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221
Exact (exponential) algorithms for treewidth and minimum fillin
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming, ICALP 2004
, 2004
"... minimum fillin ..."
Minimum Fillin on Circle and CircularArc Graphs
 J. ALGORITHMS
, 1996
"... We present two algorithms solving the minimum fillin problem on circle graphs and on circulararc graphs in time O(n³). ..."
Abstract

Cited by 10 (1 self)
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We present two algorithms solving the minimum fillin problem on circle graphs and on circulararc graphs in time O(n³).
Treewidth and Minimum Fillin: Grouping the Minimal Separators
, 1999
"... We use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph. We show that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fillin are polynomially tractable for these graphs ..."
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Cited by 37 (5 self)
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We use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph. We show that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fillin are polynomially tractable
Minimum Fillin for Chordal Bipartite Graphs
, 1993
"... Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. The MINIMUM FILLIN problem is the problem of finding a chordal embedding of the graph with a minimum number of edges. We present a polynomial time algorithm for the exact computation o ..."
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Cited by 1 (0 self)
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Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. The MINIMUM FILLIN problem is the problem of finding a chordal embedding of the graph with a minimum number of edges. We present a polynomial time algorithm for the exact computation
Computing the Treewidth and the Minimum Fillin With the Modular Decomposition
, 2001
"... Using the notion of modular decomposition we extend the class of graphs on which both the TREEWIDTH and the MINIMUMFILLIN problems can be solved in polynomial time. We show that if C is a class of graphs which is modularly decomposable into graphs that have a polynomial number of minimal separa ..."
Treewidth and Minimum Fillin of Weakly Triangulated Graphs
, 1998
"... We introduce the notion of "potential maximal clique" of a graph and we use it for computing the treewidth and the minimum fillin of graphs for which the the potential maximal cliques can be listed in polynomial time. Finally we show how to compute the potential maximal cliques of weakl ..."
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Cited by 4 (0 self)
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We introduce the notion of "potential maximal clique" of a graph and we use it for computing the treewidth and the minimum fillin of graphs for which the the potential maximal cliques can be listed in polynomial time. Finally we show how to compute the potential maximal cliques
Treewidth and minimum fillin on dtrapezoid graphs
, 1995
"... Abstract We show that the minimum fillin and the minimum interval graph completion of a dtrapezoid graph can be computed in time On d . We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed by an On twG d,1 time algorithm. For both algorithms, d is supposed to b ..."
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Abstract We show that the minimum fillin and the minimum interval graph completion of a dtrapezoid graph can be computed in time On d . We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed by an On twG d,1 time algorithm. For both algorithms, d is supposed
Exact algorithms for treewidth and minimum fillin
 In Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP 2004). Lecture Notes in Comput. Sci
, 2004
"... We show that the treewidth and the minimum fillin of an nvertex graph can be computed in time O(1.8899 n). Our results are based on combinatorial proofs that an nvertex graph has O(1.7087 n) minimal separators and O(1.8135 n) potential maximal cliques. We also show that for the class of ATfree g ..."
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Cited by 28 (17 self)
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We show that the treewidth and the minimum fillin of an nvertex graph can be computed in time O(1.8899 n). Our results are based on combinatorial proofs that an nvertex graph has O(1.7087 n) minimal separators and O(1.8135 n) potential maximal cliques. We also show that for the class of AT
Minimum Fillin of Sparse Graphs: Kernelization and Approximation
, 2011
"... The Minimum Fillin problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We obt ..."
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The Minimum Fillin problem is to decide if a graph can be triangulated by adding at most k edges. The problem has important applications in numerical algebra, in particular in sparse matrix computations. We develop kernelization algorithms for the problem on several classes of sparse graphs. We
COMPUTING THE MINIMUM FILLIN IS NPCOMPLETE
, 1981
"... We show that the following problem is NPcomplete. Given a graph, find the Minimum number of edges (fillin) whose addition makes the graph chordal. This problem arises in the solution of sparse symmetric positive definite systems of linear equations by Gaussian elimination. ..."
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Cited by 219 (0 self)
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We show that the following problem is NPcomplete. Given a graph, find the Minimum number of edges (fillin) whose addition makes the graph chordal. This problem arises in the solution of sparse symmetric positive definite systems of linear equations by Gaussian elimination.
Results 1  10
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221