16 Search Results for "Stephan, Daniel"


Document
Temporalizing Digraphs via Linear-Size Balanced Bi-Trees

Authors: Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
In a directed graph D on vertex set v₁,… ,v_n, a forward arc is an arc v_iv_j where i < j. A pair v_i,v_j is forward connected if there is a directed path from v_i to v_j consisting of forward arcs. In the Forward Connected Pairs Problem (FCPP), the input is a strongly connected digraph D, and the output is the maximum number of forward connected pairs in some vertex enumeration of D. We show that FCPP is in APX, as one can efficiently enumerate the vertices of D in order to achieve a quadratic number of forward connected pairs. For this, we construct a linear size balanced bi-tree T (an out-branching and an in-branching with same size and same root which are vertex disjoint in the sense that they share no vertex apart from their common root). The existence of such a T was left as an open problem (Brunelli, Crescenzi, Viennot, Networks 2023) motivated by the study of temporal paths in temporal networks. More precisely, T can be constructed in quadratic time (in the number of vertices) and has size at least n/3. The algorithm involves a particular depth-first search tree (Left-DFS) of independent interest, and shows that every strongly connected directed graph has a balanced separator which is a circuit. Remarkably, in the request version RFCPP of FCPP, where the input is a strong digraph D and a set of requests R consisting of pairs {x_i,y_i}, there is no constant c > 0 such that one can always find an enumeration realizing c.|R| forward connected pairs {x_i,y_i} (in either direction).

Cite as

Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot. Temporalizing Digraphs via Linear-Size Balanced Bi-Trees. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bessy_et_al:LIPIcs.STACS.2024.13,
  author =	{Bessy, St\'{e}phane and Thomass\'{e}, St\'{e}phan and Viennot, Laurent},
  title =	{{Temporalizing Digraphs via Linear-Size Balanced Bi-Trees}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{13:1--13:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.13},
  URN =		{urn:nbn:de:0030-drops-197235},
  doi =		{10.4230/LIPIcs.STACS.2024.13},
  annote =	{Keywords: digraph, temporal graph, temporalization, bi-tree, #1\{in-branching, out-branching, in-tree, out-tree\}, forward connected pairs, left-maximal DFS}
}
Document
Lossy Kernelization for (Implicit) Hitting Set Problems

Authors: Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi

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


Abstract
We re-visit the complexity of polynomial time pre-processing (kernelization) for the d-Hitting Set problem. This is one of the most classic problems in Parameterized Complexity by itself, and, furthermore, it encompasses several other of the most well-studied problems in this field, such as Vertex Cover, Feedback Vertex Set in Tournaments (FVST) and Cluster Vertex Deletion (CVD). In fact, d-Hitting Set encompasses any deletion problem to a hereditary property that can be characterized by a finite set of forbidden induced subgraphs. With respect to bit size, the kernelization complexity of d-Hitting Set is essentially settled: there exists a kernel with 𝒪(k^d) bits (𝒪(k^d) sets and 𝒪(k^{d-1}) elements) and this it tight by the result of Dell and van Melkebeek [STOC 2010, JACM 2014]. Still, the question of whether there exists a kernel for d-Hitting Set with fewer elements has remained one of the most major open problems in Kernelization. In this paper, we first show that if we allow the kernelization to be lossy with a qualitatively better loss than the best possible approximation ratio of polynomial time approximation algorithms, then one can obtain kernels where the number of elements is linear for every fixed d. Further, based on this, we present our main result: we show that there exist approximate Turing kernelizations for d-Hitting Set that even beat the established bit-size lower bounds for exact kernelizations - in fact, we use a constant number of oracle calls, each with "near linear" (𝒪(k^{1+ε})) bit size, that is, almost the best one could hope for. Lastly, for two special cases of implicit 3-Hitting set, namely, FVST and CVD, we obtain the "best of both worlds" type of results - (1+ε)-approximate kernelizations with a linear number of vertices. In terms of size, this substantially improves the exact kernels of Fomin et al. [SODA 2018, TALG 2019], with simpler arguments.

Cite as

Fedor V. Fomin, Tien-Nam Le, Daniel Lokshtanov, Saket Saurabh, Stéphan Thomassé, and Meirav Zehavi. Lossy Kernelization for (Implicit) Hitting Set Problems. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 49:1-49:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{fomin_et_al:LIPIcs.ESA.2023.49,
  author =	{Fomin, Fedor V. and Le, Tien-Nam and Lokshtanov, Daniel and Saurabh, Saket and Thomass\'{e}, St\'{e}phan and Zehavi, Meirav},
  title =	{{Lossy Kernelization for (Implicit) Hitting Set Problems}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{49:1--49:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.49},
  URN =		{urn:nbn:de:0030-drops-187020},
  doi =		{10.4230/LIPIcs.ESA.2023.49},
  annote =	{Keywords: Hitting Set, Lossy Kernelization}
}
Document
Strongly Hyperbolic Unit Disk Graphs

Authors: Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, and Daniel Stephan

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and introduce strongly hyperbolic unit disk graphs as a natural counterpart to the Euclidean variant. In contrast to the grid-like structures exhibited by Euclidean unit disk graphs, strongly hyperbolic networks feature hierarchical structures, which are also observed in complex real-world networks. We investigate basic properties of strongly hyperbolic unit disk graphs, including adjacencies and the formation of cliques, and utilize the derived insights to demonstrate that the class is useful for the development and analysis of graph algorithms. Specifically, we develop a simple greedy routing scheme and analyze its performance on strongly hyperbolic unit disk graphs in order to prove that routing can be performed more efficiently on such networks than in general.

Cite as

Thomas Bläsius, Tobias Friedrich, Maximilian Katzmann, and Daniel Stephan. Strongly Hyperbolic Unit Disk Graphs. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blasius_et_al:LIPIcs.STACS.2023.13,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Katzmann, Maximilian and Stephan, Daniel},
  title =	{{Strongly Hyperbolic Unit Disk Graphs}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.13},
  URN =		{urn:nbn:de:0030-drops-176652},
  doi =		{10.4230/LIPIcs.STACS.2023.13},
  annote =	{Keywords: hyperbolic geometry, unit disk graphs, greedy routing, hyperbolic random graphs, graph classes}
}
Document
Vision Paper
New Human Dynamics in the Emerging Metaverse: Towards a Quantum Phygital Approach by Integrating Space and Place (Vision Paper)

Authors: Daniel Sui and Shih-Lung Shaw

Published in: LIPIcs, Volume 240, 15th International Conference on Spatial Information Theory (COSIT 2022)


Abstract
With the convergence of mirror worlds, virtual worlds, lifelogging, and augmented/virtual reality, the emerging metaverse is rapidly becoming a major platform where humans work, shop, entertain themselves, and socialize with others. Human dynamics, which refers to all forms of human activities and interactions, will undergo profound transformations in the coming years with the advent of the metaverse. The new human dynamics will be neither physical nor digital but a seamless integration of both - phygital. The goal of this vision paper is to develop a phygital approach to support human dynamics research in the spirit of GIScience as a convergence. Built on our earlier work in human dynamics research, we argue that the current discussions on human dynamics are conceptually constrained by their physical and digital silos. The new phygital approach we are envisioning aims to transcend the simplistic dichotomy by integrating both space and place perspectives. This paper also draws on basic concepts in quantum physics and earlier discussions on their potential applications in geography and GIScience to espouse a quantum turn in exploring the human dynamics in the emerging metaverse. It explores how concepts, methods, and understandings from quantum physics and emerging quantum computing and communication technologies can be translated into addressing fundamental geographical analyses for this phygital world.

Cite as

Daniel Sui and Shih-Lung Shaw. New Human Dynamics in the Emerging Metaverse: Towards a Quantum Phygital Approach by Integrating Space and Place (Vision Paper). In 15th International Conference on Spatial Information Theory (COSIT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 240, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{sui_et_al:LIPIcs.COSIT.2022.11,
  author =	{Sui, Daniel and Shaw, Shih-Lung},
  title =	{{New Human Dynamics in the Emerging Metaverse: Towards a Quantum Phygital Approach by Integrating Space and Place}},
  booktitle =	{15th International Conference on Spatial Information Theory (COSIT 2022)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-257-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{240},
  editor =	{Ishikawa, Toru and Fabrikant, Sara Irina and Winter, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2022.11},
  URN =		{urn:nbn:de:0030-drops-168961},
  doi =		{10.4230/LIPIcs.COSIT.2022.11},
  annote =	{Keywords: metaverse, human dynamics, phygital, space-place, quantum, GIScience theory}
}
Document
Uncovering a Random Tree

Authors: Benjamin Hackl, Alois Panholzer, and Stephan Wagner

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)


Abstract
We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with n vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of their labels. With each new vertex, all edges to previously uncovered vertices are uncovered as well. In this way, one obtains a growing sequence of forests. Three particular aspects of this process are studied in this extended abstract: first the number of edges, which we prove to converge to a stochastic process akin to a Brownian bridge after appropriate rescaling. Second, the connected component of a fixed vertex, for which different phases are identified and limiting distributions determined in each phase. Lastly, the largest connected component, for which we also observe a phase transition.

Cite as

Benjamin Hackl, Alois Panholzer, and Stephan Wagner. Uncovering a Random Tree. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{hackl_et_al:LIPIcs.AofA.2022.10,
  author =	{Hackl, Benjamin and Panholzer, Alois and Wagner, Stephan},
  title =	{{Uncovering a Random Tree}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.10},
  URN =		{urn:nbn:de:0030-drops-160962},
  doi =		{10.4230/LIPIcs.AofA.2022.10},
  annote =	{Keywords: Labeled tree, uncover process, functional central limit theorem, limiting distribution, phase transition}
}
Document
Automorphisms of Random Trees

Authors: Christoffer Olsson and Stephan Wagner

Published in: LIPIcs, Volume 225, 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)


Abstract
We study the size of the automorphism group of two different types of random trees: Galton-Watson trees and Pólya trees. In both cases, we prove that it asymptotically follows a log-normal distribution. While the proof for Galton-Watson trees mainly relies on probabilistic arguments and a general result on additive tree functionals, generating functions are used in the case of Pólya trees.

Cite as

Christoffer Olsson and Stephan Wagner. Automorphisms of Random Trees. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{olsson_et_al:LIPIcs.AofA.2022.16,
  author =	{Olsson, Christoffer and Wagner, Stephan},
  title =	{{Automorphisms of Random Trees}},
  booktitle =	{33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-230-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{225},
  editor =	{Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2022.16},
  URN =		{urn:nbn:de:0030-drops-161026},
  doi =		{10.4230/LIPIcs.AofA.2022.16},
  annote =	{Keywords: random tree, Galton-Watson tree, P\'{o}lya tree, automorphism group, central limit theorem}
}
Document
Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games

Authors: Nathanaël Fijalkow, Paweł Gawrychowski, and Pierre Ohlmann

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)


Abstract
We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in NP ∩ coNP and not known to be in P. In a breakthrough result Calude, Jain, Khoussainov, Li, and Stephan constructed in 2017 a quasipolynomial time algorithm for solving parity games, which was quickly followed by a few other algorithms with the same complexity. Our objective is to investigate how these techniques can be extended to mean payoff games. The starting point is the combinatorial notion of universal trees: all quasipolynomial time algorithms for parity games have been shown to exploit universal trees. Universal graphs extend universal trees to arbitrary (positionally determined) objectives. We show that they yield a family of value iteration algorithms for solving mean payoff games which includes the value iteration algorithm due to Brim, Chaloupka, Doyen, Gentilini, and Raskin. The contribution of this paper is to prove tight bounds on the complexity of algorithms for mean payoff games using universal graphs. We consider two parameters: the largest weight N in absolute value and the number k of weights. The dependence in N in the existing value iteration algorithm is linear, we show that this can be improved to N^{1 - 1/n} and obtain a matching lower bound. However, we show that we cannot break the linear dependence in the exponent in the number k of weights implying that universal graphs do not yield a quasipolynomial time algorithm for solving mean payoff games.

Cite as

Nathanaël Fijalkow, Paweł Gawrychowski, and Pierre Ohlmann. Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{fijalkow_et_al:LIPIcs.MFCS.2020.34,
  author =	{Fijalkow, Nathana\"{e}l and Gawrychowski, Pawe{\l} and Ohlmann, Pierre},
  title =	{{Value Iteration Using Universal Graphs and the Complexity of Mean Payoff Games}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.34},
  URN =		{urn:nbn:de:0030-drops-127011},
  doi =		{10.4230/LIPIcs.MFCS.2020.34},
  annote =	{Keywords: Mean payoff games, Universal graphs, Value iteration}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Counting Answers to Existential Questions (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors: Holger Dell, Marc Roth, and Philip Wellnitz

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


Abstract
Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the problem’s parameterized and data complexity, where the query is considered to be small or even fixed, and the database is considered to be large. We identify two structural parameters for conjunctive queries that capture their inherent complexity: The dominating star size and the linked matching number. If the dominating star size of a conjunctive query is large, then we show that counting solution tuples to the query is at least as hard as counting dominating sets, which yields a fine-grained complexity lower bound under the Strong Exponential Time Hypothesis (SETH) as well as a #W[2]-hardness result in parameterized complexity. Moreover, if the linked matching number of a conjunctive query is large, then we show that the structure of the query is so rich that arbitrary queries up to a certain size can be encoded into it; in the language of parameterized complexity, this essentially establishes a #A[2]-completeness result. Using ideas stemming from Lovász (1967), we lift complexity results from the class of conjunctive queries to arbitrary existential or universal formulas that might contain inequalities and negations on constraints over the free variables. As a consequence, we obtain a complexity classification that refines and generalizes previous results of Chen, Durand, and Mengel (ToCS 2015; ICDT 2015; PODS 2016) for conjunctive queries and of Curticapean and Marx (FOCS 2014) for the subgraph counting problem. Our proof also relies on graph minors, and we show a strengthening of the Excluded-Grid-Theorem which might be of independent interest: If the linked matching number (and thus the treewidth) is large, then not only can we find a large grid somewhere in the graph, but we can find a large grid whose diagonal has disjoint paths leading into an assumed node-well-linked set.

Cite as

Holger Dell, Marc Roth, and Philip Wellnitz. Counting Answers to Existential Questions (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 113:1-113:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{dell_et_al:LIPIcs.ICALP.2019.113,
  author =	{Dell, Holger and Roth, Marc and Wellnitz, Philip},
  title =	{{Counting Answers to Existential Questions}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{113:1--113:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.113},
  URN =		{urn:nbn:de:0030-drops-106894},
  doi =		{10.4230/LIPIcs.ICALP.2019.113},
  annote =	{Keywords: Conjunctive queries, graph homomorphisms, counting complexity, parameterized complexity, fine-grained complexity}
}
Document
Counting Planar Tanglegrams

Authors: Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana, and Stephan Wagner

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)


Abstract
Tanglegrams are structures consisting of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the two trees. We say that a tanglegram is planar if it can be drawn in the plane without crossings. Using a blend of combinatorial and analytic techniques, we determine an asymptotic formula for the number of planar tanglegrams with n leaves on each side.

Cite as

Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana, and Stephan Wagner. Counting Planar Tanglegrams. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ralaivaosaona_et_al:LIPIcs.AofA.2018.32,
  author =	{Ralaivaosaona, Dimbinaina and Ravelomanana, Jean Bernoulli and Wagner, Stephan},
  title =	{{Counting Planar Tanglegrams}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.32},
  URN =		{urn:nbn:de:0030-drops-89259},
  doi =		{10.4230/LIPIcs.AofA.2018.32},
  annote =	{Keywords: rooted binary trees, tanglegram, planar, generating functions, asymptotic enumeration, singularity analysis}
}
Document
Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees

Authors: Dimbinaina Ralaivaosaona, Matas Sileikis, and Stephan Wagner

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)


Abstract
An additive functional of a rooted tree is a functional that can be calculated recursively as the sum of the values of the functional over the branches, plus a certain toll function. Janson recently proved a central limit theorem for additive functionals of conditioned Galton-Watson trees under the assumption that the toll function is local, i.e. only depends on a fixed neighbourhood of the root. We extend his result to functionals that are almost local, thus covering a wider range of functionals. Our main result is illustrated by two explicit examples: the (logarithm of) the number of matchings, and a functional stemming from a tree reduction process that was studied by Hackl, Heuberger, Kropf, and Prodinger.

Cite as

Dimbinaina Ralaivaosaona, Matas Sileikis, and Stephan Wagner. Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{ralaivaosaona_et_al:LIPIcs.AofA.2018.33,
  author =	{Ralaivaosaona, Dimbinaina and Sileikis, Matas and Wagner, Stephan},
  title =	{{Asymptotic Normality of Almost Local Functionals in Conditioned Galton-Watson Trees}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.33},
  URN =		{urn:nbn:de:0030-drops-89262},
  doi =		{10.4230/LIPIcs.AofA.2018.33},
  annote =	{Keywords: Galton-Watson trees, central limit theorem, additive functional}
}
Document
Routing with Congestion in Acyclic Digraphs

Authors: Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)


Abstract
We study the version of the k-disjoint paths problem where k demand pairs (s_1,t_1), ..., (s_k,t_k) are specified in the input and the paths in the solution are allowed to intersect, but such that no vertex is on more than c paths. We show that on directed acyclic graphs the problem is solvable in time n^{O(d)} if we allow congestion k-d for k paths. Furthermore, we show that, under a suitable complexity theoretic assumption, the problem cannot be solved in time f(k)n^{o(d*log(d))} for any computable function f.

Cite as

Saeed Akhoondian Amiri, Stephan Kreutzer, Dániel Marx, and Roman Rabinovich. Routing with Congestion in Acyclic Digraphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{amiri_et_al:LIPIcs.MFCS.2016.7,
  author =	{Amiri, Saeed Akhoondian and Kreutzer, Stephan and Marx, D\'{a}niel and Rabinovich, Roman},
  title =	{{Routing with Congestion in Acyclic Digraphs}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{7:1--7:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.7},
  URN =		{urn:nbn:de:0030-drops-64244},
  doi =		{10.4230/LIPIcs.MFCS.2016.7},
  annote =	{Keywords: algorithms, disjoint paths, congestion, acyclic digraphs, XP, W\lbrack1\rbrack-hard}
}
Document
Kernelization and Sparseness: the Case of Dominating Set

Authors: Pål Grønås Drange, Markus Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Felix Reidl, Fernando Sánchez Villaamil, Saket Saurabh, Sebastian Siebertz, and Somnath Sikdar

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)


Abstract
We prove that for every positive integer r and for every graph class G of bounded expansion, the r-DOMINATING SET problem admits a linear kernel on graphs from G. Moreover, in the more general case when G is only assumed to be nowhere dense, we give an almost linear kernel on G for the classic DOMINATING SET problem, i.e., for the case r=1. These results generalize a line of previous research on finding linear kernels for DOMINATING SET and r-DOMINATING SET (Alber et al., JACM 2004, Bodlaender et al., FOCS 2009, Fomin et al., SODA 2010, Fomin et al., SODA 2012, Fomin et al., STACS 2013). However, the approach taken in this work, which is based on the theory of sparse graphs, is radically different and conceptually much simpler than the previous approaches. We complement our findings by showing that for the closely related CONNECTED DOMINATING SET problem, the existence of such kernelization algorithms is unlikely, even though the problem is known to admit a linear kernel on H-topological-minor-free graphs (Fomin et al., STACS 2013). Also, we prove that for any somewhere dense class G, there is some r for which r-DOMINATING SET is W[2]-hard on G. Thus, our results fall short of proving a sharp dichotomy for the parameterized complexity of r-DOMINATING SET on subgraph-monotone graph classes: we conjecture that the border of tractability lies exactly between nowhere dense and somewhere dense graph classes.

Cite as

Pål Grønås Drange, Markus Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michal Pilipczuk, Felix Reidl, Fernando Sánchez Villaamil, Saket Saurabh, Sebastian Siebertz, and Somnath Sikdar. Kernelization and Sparseness: the Case of Dominating Set. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{drange_et_al:LIPIcs.STACS.2016.31,
  author =	{Drange, P\r{a}l Gr{\o}n\r{a}s and Dregi, Markus and Fomin, Fedor V. and Kreutzer, Stephan and Lokshtanov, Daniel and Pilipczuk, Marcin and Pilipczuk, Michal and Reidl, Felix and S\'{a}nchez Villaamil, Fernando and Saurabh, Saket and Siebertz, Sebastian and Sikdar, Somnath},
  title =	{{Kernelization and Sparseness: the Case of Dominating Set}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.31},
  URN =		{urn:nbn:de:0030-drops-57327},
  doi =		{10.4230/LIPIcs.STACS.2016.31},
  annote =	{Keywords: kernelization, dominating set, bounded expansion, nowhere dense}
}
Document
Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences

Authors: Heiner Klingenberg, Robin Martinjak, Frank Oliver Glöckner, Rolf Daniel, Thomas Lingner, and Peter Meinicke

Published in: OASIcs, Volume 34, German Conference on Bioinformatics 2013


Abstract
With the advent of metatranscriptomics it has now become possible to study the dynamics of microbial communities. The analysis of environmental RNA-Seq data implies several challenges for the development of efficient tools in bioinformatics. One of the first steps in the computational analysis of metatranscriptomic sequencing reads requires the separation of rRNA and mRNA fragments to ensure that only protein coding sequences are actually used in a subsequent functional analysis. In the context of the rRNA filtering task it is desirable to have a broad spectrum of different methods in order to find a suitable trade-off between speed and accuracy for a particular dataset. We introduce a machine learning approach for the detection of rRNA in metatranscriptomic sequencing reads that is based on support vector machines in combination with dinucleotide distance histograms for feature representation. The results show that our SVM-based approach is at least one order of magnitude faster than any of the existing tools with only a slight degradation of the detection performance when compared to state-of-the-art alignment-based methods.

Cite as

Heiner Klingenberg, Robin Martinjak, Frank Oliver Glöckner, Rolf Daniel, Thomas Lingner, and Peter Meinicke. Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences. In German Conference on Bioinformatics 2013. Open Access Series in Informatics (OASIcs), Volume 34, pp. 80-89, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{klingenberg_et_al:OASIcs.GCB.2013.80,
  author =	{Klingenberg, Heiner and Martinjak, Robin and Gl\"{o}ckner, Frank Oliver and Daniel, Rolf and Lingner, Thomas and Meinicke, Peter},
  title =	{{Dinucleotide distance histograms for fast detection of rRNA in metatranscriptomic sequences}},
  booktitle =	{German Conference on Bioinformatics 2013},
  pages =	{80--89},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-59-0},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{34},
  editor =	{Bei{\ss}barth, Tim and Kollmar, Martin and Leha, Andreas and Morgenstern, Burkhard and Schultz, Anne-Kathrin and Waack, Stephan and Wingender, Edgar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.GCB.2013.80},
  URN =		{urn:nbn:de:0030-drops-42324},
  doi =		{10.4230/OASIcs.GCB.2013.80},
  annote =	{Keywords: Metatranscriptomics, metagenomics, rRNA detection, distance histograms}
}
Document
From Visualization to Visually Enabled Reasoning

Authors: Joerg Meyer, Jim Thomas, Stephan Diehl, Brian Fisher, and Daniel A. Keim

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


Abstract
Interactive Visualization has been used to study scientific phenomena, analyze data, visualize information, and to explore large amounts of multi-variate data. It enables the human mind to gain novel insights by empowering the human visual system, encompassing the brain and the eyes, to discover properties that were previously unknown. While it is believed that the process of creating interactive visualizations is reasonably well understood, the process of stimulating and enabling human reasoning with the aid of interactive visualization tools is still a highly unexplored field. We hypothesize that visualizations make an impact if they successfully influence a thought process or a decision. Interacting with visualizations is part of this process. We present exemplary cases where visualization was successful in enabling human reasoning, and instances where the interaction with data helped in understanding the data and making a better informed decision. We suggest metrics that help in understanding the evolution of a decision making process. Such a metric would measure the efficiency of the reasoning process, rather than the performance of the visualization system or the user. We claim that the methodology of interactive visualization, which has been studied to a great extent, is now sufficiently mature, and we would like to provide some guidance regarding the evaluation of knowledge gain through visually enabled reasoning. It is our ambition to encourage the reader to take on the next step and move from information visualization to visually enabled reasoning.

Cite as

Joerg Meyer, Jim Thomas, Stephan Diehl, Brian Fisher, and Daniel A. Keim. From Visualization to Visually Enabled Reasoning. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 227-245, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InCollection{meyer_et_al:DFU.SciViz.2010.227,
  author =	{Meyer, Joerg and Thomas, Jim and Diehl, Stephan and Fisher, Brian and Keim, Daniel A.},
  title =	{{From Visualization to Visually Enabled Reasoning}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{227--245},
  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.2010.227},
  URN =		{urn:nbn:de:0030-drops-27078},
  doi =		{10.4230/DFU.SciViz.2010.227},
  annote =	{Keywords: Interactive Visualization, Reasoning}
}
Document
SAT-based Automatic Test Pattern Generation

Authors: Rolf Drechsler, Stephan Eggersglüß, Görschwin Fey, and Daniel Tille

Published in: Dagstuhl Seminar Proceedings, Volume 8351, Evolutionary Test Generation (2009)


Abstract
Due to the rapidly growing size of integrated circuits, there is a need for new algorithms for Automatic Test Pattern Generation (ATPG). While classical algorithms reach their limit, there have been recent advances in algorithms to solve Boolean Satisfiability (SAT). Because Boolean SAT solvers are working on Conjunctive Normal Forms (CNF), the problem has to be transformed. During transformation, relevant information about the problem might get lost and therefore is not available in the solving process. In the following we briefly motivate the problem and provide the latest developments in the field. The technique was implemented and experimental results are presented. The approach was combined with the ATPG framework of NXP Semiconductors. Significant improvements in overall performance and robustness are demonstrated.

Cite as

Rolf Drechsler, Stephan Eggersglüß, Görschwin Fey, and Daniel Tille. SAT-based Automatic Test Pattern Generation. In Evolutionary Test Generation. Dagstuhl Seminar Proceedings, Volume 8351, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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@InProceedings{drechsler_et_al:DagSemProc.08351.6,
  author =	{Drechsler, Rolf and Eggersgl\"{u}{\ss}, Stephan and Fey, G\"{o}rschwin and Tille, Daniel},
  title =	{{SAT-based Automatic Test Pattern Generation}},
  booktitle =	{Evolutionary Test Generation},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8351},
  editor =	{Holger Schlingloff and Tanja E. J. Vos and Joachim Wegener},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08351.6},
  URN =		{urn:nbn:de:0030-drops-20152},
  doi =		{10.4230/DagSemProc.08351.6},
  annote =	{Keywords: Circuit, ATPG, SAT, Boolean Satisfiability}
}
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