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Initial Conflicts and Dependencies: Critical Pairs Revisited [chapter]

Leen Lambers, Kristopher Born, Fernando Orejas, Daniel Strüber, Gabriele Taentzer
2018 Lecture Notes in Computer Science  
Many thanks to Leila Ribeiro and Jonas Santos Bezerra for providing us with support to CPA of our running example in Verigraph [11] .  ...  Therefore, an obvious question is the following: Does the set of initial conicts correspond to the set of essential critical pairs in the case of typed graph transformation systems?  ...  We characterize initial conicts for typed graph transformation systems and show that the set of initial conicts is eectively smaller than the set of essential critical pairs.  ... 
doi:10.1007/978-3-319-75396-6_6 fatcat:cblb7tfulvhmvdnpipccrkps24

Construction and Properties of Adhesive and Weak Adhesive High-Level Replacement Categories

Ulrike Prange, Hartmut Ehrig, Leen Lambers
2007 Applied Categorical Structures  
(Fundamentals of Algebraic Graph Transformation, EATCS Monographs, Springer, 2006) , adhesive high-level replacement (HLR) categories and systems are an adequate framework for several kinds of transformation  ...  But for the general results of transformation systems, as additional properties initial pushouts, binary coproducts compatible with a special morphism class M and a pair factorization are needed to obtain  ...  This more flexible class M is essential for some important examples, such as typed attributed graphs, to become an adhesive HLR category.  ... 
doi:10.1007/s10485-007-9106-3 fatcat:r3dxw4dx6netjkh2veyywqphti

Page 357 of Mathematical Reviews Vol. 55, Issue 2 [page]

1978 Mathematical Reviews  
M. 2629 A study of the local structure of 5-connected graphs with essential edges. (Ukrainian. Russian and English summaries) g-transformations of graphs (Ukrainian), pp. 318-327, 373. Vidannja Inst.  ...  SSR, Kiev, Authors’ summary: “In this paper the structure of some types of simple finite h-connected graphs is investigated.  ... 

A uniqueness decomposition theorem for actions of finite groups on free groups

Sava Krstić
1989 Journal of Pure and Applied Algebra  
Every H-class occupied in some TEV contains an essential H'-class for some H' 2 H. Proof. Let C be an H-class occupied in r. If it is not essential, there is r'EV in which C is not occupied.  ...  graph r we denote by V(T) the set of all graphs which can be obtained by applying a transformation to l-and call it the Nielsen class of r.  ... 
doi:10.1016/0022-4049(89)90066-2 fatcat:ufaqmvjcr5b4ze7qk46clpvfyq

On locating minimum feedback vertex sets

Errol L. Lloyd, Mary Lou Soffa, Ching-Chy Wang
1988 Journal of computer and system sciences (Print)  
First, we introduce three new transformation-based classes of graphs for which minimum feedback vertex sets can be computed in polynomial time.  ...  Among the classes of graphs included in the hierarchy are: the reducible flow graphs, the cyclically reducible graphs, the three transformation-based classes that we introduce, and an infinite sequence  ...  Each of the classes that we study can be defined using some notion of graph reducibility.  ... 
doi:10.1016/0022-0000(88)90009-8 fatcat:2ya2f6x37jboto5bzxxpig3rp4

How to Transform a Multilayer Network into a Colored Graph

Marie-emilie Voge
2006 2006 International Conference on Transparent Optical Networks  
Then the question of the transformation of a multilayer network into a colored graph is studied, since the way in which it is done can have a great impact on the quality of the solutions of some essential  ...  In this context the notion of Shared Risk Resource Group have been proposed, and then the colored graph model to answer these needs.  ...  Nevertheless, some special cases are polynomial and for some networks a good transformation into a colored graph places the network in these polynomial cases as was explained in this work.  ... 
doi:10.1109/icton.2006.248415 fatcat:7doczzudxbe4dbpthf2x2vs73u

More Forbidden Minors for Wye-Delta-Wye Reducibility

Yaming Yu
2006 Electronic Journal of Combinatorics  
A graph is $Y\Delta Y$ reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and $Y\Delta Y$ transformations.  ...  It is still an open problem to characterize $Y\Delta Y$ reducible graphs in terms of a finite set of forbidden minors.  ...  It follows that (G 11 , G 12 ) is an essential separation for G 1 + ∆, which contradicts Lemma 3.2. Suppose some of the vertices of C lie in G 1 − C and some in G 2 −C.  ... 
doi:10.37236/1033 fatcat:omlywy3wdvdqtavab4vkrde3ve

Forbidden minors for wye-delta-wye reducibility

Yaming Yu
2004 Journal of Graph Theory  
Two graphs that can be obtained from each other by a sequence of Y ∆Y transformations are called Y ∆Y equivalent.  ...  A graph is Y Delta Y reducible if it can be reduced to isolate vertices by a sequence of seriesparallel reductions and Y Delta Y transformations.  ...  It follows that (G 11 , G 12 ) is an essential separation for G 1 + ∆, which contradicts Lemma 3.2. Suppose some of the vertices of C lie in G 1 − C and some in G 2 −C.  ... 
doi:10.1002/jgt.20039 fatcat:6oc5zmjj25eoznudw5h2gywx5y

Defining Object-Oriented Execution Semantics Using Graph Transformations [chapter]

Harmen Kastenberg, Anneke Kleppe, Arend Rensink
2006 Lecture Notes in Computer Science  
In this paper we describe an application of the theory of graph transformations to the practise of language design.  ...  their effect by graph transformation rules (the dynamic semantics).  ...  This category consists of a small number of rules (usually one, in some cases two) per kind of FlowElement. These rules describe the essential function of that particular FlowElement.  ... 
doi:10.1007/11768869_15 fatcat:2wcscxxiezbqbcm6cqf6vevcey

An effective ergodic theorem and some applications

Satyadev Nandakumar
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
We prove a stronger effective ergodic theorem to include a restriction of Braverman's "graph-computable functions".  ...  In a tour-de-force, V'yugin [13] proved an effective version of the Ergodic Theorem which holds when the probability space, the transformation and the random variable are computable.  ...  Proof of Main Theorem 1 Let f be the graph computable function, as given, with essential upper semicomputation f and essential lower semicomputation f . Let ω be a random point.  ... 
doi:10.1145/1374376.1374383 dblp:conf/stoc/Nandakumar08 fatcat:e7k2fc342rd6jjii4cfozlswmi

Big data analytics on Apache Spark

Salman Salloum, Ruslan Dautov, Xiaojun Chen, Patrick Xiaogang Peng, Joshua Zhexue Huang
2016 International Journal of Data Science and Analytics  
In addition, we highlight some research and development directions on Apache Spark for big data analytics.  ...  As a rapidly evolving open source project, with an increasing number of contributors from both academia and industry, it is difficult for researchers to comprehend the full body of development and research  ...  -Graph-based Representation: It is clear that a reliable representation (e.g., RDGs or property graphs) of graphoriented data is essential for efficient processing of large graphs.  ... 
doi:10.1007/s41060-016-0027-9 dblp:journals/ijdsa/SalloumD0PH16 fatcat:gtzw3aqupnhxvcjbefovrnfhne

Describing the Set of Words Generated by Interval Exchange Transformation

A. Ya. Kanel-Belov, A. L. Chernyat'ev
2010 Communications in Algebra  
We get combinatorial criteria of existence of interval exchange transformations that generate the word W.  ...  The (k + 1)-graph is a subgraph of the follower of the k-graph; it results from the latter by removing some arcs.  ...  The Rauzy graph is said to be labeled if its arcs are assigned letters l and r and some of its vertices (perhaps, none of them) are assigned symbol "-".  ... 
doi:10.1080/00927870903032932 fatcat:6w664mcyqjgdjj34vvu3i6xsee

The automata complexity of the language transformation schema that contains operations with restricted degree

Nguyễn Văn Định
2012 Journal of Computer Science and Cybernetics  
In this paper we study the relation between the automata complexity g(E), the number of essential vertices lEI and the depth of operations 5 on a language transformation schema.  ...  The estimation of the automata complexity of a language transformation schema that holds operations with restricted degree is also given. Tom t~t.  ...  The vertex a of graph G is called an essential vertex if it is entered by at least one essential edge. The number of essential vertices of graph G is signed IGI.  ... 
doi:10.15625/1813-9663/17/2/2442 fatcat:aliuydfm7jgczkymelbkkyk4iy

Pattern-based design evolution using graph transformation

Chunying Zhao, Jun Kong, Jing Dong, Kang Zhang
2007 Journal of Visual Languages and Computing  
The graph-transformation approach preserves the integrity and consistency of design patterns in the system when designs change.  ...  A prototype system is built and a case study on the Strategy pattern demonstrates the feasibility of pattern-based design validation and evolution using graph transformation techniques.  ...  Therefore, each design pattern has some essential properties.  ... 
doi:10.1016/j.jvlc.2007.07.004 fatcat:4qj343uahvcu7gu7aowgptkuvy

Dynkin Graphs and Triangle Singularities [article]

Tohsuke Urabe
1994 arXiv   pre-print
We consider what kind of combinations of rational double points can appear on their small deformation fibers. We show their combinations are described by a simple priciple using Dynkin graphs.  ...  We treat nine of fourteen triangle singularities in Arnold's classification list of singularities.  ...  (B) The Dynkin graph Γ has only components of type A, D or E, and can be made from the essential basic graph depending on Ξ by a combination of two of elementary transformations and tie transformations  ... 
arXiv:alg-geom/9409002v1 fatcat:kfxfoh5kmvdjhjyr3zpxrt3agy
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