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18
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 255 (38 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 such classes are discussed.
Diagram Editing with Hypergraph Parser Support
 PROC. 1997 IEEE SYMP. ON VISUAL LANGUAGES
, 1997
"... Diagrams are always used when communicating complex situations. Diagram editors support the user when editing diagrams on a computer. However, creating diagram editors is expensive and timeconsuming. Frameworks that can be customized for the specific diagram classes considerably reduce these costs. ..."
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Cited by 18 (13 self)
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Diagrams are always used when communicating complex situations. Diagram editors support the user when editing diagrams on a computer. However, creating diagram editors is expensive and timeconsuming. Frameworks that can be customized for the specific diagram classes considerably reduce these costs. In previous work, the framework DiaGen using an internal hypergraph model and offering syntaxdirected editing had been introduced. This paper presents an incremental hypergraph parser and an extension of DiaGen that allows for editing diagrams like in a drawing tool. The hypergraph parser detects correct (sub) diagrams online and notifies the user of incorrect diagram parts. This allows editing with temporally inconsistent diagrams which supports a natural editing style.
Specification of Diagram Editors Providing Layout Adjustment with Minimal Change
 In Proc. 1993 IEEE Symposium on Visual Languages
, 1993
"... Editing diagrams conveniently requires edit operations and automatic layout tailored to the type of diagram. This necessitates a syntaxdirected editor for diagrams, called diagram editor herein. We describe the basics of a generator for interactive diagram editors that offers a number of significan ..."
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Cited by 17 (13 self)
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Editing diagrams conveniently requires edit operations and automatic layout tailored to the type of diagram. This necessitates a syntaxdirected editor for diagrams, called diagram editor herein. We describe the basics of a generator for interactive diagram editors that offers a number of significant advantages over previous approaches. The foundation is a new incremental algorithm for constraint evaluation. Constraints can be specified not only by equations, as in earlier work, but also by linear inequalities. This opens the door to integrating automatic diagram layout with userdefined modifications. Furthermore, the algorithm ensures that layout adjustments initiated by user action are confined to the smallest possible part of the diagram around the point of modification, thus realizing a principle of minimal change. 1 Introduction Diagrams are of fundamental importance to visual languages and, more generally, invaluable to everybody who wants to communicate complex information in ...
Treewidth and Duality for Planar Hypergraphs.
"... We prove a conjecture of Robertson and Seymour (Graph Minors. III. Planar treewidth): the treewidth of a planar graph is at most the treewidth of its dual plus one. To this purpose, we study hypermaps, which represent hypergraphs on a surface. We dene a parallel composition on hypermaps which v ..."
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Cited by 10 (2 self)
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We prove a conjecture of Robertson and Seymour (Graph Minors. III. Planar treewidth): the treewidth of a planar graph is at most the treewidth of its dual plus one. To this purpose, we study hypermaps, which represent hypergraphs on a surface. We dene a parallel composition on hypermaps which veries ve properties: it is commutative, associative, preserves planarity, commutes with the duality and with the parallel composition on hypergraphs. Finally, we introduce the notion of a equationel set of hypermaps and of a treewidth of a hypermap. In their study of minors, Robertson and Seymour [8] introduce the notions of treewidth and treedecomposition of a graph. These notions are essential in a algorithmical point of view: a lot of NPproblems become polynomial, when they are restricted to graphs of bounded treewidth (see [1]). In his study of equational sets of graphs, Courcelle [4] (see also [2, 6]) introduces a parallelcomposition of (hyper)graphs. This operation is com...
Fusion in Relational Structures and the Verification of Monadic SecondOrder Properties
, 2001
"... Relational structures offer a common framework to handle graphs and hypergraphs of various kinds. Operations like disjoint union, creation of newrelations by meansof quantifierfree formulas, relabellings of relations make it possible to denote them by algebraic expressions. It is known that every m ..."
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Cited by 10 (3 self)
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Relational structures offer a common framework to handle graphs and hypergraphs of various kinds. Operations like disjoint union, creation of newrelations by meansof quantifierfree formulas, relabellings of relations make it possible to denote them by algebraic expressions. It is known that every monadic secondorder property of a structure is verifiable in time proportional to the size of such an algebraic expression defining it. We prove here that this result remains true if we also use in these algebraic expressions a fusion operation that fuses all elements of the domain satisfying some unary predicate. The value mapping from these algebraic expressions to the structures they denote is a monadic secondorder definable transduction, which means that the structure is definable inside the tree representing the algebraic expression by monadic secondorder formulas. It follows (by using results of other articles) that, with this fusion operation, we cannot generate more graph families, b...
The Equivalence of BottomUp and TopDown TreetoGraph Transducers
 J. COMPUT. SYST. SCI
, 1996
"... We introduce the bottomup treetograph transducer, which is very similar to the usual (total deterministic) bottomup tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the tr ..."
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Cited by 7 (4 self)
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We introduce the bottomup treetograph transducer, which is very similar to the usual (total deterministic) bottomup tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the transducer is a jungle, i.e., a hypergraph that can be unfolded into a tree, then the treetograph transducer is said to be treegenerating and naturally defines a treetotree translation. We prove that bottomup treetograph transducers define the same treetotree translations as the previously introduced topdown treetograph transducers. This is in contrast with the wellknown incomparability of the usual bottomup and topdown tree transducers.
Parallel HighLevel Replacement Systems
 Theoretical Computer Science
, 1994
"... Highlevel replacement systems are an axiomatic categorical framework based on doublepushouts in order to unify replacement systems like grammars for different kinds of graphs and relational structures or other types of structures like algebraic specifications. Parallel highlevel replacement syste ..."
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Cited by 6 (4 self)
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Highlevel replacement systems are an axiomatic categorical framework based on doublepushouts in order to unify replacement systems like grammars for different kinds of graphs and relational structures or other types of structures like algebraic specifications. Parallel highlevel replacement systems are introduced to formalize parallel rewriting of these highlevel structures. On one hand this concept generalizes and extends parallel graph grammars presented so far in the algebraic approach by allowing other structures than graphs, on the other hand the kinds of replacement introduced for highlevel replacement systems are extended by different types of parallel replacement which are compared to each other in different parallel replacement theorems. An abstract version of a windowbased graph editor and movement of objects in configuration spaces are presented as examples of parallel highlevel replacement systems. Contents 1 Introduction 2 2 Basic concepts of highlevel replacement...
Operations on Relational Structures and their Compatibility with Monadic Second Order Logic
, 2000
"... Relational structures offer a common framework to handle graphs and hypergraphs of various kinds. Operations like disjoint union, creation of new relations, relabellings of relations make it possible to denote them by algebraic expressions. We consider operations such that every Monadic SecondOrder ..."
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Cited by 3 (3 self)
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Relational structures offer a common framework to handle graphs and hypergraphs of various kinds. Operations like disjoint union, creation of new relations, relabellings of relations make it possible to denote them by algebraic expressions. We consider operations such that every Monadic SecondOrder expressible property can be verified efficiently on the expression denoting the considered structure. This is the case for disjoint union and unary operations that define new relations by quantifier free formulas. We prove here that we can also use a fusion operation that fuses all elements of the domain satisfying a same unary predicate while keeping compatibility with monadic secondorder properties. The value mapping from expressions to the structures they denote is a monadic secondorder de nable transduction. It follows that, with these fusion operations, we cannot generate more graph families but we can generate them with less unary auxiliary predicates.
Attributed ContextFree Hypergraph Grammars
, 1998
"... The concept of contextfree hypergraph grammars (cfhg grammars) has been studied extensively over the past decade. In this paper we introduce attributed contextfree hypergraph grammars (acfhg grammars) as an extension of cfhg grammars. An acfhg grammar consists of an underlying contextfree hypergr ..."
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Cited by 2 (2 self)
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The concept of contextfree hypergraph grammars (cfhg grammars) has been studied extensively over the past decade. In this paper we introduce attributed contextfree hypergraph grammars (acfhg grammars) as an extension of cfhg grammars. An acfhg grammar consists of an underlying contextfree hypergraph grammar G 0 and an attribution which associates attributes with the nonterminal symbols of G 0 analogous to the classical attribute grammars (ag's) by Knuth. We show that acfhg grammars and ag's are closely related in such a way that an ag can be used to compute the attribute values of an acfhg grammar. Due to this relationship the known techniques for attribute evaluation for ag's can be exploited for acfhg grammars. Also we show that attributed tree grammars can be embedded into the concept of acfhg grammars, provided an appropriate semantics is associated with the acfhg grammar. Finally, we show how an acfhg grammar can be used to associate semantics with programs of some programming ...
Transformational Design Of Digital Systems Related To Graph Rewriting
 PROC. OF WORKSHOP ON DESIGN METHODOLOGIES FOR MICRO ELECTRONICS
, 1995
"... For highlevel synthesis transformational design is a promising design methodology which combines correctness by construction and interactive design. In this design methodology the design steps are behaviour preserving transformations of one design representation into another. Because of the import ..."
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Cited by 2 (2 self)
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For highlevel synthesis transformational design is a promising design methodology which combines correctness by construction and interactive design. In this design methodology the design steps are behaviour preserving transformations of one design representation into another. Because of the importance of visualisation of designinformation several kinds of graphs are used as design representations. Transformational design based on graph representation is closely related to rewriting of (sub)graphs. In this paper the formal aspects of transformational design are related to graph rewriting theory. It is shown how a formal framework for transformational design can benefit from graph rewriting theory. Especially preconditions for the application of transformation rules can be based on generally formulated preconditions from graph rewriting theory. Moreover a general graph concept unifies graph representations and a formal framework for transformational design based on this general graph...