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2,161
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 ..."
Treewidth and Minimum Fillin on DTrapezoid Graphs
, 1998
"... We show that the minimum llin and the minimum interval graph completion of a dtrapezoid graph can be computed in time O(n d). We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed in time O(n tw(G)^{d1}). In both cases, d is supposed to be a fixed positive integ ..."
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Cited by 13 (5 self)
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We show that the minimum llin and the minimum interval graph completion of a dtrapezoid graph can be computed in time O(n d). We also show that the treewidth and the pathwidth of a dtrapezoid graph can be computed in time O(n tw(G)^{d1}). In both cases, d is supposed to be a fixed positive
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 ..."
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Cited by 9 (2 self)
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separators, or graphs formed by adding a matching between two cliques, then both the TREEWIDTH and the MINIMUMFILLIN problems on C can be solved in polynomial time. For the graphs that are modular decomposable into cycles we give algorithms, that use respectively O(n) and O(n³) time for TREEWIDTH
Algorithms for the Treewidth and Minimum Fillin of HHDFree Graphs
"... Abst ract. A graph is HHDfree is it does not contain a house (i.e., the complement of Ps), a hole (a cycle of length at least 5) or a domino (the graph obtained from two 4cycles by identifying an edge in one 6'4 with an edge in the other C4) as an induced subgraph. The MINIMUM FILLIN problem ..."
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Abst ract. A graph is HHDfree is it does not contain a house (i.e., the complement of Ps), a hole (a cycle of length at least 5) or a domino (the graph obtained from two 4cycles by identifying an edge in one 6'4 with an edge in the other C4) as an induced subgraph. The MINIMUM FILLIN
An Effective Upperbound on Treewidth Using Partial Fillin of Separators
, 2009
"... Partitioning a graph using graph separators, and particularly clique separators, are wellknown techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded above by the sum of the size of the separator plus the treewid ..."
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the treewidth of disjoint components, and this was obtained by the heuristic of filling in all edges of the separator making it into a clique. In this paper, we present a new, tighter upper bound on the treewidth of a graph obtained by only partially filling in the edges of a separator. In particular
Minimum Fillin and Treewidth for Graphs Modularly Decomposable into Chordal Graphs
 WG98, LLNCS
, 1998
"... We show that a minimum fillin ordering of a graph can be determined in linear time if it can be modularly decomposed into chordal graphs. This generalizes results of [2]. We show that the treewidth of these graphs can be determined in O((n +m) log n) time. ..."
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Cited by 1 (0 self)
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We show that a minimum fillin ordering of a graph can be determined in linear time if it can be modularly decomposed into chordal graphs. This generalizes results of [2]. We show that the treewidth of these graphs can be determined in O((n +m) log n) time.
A Partial KArboretum of Graphs With Bounded Treewidth
 J. Algorithms
, 1998
"... The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes ..."
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Cited by 328 (34 self)
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The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs
A Tourist Guide through Treewidth
 Acta Cybernetica
, 1993
"... A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find treedecompositions, algorithms that use treedecompositions to solve hard problems efficiently, graph minor theory, and some applications ..."
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Cited by 270 (22 self)
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A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find treedecompositions, algorithms that use treedecompositions to solve hard problems efficiently, graph minor theory, and some
Results 1  10
of
2,161