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Algorithms for Graphs of (Locally) Bounded Treewidth
, 2001
"... Many reallife problems can be modeled by graphtheoretic problems. These graph problems are usually NPhard and hence there is no efficient algorithm for solving them, unless P= NP. One way to overcome this hardness is to solve the problems when restricted to special graphs. Trees are one kind of g ..."
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Cited by 4 (3 self)
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of graph for which several NPcomplete problems can be solved in polynomial time. Graphs of bounded treewidth, which generalize trees, show good algorithmic properties similar to those of trees. Using ideas developed for tree algorithms, Arnborg and Proskurowski introduced a general dynamic programming
Treewidth, partial ktrees, and chordal graphs
, 2006
"... Many graph problems that are NPhard on general graphs, have polynomial time solutions if the input graph has bounded treewidth or if it belongs to a restricted graph class. In this document, we review some of the techniques for coping with NPhardness of graph problems. In particular, we explain gr ..."
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Cited by 2 (0 self)
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Many graph problems that are NPhard on general graphs, have polynomial time solutions if the input graph has bounded treewidth or if it belongs to a restricted graph class. In this document, we review some of the techniques for coping with NPhardness of graph problems. In particular, we explain
Treewidth: Algorithmic techniques and results
 In Mathematical foundations of computer science
, 1998
"... This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed. ..."
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Cited by 156 (10 self)
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This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more efficiently. Also, several results on graph minors are reviewed.
Treewidth and Small Separators for Graphs with Small Chordality
, 1995
"... A graph G kchordal, if it does not contain chordless cycles of length larger than k. The chordality cl of a graph G is the minimum k for which G is kchordal. The degeneracy or the width of a graph is the maximum mindegree of any of its subgraphs. Our results are the following: 1. The problem of ..."
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Cited by 3 (1 self)
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of treewidth remains NPcomplete when restricted on graphs with small maximum degree. 2. An upper bound is given for the treewidth of a graph as a function of its maximum degree and chordality. A consequence of this result is that when maximum degree and chordality are fixed constants, then there is a linear
Treewidth Computations I. Upper Bounds
, 2008
"... For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining the tr ..."
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Cited by 26 (3 self)
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For more and more applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. This paper gives an overview of several upper bound heuristics that have been proposed and tested for the problem of determining
Treewidth Computations II. Lower Bounds
, 2010
"... For several applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. Good lower bounds on the treewidth of a graph can, amongst others, help to speed up branch and bound algorithms that compute the treewidth of ..."
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Cited by 9 (1 self)
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For several applications, it is important to be able to compute the treewidth of a given graph and to find tree decompositions of small width reasonably fast. Good lower bounds on the treewidth of a graph can, amongst others, help to speed up branch and bound algorithms that compute the treewidth
Layout of Graphs with Bounded TreeWidth
 2002, SUBMITTED. STACKS, QUEUES AND TRACKS: LAYOUTS OF GRAPH SUBDIVISIONS 41
, 2004
"... A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queuenumber. A threedimensional (straightline grid) drawing of a gra ..."
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Cited by 31 (23 self)
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A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queuenumber. A threedimensional (straightline grid) drawing of a
Treewidth Lower Bounds with Brambles
, 2005
"... In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm fo ..."
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Cited by 12 (3 self)
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In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm
New Upper Bound Heuristics for Treewidth
, 2004
"... In this paper, we introduce and evaluate some heuristics to find an upper bound on the treewidth of a given graph. Each of the heuristics selects the vertices of the graph one by one, building an elimination list. The heuristics differ in the criteria used for selecting vertices. These criteria depe ..."
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Cited by 9 (4 self)
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In this paper, we introduce and evaluate some heuristics to find an upper bound on the treewidth of a given graph. Each of the heuristics selects the vertices of the graph one by one, building an elimination list. The heuristics differ in the criteria used for selecting vertices. These criteria
Results 11  20
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