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301
Linear time solvable optimization problems on graphs of bounded clique-width
, 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 tree-width 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 170 (24 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 tree-width 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 second-order logic has a linear algorithm. We prove that this is also the case for graphs of clique-width 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 Second-Order Logic
, 1997
"... By considering graphs as logical structures, one... ..."
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Cited by 162 (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 126 (10 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 doubly-linked 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 second-order monadic logic to decide well-formedness of graph type specifications. This logic can also be used for automated reasoning about pointer structures.
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 tuple-generating dependencies (TGDs) and equality-generating 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 104 (16 self)
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The chase algorithm is a fundamental tool for query evaluation and for testing query containment under tuple-generating dependencies (TGDs) and equality-generating 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 (WGT-GDs). 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 conjunctive-query 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 F-Logic Lite, an object-oriented ontology language, and in some tractable Description Logics. 1.
Monadic second–order evaluations on tree-decomposable graphs
- Theoret. Comput. Sci
, 1993
"... Courcelle, B. and M. Mosbah, Monadic second-order evaluations on tree-decomposable graphs, ..."
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Cited by 93 (25 self)
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Courcelle, B. and M. Mosbah, Monadic second-order evaluations on tree-decomposable graphs,
On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic
, 2001
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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 tree-decompositions 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 72 (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 tree-decompositions 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 vertex-replacement context-free 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
Upper Bounds to the Clique-Width of Graphs
- Discrete Applied Mathematics
, 1997
"... A graph complexity measure that we call clique-width is associated in a natural way with certain graph decompositions, more or less like tree-width is associated with tree-decomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can be viewe ..."
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Cited by 66 (16 self)
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A graph complexity measure that we call clique-width is associated in a natural way with certain graph decompositions, more or less like tree-width is associated with tree-decomposition 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 NP-complete problems have linear algorithms on graphs of tree-width or of clique-width bounded by some fixed k, and the same will hold for graphs of clique-width at most k. The graph operations upon which clique-width and the related decomp...
Beyond NP-Completeness 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 well-known problems including: Bandwidth, Precedence constrained k-processor 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 60 (20 self)
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The parameterized computational complexity of a collection of well-known problems including: Bandwidth, Precedence constrained k-processor 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 k-processor 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.
Algorithms For Vertex Partitioning Problems On Partial k-Trees
, 1997
"... In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial k-trees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutio ..."
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Cited by 59 (6 self)
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In this paper, we consider a large class of vertex partitioning problems and apply to those the theory of algorithm design for problems restricted to partial k-trees. We carefully describe the details of algorithms and analyze their complexity in an attempt to make the algorithms feasible as solutions for practical applications.
