Results 1  10
of
91
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 ..."
Abstract

Cited by 328 (34 self)
 Add to MetaCart
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 are discussed.
Linear time solvable optimization problems on graphs of bounded cliquewidth
, 2000
"... Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every dec ..."
Abstract

Cited by 168 (22 self)
 Add to MetaCart
(Show Context)
Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every decision or optimization problem expressible in monadic secondorder logic has a linear algorithm. We prove that this is also the case for graphs of cliquewidth at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications. We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with “too many” induced paths with four vertices.
The Expression Of Graph Properties And Graph Transformations In Monadic SecondOrder Logic
, 1997
"... By considering graphs as logical structures, one... ..."
Abstract

Cited by 160 (40 self)
 Add to MetaCart
(Show Context)
By considering graphs as logical structures, one...
On the fixed parameter complexity of graph enumeration problems definable in monadic secondorder logic
, 2001
"... ..."
Upper bounds to the clique width of graphs
, 2000
"... Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with treedecompositions of bounded width. We investigate alternate hierarchical decompositions that apply to wider classes of graphs and still enjoy good algori ..."
Abstract

Cited by 69 (6 self)
 Add to MetaCart
Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with treedecompositions of bounded width. We investigate alternate hierarchical decompositions that apply to wider classes of graphs and still enjoy good algorithmic properties. These decompositions are motivated and inspired by the study of vertexreplacement contextfree graph grammars. The complexity measure of graphs associated with these decompositions is called clique width. In this paper we bound the clique width of a graph in terms of its tree width on the one hand, and of the clique width of its edge
Structured Programs have Small TreeWidth and Good Register Allocation
 Information and Computation
, 1995
"... The register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the controlflow graph of the program. The interference graph of a flow graph G is the intersection graph of some connected subgraphs of G. These connected subgraphs repre ..."
Abstract

Cited by 68 (1 self)
 Add to MetaCart
(Show Context)
The register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the controlflow graph of the program. The interference graph of a flow graph G is the intersection graph of some connected subgraphs of G. These connected subgraphs represent the lives, or life times, of variables, so the coloring problem models that two variables with overlapping life times should be in different registers. For general programs with unrestricted gotos, the interference graph can be any graph, and hence we cannot in general color within a factor O(n " ) from optimality unless NP=P. It is shown that if a graph has treewidth k, we can efficiently color any intersection graph of connected subgraphs within a factor (bk=2c + 1) from optimality. Moreover, it is shown that structured (j gotofree) programs, including, for example, short circuit evaluations and multiple exits from loops, have treewidth at most 6. Thus, for every structured progr...
Upper Bounds to the CliqueWidth of Graphs
 Discrete Applied Mathematics
, 1997
"... A graph complexity measure that we call cliquewidth is associated in a natural way with certain graph decompositions, more or less like treewidth is associated with treedecomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can be viewe ..."
Abstract

Cited by 67 (16 self)
 Add to MetaCart
(Show Context)
A graph complexity measure that we call cliquewidth is associated in a natural way with certain graph decompositions, more or less like treewidth is associated with treedecomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can be viewed as a finite term, written with appropriate operations on graphs, that evaluates to G. Infinitely many operations are necessary to define all graphs. By limiting the operations in terms of some integer parameter k, one obtains complexity measures of graphs. Specifically, a graph G has complexity at most k iff it has a decomposition defined in terms of k operations. Hierarchical graph decompositions are interesting for algorithmic purposes. In fact, many NPcomplete problems have linear algorithms on graphs of treewidth or of cliquewidth bounded by some fixed k, and the same will hold for graphs of cliquewidth at most k. The graph operations upon which cliquewidth and the related decomp...
Bidimensionality and Kernels
, 2010
"... Bidimensionality theory appears to be a powerful framework in the development of metaalgorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain subexponential time parameterized algorithms for bidimensional problems on Hminor free graphs. Demaine and Hajiaghayi ..."
Abstract

Cited by 61 (24 self)
 Add to MetaCart
(Show Context)
Bidimensionality theory appears to be a powerful framework in the development of metaalgorithmic techniques. It was introduced by Demaine et al. [J. ACM 2005] as a tool to obtain subexponential time parameterized algorithms for bidimensional problems on Hminor free graphs. Demaine and Hajiaghayi [SODA 2005] extended the theory to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this paper, we establish a third metaalgorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In parameterized complexity, each problem instance comes with a parameter k and the parameterized problem is said to admit a linear kernel if there is a polynomial time algorithm, called
Monadic secondorder definable graph transductions: A survey
 TCS
, 1994
"... Courcelle, B., Monadic secondorder definable graph transductions: a survey, Theoretical Computer Science 126 (1994) 5375. Formulas of monadic secondorder logic can be used to specify graph transductions, i.e., multivalued functions from graphs to graphs. We obtain in this way classes of graph tr ..."
Abstract

Cited by 60 (8 self)
 Add to MetaCart
(Show Context)
Courcelle, B., Monadic secondorder definable graph transductions: a survey, Theoretical Computer Science 126 (1994) 5375. Formulas of monadic secondorder logic can be used to specify graph transductions, i.e., multivalued functions from graphs to graphs. We obtain in this way classes of graph transductions, called monadic secondorder definable graph transductions (or, more simply, d&able transductions) that are closed under composition and preserve the two known classes of contextfree sets of graphs, namely the class of hyperedge replacement (HR) and the class of vertex replacement (VR) sets. These two classes can be characterized in terms of definable transductions and recognizable sets of finite trees, independently of the rewriting mechanisms used to define the HR and VR grammars. When restricted to words, the definable transductions are strictly more powerful than the rational transductions such that the image of every finite word is finite; they do not preserve contextfree languages. We also describe the sets of discrete (edgeless) labelled graphs that are the images of HR and VR sets under definable transductions: this gives a version of Parikh’s theorem (i.e., the characterization of the commutative images of contextfree languages) which extends the classical