Varró, Gergely

Varró Gergely

University of Szeged

Incremental Graph Transformation in Relational DatabasesGergely VarróThe theory of graph transformation [2] was originally developed as a generalization ofChomsky grammars from strings to graphs. Methods, techniques, and tools from the areaof graph transformations have already been studied and applied in many fields of computerscience such as formal language theory, pattern recognition and generation, compiler construc-tion, software engineering, etc.Despite the large variety of existing graph transformation tools, the implementation of theirgraph transformation engine typically follows the same principle. In this respect, first a match-ing occurrence of the left-hand side (LHS) of the graph transformation rule is being found bysome sophisticated graph pattern matching algorithm. Then the engine performs some localmodifications to add or remove graph elements to the matching pattern, and the entire processstarts all over again.Since graph pattern matching leads to the subgraph isomorphism problem that is knownto be NP complete in general, this step is considered to be the most crucial in the overall per-formance of a graph transformation engine. Current tools (e.g., PROGRES [4]) use differentefficient strategies for the graph pattern matching phase.However, I argue that the overall complexity of a graph transformation engine is not neces-sarily equal to the complexity of the graph pattern matching phase, especially for long trans-formation sequences. During the execution of a transformation step, instance models are onlymodified locally in the context of the matching occurrence of the LHS and the rest of the in-stance model left unchanged. Thus any implementation that does not reuse the informationcollected for the previous matching and that restarts the complex and expensive pattern match-ing phase from scratch is not optimal.I propose a technique based on incremental updates [3] which, in itself, is not a new idea,since it has been widely accepted and successfully used in relational databases, but it providesa new philosophy for implementing efficient graph transformation engines.The main idea of incremental updates in graph transformation systems is to keep track of allpossible matchings of graph transformation rules (e.g., in database tables) to make the graphpattern matching step very fast. Afterwards when a rule is applied we update data in all lo-cations it is required. Since graph transformation typically manipulates only a small fragmentof the instance model, incremental updates require minor changes to the stored data. Natu-rally, the initialization phase needs some considerable amount of pre-processing prior to thetransformation, but the subsequent transformation process itself becomes much faster.Relational databases give several supporting features (e.g., foreign key constraints, databaseviews) for preserving data consistency. A view is a query that defines a computed relation inthe database (see [1] for details). It is updated incrementally in most off-the-shelf relationaldatabases. Our idea is to build a graph transformation engine on the top of a relational databaseto exploit various results of database theory.References[1] A. Gupta and I. S. Mumick. Maintenance of materialized views: Problems, techniques andapplications. IEEE Quarterly Bulletin on Data Engineering; Special Issue on MaterializedViews and Data Warehousing, 1995.[2] G. Rozenberg, editor. Handbook of Graph Grammars and Computing by Graph Transfor-mation. Vol. 1: Foundations. World Scientific, 1997.[3] G. Varró and D. Varró. Graph transformation with incremental updates. In Proc. 4th Int.Workshop on Graph Transformation and Visual Modeling Techniques, 2004.[4] A. Zündorf. Graph pattern-matching in PROGRES. In Proc. 5th Int. Workshop on GraphGrammars and their Application to Computer Science, volume 1073 of LNCS, pages 454-468. Springer-Verlag, 1996.124

Incremental graph transformation in relational databases : [abstract]

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Incremental graph transformation in relational databases

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