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Graph Transformation in Relational Databases

Graph Transformation in Relational Databases. Gergely Varró Katalin Friedl Dániel Varró {gervarro,friedl}@cs.bme.hu varro@mit.bme.hu. Introduction. Graph transformation graph query + manipulation at very high abstraction level Relational database management systems

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Graph Transformation in Relational Databases

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  1. Graph Transformation in Relational Databases Gergely VarróKatalin Friedl Dániel Varró {gervarro,friedl}@cs.bme.huvarro@mit.bme.hu

  2. Introduction • Graph transformation • graph query + manipulation • at very high abstraction level • Relational database management systems • storage medium for business critical data • the most successful field of SW engineering • close synergy between theory and practice: SQL • manipulation on a low level of abstraction

  3. Motivation • GT for databases • hybrid (visual + textual) query language based upon GT [Andries, Engels] • Varlet framework [Jahnke, Zündorf]: TGGs for database re-engineering • GRAS (graph-oriented DBMS, underlying database for PROGRES) [Kiesel, Schürr, Westfechtel] • Databases for GT • How to do? (Mapping) • How fast? (Performance)

  4. next p1:Process p2:Process Process Resource Graph transformation n1 : next n2 : next Instance model (instance graph) R. Heckel: Compositional verification of reactive systems specified by graph transformation,FASE’98, vol. 1382 of LNCS, pages 138-153 held_by token release Metamodel (type graph) blocked request

  5. p:Process rn:Resource reqn:request hb:held_by r:Resource Rules • A resource that has been held by a process is released. p:Process rn:Resource p:Process rqn:request rel:release hb:held_by Negative application condition Left-hand side r:Resource r:Resource ReleaseR p:Process Precondition Right-hand side

  6. p2:Process p1:Process r1:Resource r2:Resource Pattern matching phase p:Process rn:Resource p:Process rqn:request rel:release hb:held_by r:Resource r:Resource ReleaseR n1 : next rq : request h1 : held_by h2 : held_by n2 : next

  7. r2:Resource p2:Process p1:Process r1:Resource Updating phase p:Process rn:Resource p:Process rqn:request rel:release hb:held_by r:Resource r:Resource ReleaseR n1 : next rq : request h1 : held_by rl : release h2 : held_by n2 : next

  8. SELECT A SELECT * FROM t1 FROM t1, t2 SELECT * FROM t1 WHERE A=1 Database introduction I. • Projection • Selection • Cartesian product

  9. SELECT * FROM t1, t2 WHERE t1.A=t2.C SELECT * FROM t1 LEFT JOIN t2 ON t1.A=t2.C Database introduction II. • Inner join • Left outer join t1.A=t2.C No match for 2 in t2.C No match for 3 in t1.A t1.A=t2.C No match for 2 in t2.C

  10. Process Resource Metamodel representation next Standard mapping • Class  Table • Association  Table + FK • Inheritance Foreign key ... held_by token release Database schema blocked request Metamodel (type graph)

  11. r1:Resource p1:Process p2:Process r2:Resource Instance model representation n1 : next rq : request h1 : held_by h2 : held_by n2 : next Instance model (Instance graph) Data

  12. LHS computation LHS  view Computes the inner join of the corresponding tables p:Process hb:held_by r:Resource CREATE VIEW ReleaseR_lhs AS SELECT p.id AS p, hb.id AS hb, r.id AS r FROM Process AS p, held_by AS hb, Resource AS r WHERE r.id=hb.src AND p.id=hb.trg AND injectivity_constraints

  13. CREATE VIEW ReleaseR_nac AS SELECT p.id AS p, rqn.id AS rqn, rn.id AS rn Process AS p, request AS rqn, Resource AS rn FROM WHERE p.id=rqn.src AND rn.id=rqn.trg NAC computation NAC  view Computes the inner join of the corresponding tables Exactly the same method as for LHS p:Process rn:Resource rqn:request

  14. Precondition computation p:Process rn:Resource Successful matching rqn:request hb:held_by r:Resource Precondition  view CREATE VIEW ReleaseR AS Computes the left outer join of LHS and NAC SELECT lhs.* FROM ReleaseR_lhs AS lhs LEFT JOIN ReleaseR_nac ON lhs.p=nac.p WHERE nac.p IS NULL

  15. DELETE FROM held_by WHERE id=h1 r2:Resource r1:Resource p1:Process p2:Process Updating tables I. p:Process rn:Resource rqn:request hb:held_by r:Resource ReleaseR n1 : next h1 : held_by h2 : held_by n2 : next

  16. INSERT INTO release (id,src,trg) VALUES (rl,r1,p1) r1:Resource p1:Process p2:Process r2:Resource Updating tables II. p:Process rel:release r:Resource ReleaseR n1 : next h2 : held_by rl : release n2 : next

  17. Categorization • Style • interpreted: AGG, Progres • compiled: Fujaba, DB based approach • Base algorithm • constraint satisfaction: AGG, VIATRA, DB based approach • variables + constraints • local searches: Fujaba, Progres • step-by-step extension of the matching • Single pushout approach with injective matchings

  18. Tool comparison I. • Same set of test cases • Short transformation sequences • deterministic execution order • length between 25 and 5000 • Long transformation sequences • deterministic execution order (no matchings in some cases) • up to 60000 rule applications • Few matches on large models • as long as possible rule application

  19. Tool comparison II. • Tool specific issues: • AGG • Without GUI, controlled by a Java program • Progres • Interpreted version with GRAS • Prolog-style cuts (determinism) • Measurements on a second scale • Fujaba • Always (Many-)To-Many associations • Without DOBS • Additional node for storing processes and resources • Our approach • PostgreSQL + No additional optimization

  20. Quantitative comparison I.

  21. Quantitative comparison II.

  22. Evaluation I. • AGG • good PM strategy even for large models • update strategy: linear in model size (!!!) due to compilation into categories • Progres • good, if relatively large number of matches compared to the model size • worst execution results (especially if large models + few matches)

  23. Evaluation II. • Fujaba • extremely good for small models • performance problems with large models • could be much better if DFS graph traversal is supported • DB • runs on all test cases • relatively large overhead for as long as possible rule applications (always from scratch) • BUT STILL THE BEST FOR LARGE MODELS

  24. Future work • Interface definition • to enable the integration of the engine to several GT tools • Comparison to other tools • VIATRA • GReAT • Comparison on other test cases • Incremental transformations • Now in Darmstadt (Segravis)

  25. Before saying thank you for your kind attention... I have some additional surprise if you are interested.

  26. AGG (match vs. update)

  27. Fujaba extra I.

  28. Fujaba extra II.

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