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113
Bidimensional parameters and local treewidth
 SIAM Journal on Discrete Mathematics
, 2004
"... Abstract. For several graph theoretic parameters such as vertex cover and dominating set, it is known that if their values are bounded by k then the treewidth of the graph is bounded by some function of k. This fact is used as the main tool for the design of several fixedparameter algorithms on min ..."
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Cited by 31 (17 self)
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of parameters called contractionbidimensional parameters, a minorclosed graph family F has the parametertreewidth property if F has bounded local treewidth. We also show “if and only if ” for some parameters, and thus this result is in some sense tight. In addition we show that, for a slightly smaller family
Bidimensionality and Kernels
, 2010
"... Bidimensionality theory appears to be a powerful framework in 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 bidimensional problems on Hminor free graphs. Demaine and Hajiaghayi ..."
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Cited by 58 (23 self)
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Bidimensionality theory appears to be a powerful framework in 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 bidimensional problems on Hminor free graphs. Demaine and Hajiaghayi
Contraction Bidimensionality: The Accurate Picture
 Proceedings of the 17th Annual European Symposium on Algorithms, Lecture Notes in Computer Science
, 2009
"... Abstract. We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory—the meta algorithmic framework to design ..."
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Cited by 9 (5 self)
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Abstract. We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory—the meta algorithmic frame
The bidimensionality Theory and Its Algorithmic Applications
 Computer Journal
, 2005
"... This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixedparameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, boundedgenus graphs and gra ..."
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Cited by 47 (3 self)
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This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixedparameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, boundedgenus graphs
Bidimensionality: New Connections between FPT Algorithms and PTASs
, 2005
"... We demonstrate a new connection between fixedparametertractability and approximation algorithms for combinatorial optimization problems on planar graphs and their generalizations. Specifically, we extend the theory of socalled "bidimensional " problems to show that essentially ..."
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Cited by 43 (7 self)
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all such problems have both subexponential fixedparameter algorithms and PTASs. Bidimensional problems include e.g. feedbackvertex set, vertex cover, minimum maximal matching, face cover, a series of vertexremoval problems, dominating set,edge dominating set,
Bidimensionality, Map Graphs, and Grid Minors
"... In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the ..."
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In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve
Linearity of Grid Minors in Treewidth with Applications through Bidimensionality
, 2005
"... We prove that any Hminorfree graph, for a fixed graph H, of treewidth w has an \Omega (w) *\Omega ( w) grid graph as a minor. Thus grid minors suffice to certify that Hminorfree graphs havelarge treewidth, up to constant factors. This strong relationship was previously known for the special cas ..."
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Cited by 33 (1 self)
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consequences on bidimensionality theory, parametertreewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial resultshas several algorithmic consequences including subexponential fixedparameter algorithms and approximation algorithms.
Approaching Integrability in BiDimensional Nonlinear Field Equations
, 2011
"... A new, oneparameter family of potentials is introduced. This potential leads to a nonlinear field equation with kink solutions. Internal modes of these solutions are calculated. Conditions on the parameter of the model are obtained which lead to the elimination of extra bound states and nearly refl ..."
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A new, oneparameter family of potentials is introduced. This potential leads to a nonlinear field equation with kink solutions. Internal modes of these solutions are calculated. Conditions on the parameter of the model are obtained which lead to the elimination of extra bound states and nearly
SUBDIFFRACTIVE PROPAGATION IN A BIDIMENSIONAL SONIC CRYSTAL
"... Sonic crystals are media with a periodic modulation of the acoustic parameters, as the density and the bulk modulus. They have recently attracted a great interest, because of their potential applications in the control of sound propagation, used as reflectors, focusers or waveguides. All these prope ..."
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Sonic crystals are media with a periodic modulation of the acoustic parameters, as the density and the bulk modulus. They have recently attracted a great interest, because of their potential applications in the control of sound propagation, used as reflectors, focusers or waveguides. All
Hybrid Video Coding Using BiDimensional Matching Pursuit
, 2003
"... In this report we propose a new coding scheme based on the Matching Pursuit algorithm and exploiting some of the new features introduced by H.264 for motion estimation. Main points of this work are the design of a redundant dictionary suitable for coding displaced frame di#erences, the use of fast ..."
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of fast techniques for atom selection, which work in the Fourier domain and exploit the spatial localization of the atoms, the adaptive coding scheme aimed at optimizing the resouce allocation for transmitting the atom parameters and the RateDistortion optimization.
Results 1  10
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113