7 Search Results for "W�rtz, Rolf P."


Document
Multistage Vertex Cover

Authors: Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)


Abstract
Covering all edges of a graph by a small number of vertices, this is the NP-hard Vertex Cover problem, is among the most fundamental algorithmic tasks. Following a recent trend in studying dynamic and temporal graphs, we initiate the study of Multistage Vertex Cover. Herein, having a series of graphs with same vertex set but over time changing edge sets (known as temporal graph consisting of time layers), the goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that the two vertex cover sets between two subsequent layers differ not too much (specified by a given parameter). We show that, different from classic Vertex Cover and some other dynamic or temporal variants of it, Multistage Vertex Cover is computationally hard even in fairly restricted settings. On the positive side, however, we also spot several fixed-parameter tractability results based on some of the most natural parameterizations.

Cite as

Till Fluschnik, Rolf Niedermeier, Valentin Rohm, and Philipp Zschoche. Multistage Vertex Cover. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{fluschnik_et_al:LIPIcs.IPEC.2019.14,
  author =	{Fluschnik, Till and Niedermeier, Rolf and Rohm, Valentin and Zschoche, Philipp},
  title =	{{Multistage Vertex Cover}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.14},
  URN =		{urn:nbn:de:0030-drops-114753},
  doi =		{10.4230/LIPIcs.IPEC.2019.14},
  annote =	{Keywords: NP-hardness, dynamic graph problems, temporal graphs, time-evolving networks, W\lbrack1\rbrack-hardness, fixed-parameter tractability, kernelization}
}
Document
Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth

Authors: Bas A. M. van Geffen, Bart M. P. Jansen, Arnoud A. W. M. de Kroon, and Rolf Morel

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)


Abstract
Many combinatorial problems can be solved in time O^*(c^{tw}) on graphs of treewidth tw, for a problem-specific constant c. In several cases, matching upper and lower bounds on c are known based on the Strong Exponential Time Hypothesis (SETH). In this paper we investigate the complexity of solving problems on graphs of bounded cutwidth, a graph parameter that takes larger values than treewidth. We strengthen earlier treewidth-based lower bounds to show that, assuming SETH, Independent Set cannot be solved in O^*((2-epsilon)^{ctw}) time, and Dominating Set cannot be solved in O^*((3-epsilon)^{ctw}) time. By designing a new crossover gadget, we extend these lower bounds even to planar graphs of bounded cutwidth or treewidth. Hence planarity does not help when solving Independent Set or Dominating Set on graphs of bounded width. This sharply contrasts the fact that in many settings, planarity allows problems to be solved much more efficiently.

Cite as

Bas A. M. van Geffen, Bart M. P. Jansen, Arnoud A. W. M. de Kroon, and Rolf Morel. Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{vangeffen_et_al:LIPIcs.IPEC.2018.3,
  author =	{van Geffen, Bas A. M. and Jansen, Bart M. P. and de Kroon, Arnoud A. W. M. and Morel, Rolf},
  title =	{{Lower Bounds for Dynamic Programming on Planar Graphs of Bounded Cutwidth}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.3},
  URN =		{urn:nbn:de:0030-drops-102049},
  doi =		{10.4230/LIPIcs.IPEC.2018.3},
  annote =	{Keywords: planarization, dominating set, cutwidth, lower bounds, strong exponential time hypothesis}
}
Document
The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs

Authors: Vikraman Arvind, Frank Fuhlbrück, Johannes Köbler, Sebastian Kuhnert, and Gaurav Rattan

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


Abstract
In this paper we study the complexity of the following problems: 1. Given a colored graph X=(V,E,c), compute a minimum cardinality set of vertices S (subset of V) such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem is computing a minimum base S for a permutation group G <= S_n given by generators, i.e., a minimum cardinality subset S of [n] such that no nontrivial permutation in G fixes all elements of S. Our focus is mainly on the parameterized complexity of these problems. We show that when k=|S| is treated as parameter, then both problems are MINI[1]-hard. For the dual problems, where k=n-|S| is the parameter, we give FPT~algorithms. 2. A notion closely related to fixing is called individualization. Individualization combined with the Weisfeiler-Leman procedure is a fundamental technique in algorithms for Graph Isomorphism. Motivated by the power of individualization, in the present paper we explore the complexity of individualization: what is the minimum number of vertices we need to individualize in a given graph such that color refinement "succeeds" on it. Here "succeeds" could have different interpretations, and we consider the following: It could mean the individualized graph becomes: (a) discrete, (b) amenable, (c)compact, or (d) refinable. In particular, we study the parameterized versions of these problems where the parameter is the number of vertices individualized. We show a dichotomy: For graphs with color classes of size at most 3 these problems can be solved in polynomial time, while starting from color class size 4 they become W[P]-hard.

Cite as

Vikraman Arvind, Frank Fuhlbrück, Johannes Köbler, Sebastian Kuhnert, and Gaurav Rattan. The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{arvind_et_al:LIPIcs.MFCS.2016.13,
  author =	{Arvind, Vikraman and Fuhlbr\"{u}ck, Frank and K\"{o}bler, Johannes and Kuhnert, Sebastian and Rattan, Gaurav},
  title =	{{The Parameterized Complexity of Fixing Number and Vertex Individualization in Graphs}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{13:1--13:14},
  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.2016.13},
  URN =		{urn:nbn:de:0030-drops-64294},
  doi =		{10.4230/LIPIcs.MFCS.2016.13},
  annote =	{Keywords: parameterized complexity, graph automorphism, fixing number, base size, individualization}
}
Document
The Parameterized Complexity of the Minimum Shared Edges Problem

Authors: Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)


Abstract
We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP is a subset of coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].

Cite as

Till Fluschnik, Stefan Kratsch, Rolf Niedermeier, and Manuel Sorge. The Parameterized Complexity of the Minimum Shared Edges Problem. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 448-462, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{fluschnik_et_al:LIPIcs.FSTTCS.2015.448,
  author =	{Fluschnik, Till and Kratsch, Stefan and Niedermeier, Rolf and Sorge, Manuel},
  title =	{{The Parameterized Complexity of the Minimum Shared Edges Problem}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{448--462},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.448},
  URN =		{urn:nbn:de:0030-drops-56323},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.448},
  annote =	{Keywords: Parameterized complexity, kernelization, treewidth, treewidth reduction}
}
Document
06031 Abstracts Collection – Organic Computing – Controlled Emergence

Authors: Kirstie Bellman, Peter Hofmann, Christian Müller-Schloer, Hartmut Schmeck, and Rolf P. Würtz

Published in: Dagstuhl Seminar Proceedings, Volume 6031, Organic Computing - Controlled Emergence (2006)


Abstract
Organic Computing has emerged recently as a challenging vision for future information processing systems, based on the insight that we will soon be surrounded by large collections of autonomous systems equipped with sensors and actuators to be aware of their environment, to communicate freely, and to organize themselves in order to perform the actions and services required. Organic Computing Systems will adapt dynamically to the current conditions of its environment, they will be self-organizing, self-configuring, self-healing, self-protecting, self-explaining, and context-aware. From 15.01.06 to 20.01.06, the Dagstuhl Seminar 06031 ``Organic Computing – Controlled Emergence'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. The seminar was characterized by the very constructive search for common ground between engineering and natural sciences, between informatics on the one hand and biology, neuroscience, and chemistry on the other. The common denominator was the objective to build practically usable self-organizing and emergent systems or their components. An indicator for the practical orientation of the seminar was the large number of OC application systems, envisioned or already under implementation, such as the Internet, robotics, wireless sensor networks, traffic control, computer vision, organic systems on chip, an adaptive and self-organizing room with intelligent sensors or reconfigurable guiding systems for smart office buildings. The application orientation was also apparent by the large number of methods and tools presented during the seminar, which might be used as building blocks for OC systems, such as an evolutionary design methodology, OC architectures, especially several implementations of observer/controller structures, measures and measurement tools for emergence and complexity, assertion-based methods to control self-organization, wrappings, a software methodology to build reflective systems, and components for OC middleware. Organic Computing is clearly oriented towards applications but is augmented at the same time by more theoretical bio-inspired and nature-inspired work, such as chemical computing, theory of complex systems and non-linear dynamics, control mechanisms in insect swarms, homeostatic mechanisms in the brain, a quantitative approach to robustness, abstraction and instantiation as a central metaphor for understanding complex systems. Compared to its beginnings, Organic Computing is coming of age. The OC vision is increasingly padded with meaningful applications and usable tools, but the path towards full OC systems is still complex. There is progress in a more scientific understanding of emergent processes. In the future, we must understand more clearly how to open the configuration space of technical systems for on-line modification. Finally, we must make sure that the human user remains in full control while allowing the systems to optimize.

Cite as

Kirstie Bellman, Peter Hofmann, Christian Müller-Schloer, Hartmut Schmeck, and Rolf P. Würtz. 06031 Abstracts Collection – Organic Computing – Controlled Emergence. In Organic Computing - Controlled Emergence. Dagstuhl Seminar Proceedings, Volume 6031, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{bellman_et_al:DagSemProc.06031.1,
  author =	{Bellman, Kirstie and Hofmann, Peter and M\"{u}ller-Schloer, Christian and Schmeck, Hartmut and W\"{u}rtz, Rolf P.},
  title =	{{06031 Abstracts Collection – Organic Computing – Controlled Emergence}},
  booktitle =	{Organic Computing - Controlled Emergence},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6031},
  editor =	{Kirstie Bellman and Peter Hofmann and Christian M\"{u}ller-Schloer and Hartmut Schmeck and Rolf W\"{u}rtz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06031.1},
  URN =		{urn:nbn:de:0030-drops-5777},
  doi =		{10.4230/DagSemProc.06031.1},
  annote =	{Keywords: Emergence, self-organization, self-configuration, self-healing, self-protection, self-explaining, context-awareness}
}
Document
06031 Executive Summary – Organic Computing – Controlled Emergence

Authors: Kirstie Bellman, Peter Hofmann, Christian Müller-Schloer, Hartmut Schmeck, and Rolf P. Würtz

Published in: Dagstuhl Seminar Proceedings, Volume 6031, Organic Computing - Controlled Emergence (2006)


Abstract
Organic Computing has emerged recently as a challenging vision for future information processing systems, based on the insight that we will soon be surrounded by systems with massive numbers of processing elements, sensors and actuators, many of which will be autonomous. Because of the size of these systems it is infeasible for us to monitor and control them entirely from external observations; instead they will need to help us monitor, control and adapt themselves. To do so, these components will need to be aware of their environment, to communicate freely, and to organize themselves in order to perform the actions and services that are required. The presence of networks of intelligent systems in our environment opens up fascinating application areas but, at the same time, bears the problem of their controllability. Hence, we have to construct these systems which we increasingly depend on as robust, safe, flexible, and trustworthy as possible. In particular, a strong orientation towards human needs as opposed to a pure implementation of the technologically possible seems absolutely central. In order to achieve these goals, our technical systems will have to act more independently, flexibly, and autonomously, i.e., they will have to exhibit lifelike properties. We call those systems ''organic''. Hence, an ''Organic Computing System'' is a technical system which adapts dynamically to the current conditions of its environment. It will be selforganizing, selfconfiguring, selfhealing, selfprotecting, selfexplaining, and context-aware.

Cite as

Kirstie Bellman, Peter Hofmann, Christian Müller-Schloer, Hartmut Schmeck, and Rolf P. Würtz. 06031 Executive Summary – Organic Computing – Controlled Emergence. In Organic Computing - Controlled Emergence. Dagstuhl Seminar Proceedings, Volume 6031, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{bellman_et_al:DagSemProc.06031.2,
  author =	{Bellman, Kirstie and Hofmann, Peter and M\"{u}ller-Schloer, Christian and Schmeck, Hartmut and W\"{u}rtz, Rolf P.},
  title =	{{06031 Executive Summary – Organic Computing – Controlled Emergence}},
  booktitle =	{Organic Computing - Controlled Emergence},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6031},
  editor =	{Kirstie Bellman and Peter Hofmann and Christian M\"{u}ller-Schloer and Hartmut Schmeck and Rolf W\"{u}rtz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06031.2},
  URN =		{urn:nbn:de:0030-drops-5788},
  doi =		{10.4230/DagSemProc.06031.2},
  annote =	{Keywords: Emergence, self-organization, self-configuration, self-healing, self-protection, self-explaining, context-awareness}
}
Document
Feature-driven Emergence of Model Graphs for Object Recognition and Categorization

Authors: Günter Westphal, Christoph von der Malsburg, and Rolf P. Würtz

Published in: Dagstuhl Seminar Proceedings, Volume 6031, Organic Computing - Controlled Emergence (2006)


Abstract
An important requirement for the expression of cognitive structures is the ability to form mental objects by rapidly binding together constituent parts. In this sense, one may conceive the brain's data structure to have the form of graphs whose nodes are labeled with elementary features. These provide a versatile data format with the additional ability to render the structure of any mental object. Because of the multitude of possible object variations the graphs are required to be dynamic. Upon presentation of an image a so-called model graph should rapidly emerge by binding together memorized subgraphs derived from earlier learning examples driven by the image features. In this model, the richness and flexibility of the mind is made possible by a combinatorical game of immense complexity. Consequently, the emergence of model graphs is a laborious task which, in computer vision, has most often been disregarded in favor of employing model graphs tailored to specific object categories like, for instance, faces in frontal pose. Recognition or categorization of arbitrary objects, however, demands dynamic graphs. In this work we propose a form of graph dynamics, which proceeds in two steps. In the first step component classifiers, which decide whether a feature is present in an image, are learned from training images. For processing arbitrary objects, features are small localized grid graphs, so-called parquet graphs, whose nodes are attributed with Gabor amplitudes. Through combination of these classifiers into a linear discriminant that conforms to Linsker's infomax principle a weighted majority voting scheme is implemented. It allows for preselection of salient learning examples, so-called model candidates, and likewise for preselection of categories the object in the presented image supposably belongs to. Each model candidate is verified in a second step using a variant of elastic graph matching, a standard correspondence-based technique for face and object recognition. To further differentiate between model candidates with similar features it is asserted that the features be in similar spatial arrangement for the model to be selected. Model graphs are constructed dynamically by assembling model features into larger graphs according to their spatial arrangement. From the viewpoint of pattern recognition, the presented technique is a combination of a discriminative (feature-based) and a generative (correspondence-based) classifier while the majority voting scheme implemented in the feature-based part is an extension of existing multiple feature subset methods. We report the results of experiments on standard databases for object recognition and categorization. The method achieved high recognition rates on identity, object category, pose, and illumination type. Unlike many other models the presented technique can also cope with varying background, multiple objects, and partial occlusion.

Cite as

Günter Westphal, Christoph von der Malsburg, and Rolf P. Würtz. Feature-driven Emergence of Model Graphs for Object Recognition and Categorization. In Organic Computing - Controlled Emergence. Dagstuhl Seminar Proceedings, Volume 6031, pp. 1-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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@InProceedings{westphal_et_al:DagSemProc.06031.5,
  author =	{Westphal, G\"{u}nter and von der Malsburg, Christoph and W\"{u}rtz, Rolf P.},
  title =	{{Feature-driven Emergence of Model Graphs for Object Recognition and Categorization}},
  booktitle =	{Organic Computing - Controlled Emergence},
  pages =	{1--46},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6031},
  editor =	{Kirstie Bellman and Peter Hofmann and Christian M\"{u}ller-Schloer and Hartmut Schmeck and Rolf W\"{u}rtz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06031.5},
  URN =		{urn:nbn:de:0030-drops-5756},
  doi =		{10.4230/DagSemProc.06031.5},
  annote =	{Keywords: Graph matching, recognition, categorization, computer vision, self-organization, emergence}
}
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