitioning of the graph’s edges into forests, as a graph undergoes insertions and deletions of edges. We present an algorithm for maintaining partitioning into α+1 forests, provided the arboricity of the dynamic graph never exceeds α. Our algorithm has an update time of Õ(n^{3/4}) when α is at most polylogarithmic in n. Similarly, the dynamic bounded out-orientation problem is to orient the edges of the graph such that the out-degree of each vertex is at all times bounded. For this problem, we give an algorithm that orients the edges such that the out-degree is at all times bounded by α+1, with an update time of Õ(n^{5/7}), when α is at most polylogarithmic in n. Here, the choice of α+1 should be viewed in the light of the well-known lower bound by Brodal and Fagerberg which establishes that, for general graphs, maintaining only α out-edges would require linear update time. However, the lower bound by Brodal and Fagerberg is non-planar. In this paper, we give a lower bound showing that even for planar graphs, linear update time is needed in order to maintain an explicit three-out-orientation. For planar graphs, we show that the dynamic four forest decomposition and four-out-orientations, can be updated in Õ(n^{1/2}) time.

Cite as

Aleksander B. G. Christiansen, Jacob Holm, Eva Rotenberg, and Carsten Thomassen. On Dynamic α + 1 Arboricity Decomposition and Out-Orientation. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{christiansen_et_al:LIPIcs.MFCS.2022.34,
  author =	{Christiansen, Aleksander B. G. and Holm, Jacob and Rotenberg, Eva and Thomassen, Carsten},
  title =	{{On Dynamic \alpha + 1 Arboricity Decomposition and Out-Orientation}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.34},
  URN =		{urn:nbn:de:0030-drops-168320},
  doi =		{10.4230/LIPIcs.MFCS.2022.34},
  annote =	{Keywords: Dynamic graphs, bounded arboricity, data structures}
}
Document
A Family of Centrality Measures for Graph Data Based on Subgraphs

Authors: Cristian Riveros and Jorge Salas

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)


Abstract
We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of "relevant subgraphs" by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width.

Cite as

Cristian Riveros and Jorge Salas. A Family of Centrality Measures for Graph Data Based on Subgraphs. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{riveros_et_al:LIPIcs.ICDT.2020.23,
  author =	{Riveros, Cristian and Salas, Jorge},
  title =	{{A Family of Centrality Measures for Graph Data Based on Subgraphs}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.23},
  URN =		{urn:nbn:de:0030-drops-119474},
  doi =		{10.4230/LIPIcs.ICDT.2020.23},
  annote =	{Keywords: Graph data, graph centrality, centrality measures}
}
Document
Solving the Stable Set Problem in Terms of the Odd Cycle Packing Number

Authors: Adrian Bock, Yuri Faenza, Carsten Moldenhauer, and Andres Jacinto Ruiz-Vargas

Published in: LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)


Abstract
The classic stable set problem asks to find a maximum cardinality set of pairwise non-adjacent vertices in an undirected graph G. This problem is NP-hard to approximate with factor n^{1-epsilon} for any constant epsilon>0 [Hastad/Acta Mathematica/1996; Zuckerman/STOC/2006], where n is the number of vertices, and therefore there is no hope for good approximations in the general case. We study the stable set problem when restricted to graphs with bounded odd cycle packing number ocp(G), possibly by a function of n. This is the largest number of vertex-disjoint odd cycles in G. Equivalently, it is the logarithm of the largest absolute value of a sub-determinant of the edge-node incidence matrix A_G of G. Hence, if A_G is totally unimodular, then ocp(G)=0. Therefore, ocp(G) is a natural distance measure of A_G to the set of totally unimodular matrices on a scale from 1 to n/3. When ocp(G)=0, the graph is bipartite and it is well known that stable set can be solved in polynomial time. Our results imply that the odd cycle packing number indeed strongly influences the approximability of stable set. More precisely, we obtain a polynomial-time approximation scheme for graphs with ocp(G)=o(n/log(n)), and an alpha-approximation algorithm for any graph where alpha smoothly increases from a constant to n as ocp(G) grows from O(n/log(n)) to n/3. On the hardness side, we show that, assuming the exponential-time hypothesis, stable set cannot be solved in polynomial time if ocp(G)=Omega(log^{1+epsilon}(n)) for some epsilon>0. Finally, we generalize a theorem by Györi et al. [Györi et al./Discrete Mathematics/1997] and show that graphs without odd cycles of small weight can be made bipartite by removing a small number of vertices. This allows us to extend some of our above results to the weighted stable set problem.

Cite as

Adrian Bock, Yuri Faenza, Carsten Moldenhauer, and Andres Jacinto Ruiz-Vargas. Solving the Stable Set Problem in Terms of the Odd Cycle Packing Number. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 187-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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@InProceedings{bock_et_al:LIPIcs.FSTTCS.2014.187,
  author =	{Bock, Adrian and Faenza, Yuri and Moldenhauer, Carsten and Ruiz-Vargas, Andres Jacinto},
  title =	{{Solving the Stable Set Problem in Terms of the Odd Cycle Packing Number}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{187--198},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Raman, Venkatesh and Suresh, S. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.187},
  URN =		{urn:nbn:de:0030-drops-48422},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.187},
  annote =	{Keywords: stable set problem, independent set problem, approximation algorithms, odd cycle packing number, maximum subdeterminants}
}
Document
Biological Data Visualization (Dagstuhl Seminar 12372)

Authors: Carsten Görg, Lawrence Hunter, Jessie Kennedy, Sean O'Donoghue, and Jarke J. Van Wijk

Published in: Dagstuhl Reports, Volume 2, Issue 9 (2013)


Abstract
The topic of visualizing biological data has recently seen growing interest. Visualization approaches can help researchers understand and analyze today's large and complex biological datasets. The aim of this seminar was to bring together biologists, bioinformaticians, and computer scientists to survey the current state of tools for visualizing biological data and to define a research agenda for developing the next generation of tools. During the seminar, the participants formed working groups on nine different topics, reflected on the ongoing research in those areas, and discussed how to address key challenges; six talks complemented the work in the breakout groups. This report documents the program and the outcome of Dagstuhl Seminar 12372 "Biological Data Visualization".

Cite as

Carsten Görg, Lawrence Hunter, Jessie Kennedy, Sean O'Donoghue, and Jarke J. Van Wijk. Biological Data Visualization (Dagstuhl Seminar 12372). In Dagstuhl Reports, Volume 2, Issue 9, pp. 131-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@Article{gorg_et_al:DagRep.2.9.131,
  author =	{G\"{o}rg, Carsten and Hunter, Lawrence and Kennedy, Jessie and O'Donoghue, Sean and Van Wijk, Jarke J.},
  title =	{{Biological Data Visualization (Dagstuhl Seminar 12372)}},
  pages =	{131--164},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{2},
  number =	{9},
  editor =	{G\"{o}rg, Carsten and Hunter, Lawrence and Kennedy, Jessie and O'Donoghue, Sean and Van Wijk, Jarke J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.2.9.131},
  URN =		{urn:nbn:de:0030-drops-39731},
  doi =		{10.4230/DagRep.2.9.131},
  annote =	{Keywords: Information visualization, data visualization, biology, bioinformatics, user interfaces, visual analytics}
}
Document
Qualitative Abstraction and Inherent Uncertainty in Scene Recognition

Authors: Carsten Elfers, Otthein Herzog, Andrea Miene, and Thomas Wagner

Published in: Dagstuhl Seminar Proceedings, Volume 8091, Logic and Probability for Scene Interpretation (2008)


Abstract
The interpretation of scenes, e.g., in videos, is demanding at all levels. At the image processing level it is necessary to apply an "intelligent" segmentation and to determine the objects of interest. For the higher symbolic levels it is a challenging task to perform the transition between quantitative and qualitative data and to determine the relations between objects. Here we assume that the position of objects ("agents") in images and videos will already be determined as a minimal requirement for the further analysis. The interpretation of complex and dynamic scenes with embedded intentional agents is one of the most challenging tasks in current AI and imposes highly heterogeneous requirements. A key problem is the efficient and robust representation of uncertainty. We propose that uncertainty should be distinguished with respect to two different epistemological sources: (1) noisy sensor information and (2) ignorance. In this presentation we propose possible solutions to this class of problems. The use and evaluation of sensory information in the field of robotics shows impressive results especially in the fields of localization (e.g. MCL) and map building (e.g. SLAM) but also imposes serious problems on the successive higher levels of processing due to the probabilistic nature. In this presentation we propose that the use of (a) qualitative abstraction (classic approach) from quantitative to (at least partial) qualitative representations and (b) coherence-based perception validation based on Dempster-Shafer (DST) can help to reduce the problem significantly. The second important probability problem class that will be addressed is ignorance. In our presentation we will focus on reducing missing information by inference. We contrast/compare our experiences in an important field of scene interpretation namely plan and intention recognition. The first approach is based on a logical abductive approach and the second approach in contrast uses a probabilistic approach (Relational Hidden Markov Model (RHMM)).

Cite as

Carsten Elfers, Otthein Herzog, Andrea Miene, and Thomas Wagner. Qualitative Abstraction and Inherent Uncertainty in Scene Recognition. In Logic and Probability for Scene Interpretation. Dagstuhl Seminar Proceedings, Volume 8091, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{elfers_et_al:DagSemProc.08091.11,
  author =	{Elfers, Carsten and Herzog, Otthein and Miene, Andrea and Wagner, Thomas},
  title =	{{Qualitative Abstraction and Inherent Uncertainty in Scene Recognition}},
  booktitle =	{Logic and Probability for Scene Interpretation},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8091},
  editor =	{Anthony G. Cohn and David C. Hogg and Ralf M\"{o}ller and Bernd Neumann},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08091.11},
  URN =		{urn:nbn:de:0030-drops-16141},
  doi =		{10.4230/DagSemProc.08091.11},
  annote =	{Keywords: Scene interpretation, intentional agents, uncertainty, qualitative abstraction, coherence-based perception, abduction, RHMM}
}
Document
PDL with Intersection and Converse is 2EXP-complete

Authors: Stefan Göller, Markus Lohrey, and Carsten Lutz

Published in: Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)


Abstract
The logic ICPDL is the expressive extension of Propositional Dynamic Logic (PDL), which admits intersection and converse as program operators. The result of this paper is containment of ICPDL-satisfiability in $2$EXP, which improves the previously known non-elementary upper bound and implies $2$EXP-completeness due to an existing lower bound for PDL with intersection (IPDL). The proof proceeds showing that every satisfiable ICPDL formula has model of tree width at most two. Next, we reduce satisfiability in ICPDL to $omega$-regular tree satisfiability in ICPDL. In the latter problem the set of possible models is restricted to trees of an $omega$-regular tree language. In the final step,$omega$-regular tree satisfiability is reduced the emptiness problem for alternating two-way automata on infinite trees. In this way, a more elegant proof is obtained for Danecki's difficult result that satisfiability in IPDL is in $2EXP$.

Cite as

Stefan Göller, Markus Lohrey, and Carsten Lutz. PDL with Intersection and Converse is 2EXP-complete. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{goller_et_al:DagSemProc.07441.5,
  author =	{G\"{o}ller, Stefan and Lohrey, Markus and Lutz, Carsten},
  title =	{{PDL with Intersection and Converse is 2EXP-complete}},
  booktitle =	{Algorithmic-Logical Theory of Infinite Structures},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7441},
  editor =	{Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.5},
  URN =		{urn:nbn:de:0030-drops-14093},
  doi =		{10.4230/DagSemProc.07441.5},
  annote =	{Keywords: Satisfiability, Propositional Dynamic Logic, Computational Complexity}
}
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