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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 ..."
Abstract
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Cited by 6 (2 self)
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families. We say that a graph family has the domination-treewidth property if there is some function f(d) such that every graph G f(d). We show that a minor-closed 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 fixed-parameter algorithms on min ..."
Abstract
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Cited by 31 (17 self)
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of parameters called contraction-bidimensional parameters, a minor-closed graph family F has the parameter-treewidth 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 ACM-SIAM Symposium on Discrete Algorithms (SODA’04
, 2003
"... We solve an open problem posed by Eppstein in 1995 [14, 15] and re-enforced by Grohe [16, 17] concerning locally bounded treewidth in minor-closed 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 ..."
Abstract
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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 re-enforced by Grohe [16, 17] concerning locally bounded treewidth in minor-closed 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 ..."
Abstract
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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 ..."
Abstract
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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 Tree-Width of Planar Graphs
, 2009
"... We prove that every planar graph G of tree-length ℓ has a tree-decomposition for which every bag is the union of at most 10 shortest paths of length O(ℓ). As a consequence, the tree-width of G is bounded by O(ℓ), generalizing the linear local tree-width result of planar graphs, since the tree-length ..."
Abstract
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Cited by 4 (0 self)
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We prove that every planar graph G of tree-length ℓ has a tree-decomposition for which every bag is the union of at most 10 shortest paths of length O(ℓ). As a consequence, the tree-width of G is bounded by O(ℓ), generalizing the linear local tree-width 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 ..."
Abstract
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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 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
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Cited by 33 (1 self)
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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.
Results 1 - 10
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63
