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Large induced subgraphs via triangulations and CMSO
 in Proceedings of SODA 2014, SIAM
, 2014
"... We obtain an algorithmic metatheorem for the following optimization problem. Let ϕ be a Counting Monadic Second Order Logic (CMSO) formula and t ≥ 0 be an integer. For a given graph G = (V,E), the task is to maximize X  subject to the following: there is a set F ⊆ V such that X ⊆ F, the subgraph ..."
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Cited by 3 (2 self)
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We obtain an algorithmic metatheorem for the following optimization problem. Let ϕ be a Counting Monadic Second Order Logic (CMSO) formula and t ≥ 0 be an integer. For a given graph G = (V,E), the task is to maximize X  subject to the following: there is a set F ⊆ V such that X ⊆ F, the subgraph
Width parameters beyond treewidth and their applications
 Computer Journal
, 2007
"... Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compare ..."
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Cited by 40 (0 self)
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Besides the very successful concept of treewidth (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width ’ parameters in combinatorial structures delivers—besides traditional treewidth and derived dynamic programming schemes—also a number of other useful parameters like branchwidth, rankwidth (cliquewidth) or hypertreewidth. In this contribution, we demonstrate how ‘width ’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.
Bidimensionality and EPTAS
"... Bidimensionality theory appears to be a powerful framework for the development of metaalgorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain subexponential time parameterized algorithms for problems on Hminor free graphs. Demaine and Hajiaghayi [SODA 2005] e ..."
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Cited by 12 (5 self)
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Bidimensionality theory appears to be a powerful framework for the development of metaalgorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain subexponential time parameterized algorithms for problems on Hminor free graphs. Demaine and Hajiaghayi [SODA 2005] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems, and subsequently improved these results to EPTASs. Fomin et. al [SODA 2010] established a third metaalgorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In this paper we revisit bidimensionality theory from the perspective of approximation algorithms and redesign the framework for obtaining EPTASs to be more powerful, easier to apply and easier to understand. One of the important conditions required in the framework developed by Demaine and Hajiaghayi [SODA 2005] is that to obtain an EPTAS for a graph optimization problem Π, we have to know a constantfactor approximation algorithm for Π. Our approach eliminates this strong requirement, which makes it amenable to more problems. At the heart of our framework is a decomposition lemma which states that for “most ” bidimensional problems, there is a polynomial time algorithm which given an Hminorfree graph G as input and an ɛ> 0 outputs a vertex set X of size ɛ · OP T such that the treewidth of G \ X is O(1/ɛ). Here, OP T is the objective function value of the problem in question This allows us to obtain EPTASs on (apex)minorfree graphs for all problems covered by the previous framework, as well as for a wide range of packing problems, partial covering problems and problems that are neither closed under taking minors, nor contractions. To the best of our knowledge for many of these problems including Cycle Packing, VertexH
unknown title
"... Algorithms parameterized by vertex cover and modular width, through potential maximal cliques ..."
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Algorithms parameterized by vertex cover and modular width, through potential maximal cliques
Width parameters beyond treewidth and their applications
, 2007
"... Besides the very successful concept of treewidth (see [H. Bodlaender, A. Koster: Combinatorial optimisation on graphs of bounded treewidth. These special issues on Parametrized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have ..."
Abstract

Cited by 1 (0 self)
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Besides the very successful concept of treewidth (see [H. Bodlaender, A. Koster: Combinatorial optimisation on graphs of bounded treewidth. These special issues on Parametrized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these “width” parameters in combinatorial structures delivers — besides traditional treewidth and derived dynamic programming schemes — also a number of other useful parameters like branchwidth, rankwidth (cliquewidth), or hypertreewidth. In this contribution we demonstrate how “width ” parameters of graphs and generalized structures (like matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.
Graph Complexity Measures and Monotonicity
, 2012
"... The structural complexity of instances of computational problems has been an important research area in theoretical computer science in the last decades. Its success manifested itself in treewidth—a complexity measure for undirected graphs. Many practically relevant problems that are difficult in g ..."
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Cited by 2 (2 self)
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The structural complexity of instances of computational problems has been an important research area in theoretical computer science in the last decades. Its success manifested itself in treewidth—a complexity measure for undirected graphs. Many practically relevant problems that are difficult in general, can be efficiently solved on graphs of bounded treewidth. For directed graphs, there are several similar measures, among others entanglement, directed treewidth, DAGwidth and Kellywidth, that have shown their advantages as well as disadvantages. In this thesis, we work on complexity measures for directed graphs that can be described in terms of graph searching games. A graph searching game is played on a given graph by a team of cops and a robber. The cops try to capture the robber whose intent is to escape. Precise rules define a game and a complexity measure on graphs. The complexity of a graph is usually the minimal number of cops needed to capture the robber. Hereby, an important issue is monotonicity, a property of winning cop strategies. It implies the existence of suitable decompositions of the given graphs which allow for efficient algorithms for difficult computational problems. We discuss
h. geckeis, T. Stumpf (eds.)
"... Cover illustration (from left to right): SEM image of a polished UO2 surface with studtite crystals, uranyl peroxide hydrate, grown as secondary phase in water under γirradtiation (acquired energy dose 1.5 MGy). Artificial view with pseudocolors. SEM image of a spherical crystalline molybdate parti ..."
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Cover illustration (from left to right): SEM image of a polished UO2 surface with studtite crystals, uranyl peroxide hydrate, grown as secondary phase in water under γirradtiation (acquired energy dose 1.5 MGy). Artificial view with pseudocolors. SEM image of a spherical crystalline molybdate particle formed on the surface of a simulated nuclear waste glass containing 5.5 wt % MoO3. Eu(III) fluorescence of calcite and clay containing sample after excitation at 394 nm.
Editors
"... The 9th Open GermanRussianWorkshop continues the successful series of international workshops ..."
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The 9th Open GermanRussianWorkshop continues the successful series of international workshops
SIMULATION MODELING AND WORKFLOW DESIGN AN APPROACH TO GRID ENABLED DISTRIBUTED APPLICATIONS
"... Dottorato di Ricerca in Matematica ed Informatica per il trattamento dell’informazione e della conoscenza XXV ciclo Settore scientifico disciplinare INF/01 ..."
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Dottorato di Ricerca in Matematica ed Informatica per il trattamento dell’informazione e della conoscenza XXV ciclo Settore scientifico disciplinare INF/01
Results 1  10
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