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175
The Expression Of Graph Properties And Graph Transformations In Monadic SecondOrder Logic
, 1997
"... By considering graphs as logical structures, one... ..."
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Cited by 142 (40 self)
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By considering graphs as logical structures, one...
Graph Types
 IN PROC. 20TH ACM POPL
, 1993
"... Recursive data structures are abstractions of simple records and pointers. They impose a shape invariant, which is verified at compiletime and exploited to automatically generate code for building, copying, comparing, and traversing values without loss of efficiency. However, such values are alw ..."
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Cited by 124 (9 self)
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Recursive data structures are abstractions of simple records and pointers. They impose a shape invariant, which is verified at compiletime and exploited to automatically generate code for building, copying, comparing, and traversing values without loss of efficiency. However, such values are always tree shaped, which is a major obstacle to practical use. We propose a notion of graph types , which allow common shapes, such as doublylinked lists or threaded trees, to be expressed concisely and efficiently. We define regular languages of routing expressions to specify relative addresses of extra pointers in a canonical spanning tree. An efficient algorithm for computing such addresses is developed. We employ a secondorder monadic logic to decide wellformedness of graph type specifications. This logic can also be used for automated reasoning about pointer structures.
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 ..."
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Cited by 112 (22 self)
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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.
Monadic second–order evaluations on treedecomposable graphs
 Theoret. Comput. Sci
, 1993
"... Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs, ..."
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Cited by 80 (24 self)
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Courcelle, B. and M. Mosbah, Monadic secondorder evaluations on treedecomposable graphs,
On the fixed parameter complexity of graph enumeration problems definable in monadic secondorder logic
, 2001
"... ..."
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 ..."
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Cited by 58 (16 self)
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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...
Beyond NPCompleteness for Problems of Bounded Width: Hardness for the W Hierarchy (Extended Abstract)
 In Proceedings of the 26th Annual ACM Symposium on the Theory of Computing
, 1994
"... The parameterized computational complexity of a collection of wellknown problems including: Bandwidth, Precedence constrained kprocessor scheduling, Longest Common Subsequence, DNA physical mapping (or Intervalizing colored graphs), Perfect phylogeny (or Triangulating colored graphs), Colored cutw ..."
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Cited by 57 (21 self)
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The parameterized computational complexity of a collection of wellknown problems including: Bandwidth, Precedence constrained kprocessor scheduling, Longest Common Subsequence, DNA physical mapping (or Intervalizing colored graphs), Perfect phylogeny (or Triangulating colored graphs), Colored cutwidth, and Feasible register assignment is explored. It is shown that these problems are hard for various levels of the W hierarchy. In the case of Precedence constrained kprocessor scheduling the results can be interpreted as providing substantial new complexity lower bounds on the outcome of [OPEN 8] of the Garey and Johnson list. We also obtain the conjectured "third strike" against Perfect phylogeny.
Duality and polynomial testing of tree homomorphisms
 Trans. Amer. Math. Soc
, 1996
"... Abstract. Let H be a fixed digraph. We consider the Hcolouring problem, i.e., the problem of deciding which digraphs G admit a homomorphism to H. We are interested in a characterization in terms of the absence in G of certain treelike obstructions. Specifically, we say that H has tree duality if, ..."
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Cited by 53 (16 self)
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Abstract. Let H be a fixed digraph. We consider the Hcolouring problem, i.e., the problem of deciding which digraphs G admit a homomorphism to H. We are interested in a characterization in terms of the absence in G of certain treelike obstructions. Specifically, we say that H has tree duality if, for all digraphs G, G is not homomorphic to H if and only if there is an oriented tree which is homomorphic to G but not to H. Weprovethatif Hhas tree duality then the Hcolouring problem is polynomial. We also generalize tree duality to bounded treewidth duality and prove a similar result. We relate these duality concepts to the notion of the Xproperty studied by Gutjahr, Welzl, and Woeginger. We then focus on the case when H itself is an oriented tree. In fact, we are particularly interested in those trees that have exactly one vertex of degree three and all other vertices of degree one or two. Such trees are called triads. We have shown in a companion paper that there exist oriented triads H for which the Hcolouring problem is NPcomplete. We contrast these with several families of oriented triads H which have tree duality, or bounded treewidth duality, and hence polynomial Hcolouring problems. If P � = NP, then no oriented triad H with an NPcomplete Hcolouring problem can have bounded treewidth duality; however no proof of this is known, for any oriented triad H. We prove that none of the oriented triads H with NPcomplete Hcolouring problems given in the companion paper has tree duality. 1.
Taming the infinite chase: Query answering under expressive relational constraints
 In Proc. of KR 2008
, 2008
"... The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuplegenerating dependencies (TGDs) and equalitygenerating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper in ..."
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Cited by 52 (12 self)
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The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuplegenerating dependencies (TGDs) and equalitygenerating dependencies (EGDs). So far, most of the research on this topic has focused on cases where the chase procedure terminates. This paper introduces expressive classes of TGDs defined via syntactic restrictions: guarded TGDs (GTGDs) and weakly guarded sets of TGDs (WGTGDs). For these classes, the chase procedure is not guaranteed to terminate and thus may have an infinite outcome. Nevertheless, we prove that the problems of conjunctivequery answering and query containment under such TGDs are decidable. We provide decision procedures and tight complexity bounds for these problems. Then we show how EGDs can be incorporated into our results by providing conditions under which EGDs do not harmfully interact with TGDs and do not affect the decidability and complexity of query answering. We show applications of the aforesaid classes of constraints to the problem of answering conjunctive queries in FLogic Lite, an objectoriented ontology language, and in some tractable Description Logics. 1.
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 ..."
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Cited by 45 (6 self)
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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