Results 1  10
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63
Dominating Sets and Local Treewidth
 In Proc. 11th Annual European Symposium on Algorithms ESA
, 2003
"... It is known that the treewidth of a planar graph with a dominating set of size d is O( # d) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph ..."
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Cited by 6 (2 self)
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families. We say that a graph family has the dominationtreewidth property if there is some function f(d) such that every graph G f(d). We show that a minorclosed graph family has bounded local treewidth. This result has important algorithmic consequences.
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
Equivalence of Local Treewidth and Linear Local Treewidth and its Algorithmic Applications
 In Proceedings of the 15th ACMSIAM Symposium on Discrete Algorithms (SODA’04
, 2003
"... We solve an open problem posed by Eppstein in 1995 [14, 15] and reenforced by Grohe [16, 17] concerning locally bounded treewidth in minorclosed families of graphs. A graph has bounded local treewidth if the subgraph induced by vertices within distance r of any vertex has treewidth bounded by a f ..."
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Cited by 31 (10 self)
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We solve an open problem posed by Eppstein in 1995 [14, 15] and reenforced by Grohe [16, 17] concerning locally bounded treewidth in minorclosed families of graphs. A graph has bounded local treewidth if the subgraph induced by vertices within distance r of any vertex has treewidth bounded by a
Fast algorithms for hard graph problems: Bidimensionality, minors, and local treewidth
 In Proceedings of the 12th International Symposium on Graph Drawing, volume 3383 of Lecture Notes in Computer Science
, 2004
"... Abstract. This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems. 1 ..."
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Cited by 13 (3 self)
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Abstract. This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems. 1
Treewidth in Verification: Local vs. Global
 In LPAR 2005
, 2005
"... this paper concurrent transition systems, where communication between concurrent components is modeled explicitly. Assuming boundedness of the treewidth of the communication graph, which we refer to as local treewidth, is reasonable, since the topology of communication in concurrent systems is oft ..."
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Cited by 13 (3 self)
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this paper concurrent transition systems, where communication between concurrent components is modeled explicitly. Assuming boundedness of the treewidth of the communication graph, which we refer to as local treewidth, is reasonable, since the topology of communication in concurrent systems
On the TreeWidth of Planar Graphs
, 2009
"... We prove that every planar graph G of treelength ℓ has a treedecomposition for which every bag is the union of at most 10 shortest paths of length O(ℓ). As a consequence, the treewidth of G is bounded by O(ℓ), generalizing the linear local treewidth result of planar graphs, since the treelength ..."
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Cited by 4 (0 self)
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We prove that every planar graph G of treelength ℓ has a treedecomposition for which every bag is the union of at most 10 shortest paths of length O(ℓ). As a consequence, the treewidth of G is bounded by O(ℓ), generalizing the linear local treewidth result of planar graphs, since the tree
References [DH04]
"... of local treewidth and linear local treewidth and its algorithmic applications. In SODA ’04: Proceedings of the 15th annual ..."
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of local treewidth and linear local treewidth and its algorithmic applications. In SODA ’04: Proceedings of the 15th annual
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.
Results 1  10
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63