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Bidimensional parameters and local treewidth

by Erik D. Demaine, Fedor V. Fomin, Mohammadtaghi Hajiaghayi, Dimitrios M. Thilikos - 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 fixed-parameter algorithms on min ..."
Abstract - Cited by 31 (17 self) - Add to MetaCart
of parameters called minor-bidimensional parameters, all minor-closed graph families F excluding some fixed graphs have the parameter-treewidth property. The bidimensional parameters include many domination and covering parameters such as vertex cover, feedback vertex set, dominating set, edge-dominating set, q

Bidimensionality, Map Graphs, and Grid Minors

by Erik D. Demaine, MohammadTaghi Hajiaghayi
"... 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

by Erik D. Demaine, MohammadTaghi Hajiaghayi , 2005
"... We prove that any H-minor-free 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 H-minor-free graphs havelarge treewidth, up to constant factors. This strong relationship was previously known for the special cas ..."
Abstract - Cited by 33 (1 self) - Add to MetaCart
consequences on bidimensionality theory, parameter-treewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial resultshas several algorithmic consequences including subexponential fixed-parameter algorithms and approximation algorithms.

Graphs Excluding a Fixed Minor have Grids as Large as Treewidth, with Combinatorial and Algorithmic Applications through Bidimensionality

by Erik D. Demaine, MohammadTaghi Hajiaghayi , 2005
"... We prove that any H-minor-free graph, for a fixed graph H, of treewidth w has an Ω(w) × Ω(w) grid graph as a minor. Thus grid minors suffice to certify that H-minor-free graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of plana ..."
Abstract - Cited by 28 (8 self) - Add to MetaCart
on bidimensionality theory, parameter-treewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial results has several algorithmic consequences including subexponential fixed-parameter algorithms and approximation algorithms.

Bidimensionality and Kernels

by Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos , 2010
"... Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on H-minor free graphs. Demaine and Hajiaghayi ..."
Abstract - Cited by 58 (23 self) - Add to MetaCart
Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on H-minor free graphs. Demaine and Hajiaghayi

The bidimensionality Theory and Its Algorithmic Applications

by Erik D. Demaine, Mohammadtaghi Hajiaghayi - 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 fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs and gra ..."
Abstract - Cited by 47 (3 self) - Add to MetaCart
This paper surveys the theory of bidimensionality. This theory characterizes a broad range of graph problems (‘bidimensional’) that admit efficient approximate or fixed-parameter solutions in a broad range of graphs. These graph classes include planar graphs, map graphs, bounded-genus graphs

Fixed-Parameter Algorithms for Minor-Closed Graphs (of Locally Bounded Treewidth)

by Erik D. Demaine, Mohammadtaghi Hajiaghayi
"... Frick and Grohe [7] showed that for each property that is de nable in rstorder logic, and for each class of minor-closed graphs of locally bounded treewidth, there is an O(n )-time algorithm deciding whether a given graph has property . In this paper, we extend this result for xed-paramete ..."
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algorithms and show that any minor-closed [contraction-closed] bidimensional parameter which can be computed in polynomial time on graphs of bounded treewidth is also xed-parameter tractable on general minor-closed graphs [minor-closed class of graphs of locally bounded treewidth]. These parameters

Subexponential parameterized . . .

by Erik D. Demaine, Dimitrios M. Thilikos, et al. - A PRELIMINARY VERSION OF THIS ARTICLE APPEARED IN PROCEEDINGS OF THE 15TH ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, ACM, NEW YORK, 2004, PP. 823–832 , 2004
"... We introduce a new framework for designing fixed-parameter algorithms with subexponential running time—2 O( √ k) n O(1). Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and problems such as vertex cover, feedback vertex set, minimu ..."
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We introduce a new framework for designing fixed-parameter algorithms with subexponential running time—2 O( √ k) n O(1). Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and problems such as vertex cover, feedback vertex set

unknown title

by Thèse De, L'université De Lyon, Délivrée Par, Bernard Lyon, École Doctorale Infomaths, Diplôme De Doctorat, Mme Anne-laure Fougères, Mme Anne-laure Fougères, Mme Clémentine Prieur, M. Stéphane Robin, M. Éric Sauquet
"... Anne SABOURIN Mélanges bayésiens de modèles d'extrêmes multivariés, Application à la prédétermination régionale des crues avec données incomplètes. Sous la direction de: ..."
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Anne SABOURIN Mélanges bayésiens de modèles d'extrêmes multivariés, Application à la prédétermination régionale des crues avec données incomplètes. Sous la direction de:
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