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Graph theory and model collection management: conceptual framework and runtime analysis of selected graph algorithms

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Abstract

Analysing conceptual models is a frequent task of business process management (BPM), for instance to support comparison or integration of business processes, to check business processes for compliance or weaknesses, or to tailor conceptual models for different audiences. As recently, many companies have started to maintain large model collections and analysing such collections manually may be laborious, practitioners have articulated a demand for automatic model analysis support. Hence, BPM scholars have proposed a plethora of different model analysis techniques. As virtually any conceptual model can be interpreted as a mathematical graph and model analysis techniques often include some kind of graph problem, in this paper, we introduce a graph algorithm based model analysis framework that can be accessed by specialized model analysis techniques. To prove that basic graph algorithms are feasible to support such a framework, we conduct a performance analysis of selected graph algorithms.

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Notes

  1. See http://de.talend.com/download for an example of such software.

  2. http://www.cs.sunysb.edu/~algorith/implement/vflib/implement.shtml.

  3. http://www2.informatik.uni-erlangen.de/EN/research/ParSeMiS/download/index.html.

  4. http://www.brics.dk/automaton/.

References

  • Aalst WMP, Hee KM, Hofstede AHM, Sidorova N, Verbeek HMW, Voorhoeve M, Wynn MT (2010) Soundness of workflow nets: classification, decidability, and analysis. Form Asp Comput 23:333–363

    Article  Google Scholar 

  • Awad A (2007) BPMN-Q: a language to query business processes. In: Reichert M, Strecker S, Turowski K (eds) In: Proceedings of the 2nd international workshop on enterprise modelling and information systems architectures (EMISA’07). St. Goar, pp 115–128

  • Awad A, Sakr S (2010) Querying graph-based repositories of business process models. In: Yoshikawa M, Meng X, Yumoto T, Ma Q, Sun L, Watanabe C (eds) Proceedings of the 15th international workshops on database systems for advanced applications. Springer, Berlin, pp 33–44

  • Awad A, Polyvyanyy A, Weske M (2008) Semantic querying of business process models. In: 12th international IEEE enterprise distributed object computing conference (EDOC 2008). IEEE, Munich, pp 85–94

  • Awad A, Decker G, Weske M (2008) Efficient compliance checking using BPMN-Q and temporal logic. In: Dumas M, Reichert M, Shan M-C (eds) Proceedings of the 6th international conference on business process management (BPM’08). Springer, Berlin, pp 326–341

  • Batra D (2005) Conceptual data modeling patterns. J Database Manag 16:84–106

    Article  Google Scholar 

  • Becker J, Schütte R (2004) Handelsinformationssysteme. Redline Wirtschaft, Frankfurt

    Google Scholar 

  • Becker J, Breuker D, Weiß B, Winkelmann A (2010a) Exploring the status quo of business process modelling languages in the banking sector—an empirical insight into the usage of methods in banks. 21st Australasian Conference on Information Systems (ACIS 2010). Brisbane, Australia

  • Becker J, Bergener P, Räckers M, Weiß B, Winkelmann A (2010b) Pattern-based semi-automatic analysis of weaknesses in semantic business process models in the banking sector. Proceedings of the European conference on information systems (ECIS’10). Pretoria, South Africa

  • Becker J, Breuker D, Delfmann P, Dietrich H-A, Steinhorst M (2012a) Identifying business process activity mappings by optimizing behavioral similarity. In: Proceedings of the 18th Americas conference on information systems (AMCIS 2012). Seattle, Washington

  • Becker J, Breuker D, Delfmann P, Dietrich H-A, Steinhorst M (2012b) A runtime analysis of graph-theoretical algorithms to detect patterns in process model collections. In: La Rosa M, Soffer P (eds) Proceedings of the 2nd International Workshop on Process Model Collections. Tallinn, Estonia, pp 31–42

  • Beeri C, Eyal A, Kamenkovich S, Milo T (2005) Querying business processes with BP-QL. In: Proceedings of the 31st international conference on very large data bases (VLDB’05). VLDB Endowment, Trondheim, pp 1255–1258

  • Beeri C, Eyal A, Kamenkovich S, Milo T (2006) Querying business processes. In: Dayal U, Whang K-Y, Lomet D, Alonso G, Lohman G, Kersten M, Cha SK, Kim Y-K (eds) Proceedings of the 32nd international conference on very large data bases (VLDB’06). VLDB Endowment, Seoul, pp 343–354

  • Beeri C, Eyal A, Kamenkovich S, Milo T (2008) Querying business processes with BP-QL. Inf Syst 33:477–507

    Article  Google Scholar 

  • Bräuer S, Delfmann P, Dietrich H-A, Steinhorst M (2013) Using a generic model query approach to allow for process model compliance checking—an algorithmic perspective. In: Alt R, Franczyk B (eds) In: Proceedings of the 11th International Conference on Wirtschaftsinformatik (WI) 2013. Universität Leipzig, Leipzig, pp 1245–1259

  • Brzozowski JA (1962) Canonical regular expressions and minimal state graphs for definite events. Symposium on the mathematical theory of automata. New York, pp 529–561

  • Cordella LP, Foggia P, Sansone C, Vento M (2004) A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans Pattern Anal Mach Intell 26:1367–1372

    Article  Google Scholar 

  • Curran TA, Keller G (1998) SAP R/3 business blueprint: business engineering mit den R/3-referenzprozessen. Addison-Wesley, Bonn

    Google Scholar 

  • Delfmann P, Herwig S, Lis L (2009) Unified enterprise knowledge representation with conceptual models—capturing corporate language in naming conventions. 30th International conference on information systems (ICIS 2009). Phoenix, Arizona

  • Derguech W, Vulcu G, Bhiri S (2010) An indexing structure for maintaining configurable process models. In: Bider I, Halpin T, Krogstie J, Nurcan S, Proper E, Schmidt R, Ukor R (eds) Enterprise, business-process and information systems modeling. Springer, Berlin, pp 157–168

    Chapter  Google Scholar 

  • Deutch D, Milo T (2007) Querying structural and behavioral properties of business processes. In: Arenas M, Schwartzbach MI (eds) 11th International symposium on database programming languages (DBPL 2007). Springer, Berlin, pp 169–185

  • Dijkman R, Dumas M, van Dongen B, Käärik R, Mendling J (2011a) Similarity of business process models: metrics and evaluation. Inf Syst 36:498–516

    Article  Google Scholar 

  • Dijkman R, Gfeller B, Küster J, Völzer H (2011b) Identifying refactoring opportunities in process model repositories. Inf Softw Technol 53:937–948

    Article  Google Scholar 

  • Dijkman R, La Rosa M, Reijers HA (2012) Managing large collections of business process models—current techniques and challenges. Comput Ind 63:91–97

    Article  Google Scholar 

  • Dumas M, García-Bañuelos L, Dijkman R (2009) Similarity search of business process models. IEEE Comput Soc Tech Comm Data Eng 32:23–28

    Google Scholar 

  • Dumas M, García-Bañuelos L, La Rosa M, Uba R (2013) Fast detection of exact clones in business process model repositories. Inf Syst 38:619–633

    Article  Google Scholar 

  • Ekanayake C, Rosa M, Hofstede AM, Fauvet M-C (2011) Fragment-based version management for repositories of business process models. In: Meersman R, Dillon T, Herrero P, Kumar A, Reichert M, Qing L, Ooi B-C, Damiani E, Schmidt D, White J, Hauswirth M, Hitzler P, Mohania M (eds) On the move to meaningful internet systems: OTM 2011. Springer, Berlin, pp 20–37

    Chapter  Google Scholar 

  • Ekanayake CC, Dumas M, García-Bañuelos L, La Rosa M, ter Hofstede AHM (2012) Approximate clone detection in repositories of business process models. In: Barros A, Gal A, Kindler E (eds) Proceedings of the 10th international conference on business process management (BPM 2012). Springer, Berlin, pp 302–318

  • Fahland D, Jobstmann B, Koehler J, Lohmann N, Hagen V, Wolf K (2009) Instantaneous soundness checking of industrial business process models. In: Dayal U, Eder J, Koehler J, Reijers HA (eds) 7th International Conference on Business Process Management (BPM 2009). Springer, Berlin, pp 278–293

  • Fauvet MC, La Rosa M, Sadegh M, Alshareef A, Dijkman RM, García-Bañuelos L, Reijers HA, van der Aalst WMP, Dumas M, Mendling J (2010) Managing process model collections with AProMoRe. Service-Oriented Computing, pp 699–701

  • Feja S, Speck A, Witt S, Schulz M (2011) Checkable graphical business process representation. In: Catania B, Ivanović M, Thalheim B (eds) 14th East European conference on advances in databases and information systems (ADBIS 2010). Springer, Berlin, pp 176–189

  • Fettke P, Loos P (2005) Zur Identifikation von Strukturanalogien in Datenmodellen—Ein Verfahren und seine Anwendung am Beispiel des Y-CIM-Referenzmodells von Scheer. Wirtschaftsinformatik 47:89–100

    Article  Google Scholar 

  • García-Bañuelos L (2008) Pattern identification and classification in the translation from BPMN to BPEL. In: Meersman R, Tari Z (eds) Proceedings of the international conference on the move to meaningful internet systems (OTM’08). Springer, Berlin, pp 436–444

  • Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company, New York

    Google Scholar 

  • Gottschalk F, Aalst WP, Jansen-Vullers M (2008a) Merging event-driven process chains. In: Meersman R, Tari Z (eds) On the move to meaningful internet systems (OTM 2008). Springer, Berlin, pp 418–426

    Chapter  Google Scholar 

  • Gottschalk F, van der Aalst WMP, Jansen-Vullers MH, La Rosa M (2008b) Configurable workflow models. Int J Coop Inf Syst 17:177–221

    Article  Google Scholar 

  • Hallerbach A, Bauer T, Reichert M (2009) Capturing variability in business process models: the provop approach. J Softw Maint Evol Res Pract 22:519–546

    Article  Google Scholar 

  • Hopcroft JE (1971) An n log n algorithm for minimizing states in a finite automaton. In: Kohavi Z (ed) Theory of machines and computations. Academic Press, London, pp 189–196

    Chapter  Google Scholar 

  • Hopcroft JE, Motwani R, Ullman JD (2008) Introduction to automata theory, languages, and computation. Pearson Education

  • Houy C, Fettke P, Loos P, Aalst WMP, Krogstie J (2011) Business process management in the large. Bus Inf Syst Eng 3:385–388

    Article  Google Scholar 

  • Huffman DA (1954) The synthesis of sequential switching circuits. J Frankl Inst 257:161–190

    Article  Google Scholar 

  • Jin T, Wang J, Wu N, La Rosa M, Ter Hofstede AHM (2010) Efficient and accurate retrieval of business process models through indexing. In: Meersman R, Dillon T, Herrero P (eds) Proceedings of the 2010 international conference on on the move to meaningful internet systems (OTM’10). Springer, Berlin, pp 402–409

  • Jin T, Wang J, Wen L (2011a) Efficient retrieval of similar business process models based on structure. In: Meersman R, Dillon T, Herrero P, Kumar A, Reichert M, Qing L, Ooi B-C, Damiani E, Schmidt D, White J, Hauswirth M, Hitzler P, Mohania M (eds) On the move to meaningful internet systems (OTM 2011). Springer, Berlin, pp 56–63

    Chapter  Google Scholar 

  • Jin T, Wang J, Wen L (2011b) Querying business process models based on semantics. In: Yu JX, Kim MH, Unland R (eds) 16th International conference on database systems for advanced applications (DASFAA 2011). Springer, Berlin, pp 164–178

  • Jin T, Wang J, Wen L (2012) Efficient retrieval of similar workflow models based on behavior. In: Sheng QZ, Wang GSC, Xu G (eds) 14th Asia-Pacific web conference (APWeb 2012). Springer, Berlin, pp 677–684

  • Knuplesch D, Ly L, Rinderle-Ma S, Pfeifer H, Dadam P (2010) On enabling data-aware compliance checking of business process models. In: Parsons J, Saeki M, Shoval P, Woo C, Wand Y (eds) 29th International conference on conceptual modeling (ER 2010). Springer, Berlin, pp 332–346

  • Koch I (2001) Enumerating all connected maximal common subgraphs in two graphs. Theor Comput Sci 250:1–30

    Article  Google Scholar 

  • Kunze M, Weske M (2011) Metric trees for efficient similarity search in large process model repositories. In: Muehlen M, Su J (eds) Business process management workshops. Springer, Berlin, pp 535–546

    Chapter  Google Scholar 

  • Kunze M, Weidlich M, Weske M (2011) Behavioral similarity—a proper metric. In: Rinderle-Ma S, Toumani F, Wolf K (eds) 9th International conference on business process management (BPM 2011). Springer, Berlin, pp 166–181

  • La Rosa M, Dumas M, Uba R, Dijkman R (2010) Merging business process models. In: Meersman R, Dillon T, Herrero P (eds) On the move to meaningful internet systems: OTM 2010. Springer, Berlin, pp 96–113

    Chapter  Google Scholar 

  • La Rosa M, Reijers HA, van der Aalst WMP, Dijkman RM, Mendling J, Dumas M, García-Bañuelos L (2011a) APROMORE: an advanced process model repository. Expert Syst Appl 38:7029–7040

    Article  Google Scholar 

  • La Rosa M, Dumas M, ter Hofstede AHM, Mendling J (2011b) Configurable multi-perspective business process models. Inf Syst 36:313–340

    Article  Google Scholar 

  • La Rosa M, Dumas M, Uba R, Dijkman R (2013) Business process model merging: an approach to business process consolidation. ACM Trans Softw Eng Methodol 22:1–42

    Article  Google Scholar 

  • Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Dokl 10:707–710

    Google Scholar 

  • Levi G (1973) A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9:341–352

    Article  Google Scholar 

  • Li C, Reichert M, Wombacher A (2009) Discovering reference models by mining process variants using a heuristic approach. In: Dayal U, Eder J, Koehler J, Reijers HA (eds) 7th International Conference on Business Process Management (BPM 2009). Springer, Berlin, pp 344–362

  • Li C, Reichert M, Wombacher A (2010) The minadept clustering approach for discovering reference process models out of process variants. Int J Coop Inf Syst 19:159–203

    Article  Google Scholar 

  • Lincoln M, Gal A (2011) Searching business process repositories using operational similarity. In: Meersman R, Dillon T, Herrero P, Kumar A, Reichert M, Qing L, Ooi B-C, Damiani E, Schmidt D, White J, Hauswirth M, Hitzler P, Mohania M (eds) International conference on the move to meaningful internet systems (OTM 2011). Springer, Berlin, pp 2–19

  • Lu R, Sadiq S, Governatori G (2009) On managing business processes variants. Data Knowl Eng 68:642–664

    Article  Google Scholar 

  • Mahleko B, Wombacher A (2006) Indexing business processes based on annotated finite state automata. In: 2006 IEEE International Conference on Web Services (ICWS’06). IEEE, Washington, pp 303–311

  • Marc W, Meinl T, Fischer I, Philippsen M (2005) A quantitative comparison of the subgraph miners MoFa, gSpan, FFSM, and Gaston. In: Jorge AM, Torgo L, Brazdil P, Camacho R, Gama J (eds) 9th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD 2005). Springer, Berlin, pp 392–403

  • McGregor JJ (1982) Backtrack search algorithms and the maximal common subgraph problem. Softw Pract Exp 12:23–34

    Article  Google Scholar 

  • Mendling J, Simon C (2006) Business process design by view integration. In: Eder J, Dustdar S (eds) Business process management workshops. Springer, Berlin, pp 55–64

    Chapter  Google Scholar 

  • Mendling J, Neumann G, van der Aalst WMP (2007) Understanding the occurrence of errors in process models based on metrics. In: Meersman R, Tari Z (eds) On the move to meaningful internet systems (OTM 2007). Springer, Berlin, pp 113–130

    Google Scholar 

  • Mendling J, Verbeek HMW, van Dongen BF, van der Aalst WMP, Neumann G (2008) Detection and prediction of errors in EPCs of the SAP reference model. Data Knowl Eng 64:312–329

    Article  Google Scholar 

  • Momotko M, Subieta K (2004) Process query language: a way to make workflow processes more flexible. In: Benczúr A, Demetrovics J, Gottlob G (eds) 8th East European conference on advances in databases and information systems (ADBIS 2004). Springer, Berlin, pp 306–321

  • Nijssen S, Kok JN (2005) The gaston tool for frequent subgraph mining. Electron Notes Theor Comput Sci 127:77–87

    Article  Google Scholar 

  • Nijssen S, Kok JN (2006) Frequent subgraph miners: runtimes don’t say everything. international workshop on mining and learning with graphs (MLG 2006), pp 173–180

  • Object Management Group (2003) Common warehouse metamodel 1.1. http://www.omg.org/spec/CWM/1.1/

  • Ouyang C, Dumas M, Arthur HM, van der Aalst WMP (2008) Pattern-Based translation of BPMN process models to BPEL web services. Int J Web Serv Res 5:42–62

    Article  Google Scholar 

  • Pascalau E, Awad A, Sakr S, Weske M (2011) On maintaining consistency of process model variants. In: Muehlen M, Su J (eds) Business process management workshops. Springer, Berlin, pp 289–300

    Chapter  Google Scholar 

  • Polyvyanyy A, Smirnov S, Weske M (2010) Business process model abstraction. In: Brocke J, Rosemann M (eds) Handbook on business process management 1. Springer, Berlin, pp 149–166

    Chapter  Google Scholar 

  • Qiao M, Akkiraju R, Rembert AJ (2011) Towards efficient business process clustering and retrieval: combining language modeling and structure matching. In: Rinderle-Ma S, Toumani F, Wolf K (eds) 9th International conference on business process management (BPM 2011). Springer, Berlin, pp 199–214

  • Rahm E, Bernstein PA (2001) A survey of approaches to automatic schema matching. VLDB J 10:334–350

    Article  Google Scholar 

  • Reijers HA, Mans RS, van der Toorn RA (2009) Improved model management with aggregated business process models. Data Knowl Eng 68:221–243

    Article  Google Scholar 

  • Reijers HA, Mendling J, Dijkman RM (2011) Human and automatic modularizations of process models to enhance their comprehension. Inf Syst 36:881–897

    Article  Google Scholar 

  • Rosemann M (2006) Potential pitfalls of process modeling: part A. Bus Process Manag J 12:249–254

    Article  Google Scholar 

  • Rosemann M, van der Aalst WMP (2007) A configurable reference modelling language. Inf Syst 32:1–23

    Article  Google Scholar 

  • Sakr S, Awad A (2010) A framework for querying graph-based business process models. In: Proceedings of the 19th international conference on World Wide Web (WWW’10). ACM Press, New York, pp 1297–1300

  • Scheer A-W (1992) Architecture of integrated information systems: foundations of enterprise modelling. Springer, Berlin

    Book  Google Scholar 

  • Scheidegger CE, Vo HT, Koop D, Freire J, Silva CT, Silva T (2008) Querying and re-using workflows with VsTrails. In: Proceedings of the 2008 ACM SIGMOD international conference on Management of data—SIGMOD’08. ACM Press, New York, pp 1251–1254

  • Shao Q, Sun P, Chen Y (2009) WISE: a workflow information search engine. In: 25th International conference on data engineering (ICDE’09). IEEE, Shanghai, pp 1491–1494

  • Sun S, Kumar A, Yen J (2006) Merging workflows: a new perspective on connecting business processes. Decis Support Syst 42:844–858

    Article  Google Scholar 

  • Thomas O, Fellmann MA (2009) Semantic process modeling—design and implementation of an ontology-based representation of business processes. Bus Inf Syst Eng 1:438–451

    Article  Google Scholar 

  • Ullmann JR (1976) An algorithm for subgraph isomorphism. J ACM 23:31–42

    Article  Google Scholar 

  • Van der Aalst WMP (1998) The APPLICATION OF PETRI NETS TO WORKflOW MANAGEMENT. J Circuits Syst Comput 08:21–66

    Article  Google Scholar 

  • Van der Aalst WMP (2013) Business process management: a comprehensive survey. ISRN Softw Eng 2013:1–37

    Article  Google Scholar 

  • Vardi MY (2007) Automata-theoretic model checking revisited. In: Cook B, Podelski A (eds) Verification, model checking, and abstract interpretation (VMCAI 2007). Springer, Berlin, pp 137–150

    Chapter  Google Scholar 

  • Wang J, Jin T, Wong RK, Wen L (2013) Querying business process model repositories—a survey of current approaches and issues. World Wide Web

  • Weber B, Reichert M, Mendling J, Reijers HA (2011) Refactoring large process model repositories. Comput Ind 62:467–486

    Article  Google Scholar 

  • Weidlich M, Mendling J, Weske M (2011) A foundational approach for managing process variability. In: Mouratidis H, Rolland C (eds) 23rd International conference on advanced information systems engineering (CAiSE 2011). Springer, Berlin, pp 267–282

  • Welling R (2011) A performance analysis on maximal common subgraph algorithms. In: 15th Twente Student Conference on IT., Enschede, Netherlands

  • Wynn M, Verbeek HMW, van der Aalst WMP, ter Hofstede AHM, Edmond D (2009) Business process verification—finally a reality! Bus Process Manag J 15:74–92

    Article  Google Scholar 

  • Yan X, Han J (2002) gSpan: graph-based substructure pattern mining. IEEE international conference on data mining. IEEE Comput. Soc, Maebashi City, Japan, pp 721–724

  • Yan Z, Dijkman R, Grefen P (2012) Fast business process similarity search. Distrib Parallel Databases 30:105–144

    Article  Google Scholar 

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  1. WWU Muenster - ERCIS, Leonardo-Campus 3, 48149, Muenster, Germany

    Dominic Breuker, Patrick Delfmann, Hanns-Alexander Dietrich & Matthias Steinhorst

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  1. Dominic Breuker
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Breuker, D., Delfmann, P., Dietrich, HA. et al. Graph theory and model collection management: conceptual framework and runtime analysis of selected graph algorithms. Inf Syst E-Bus Manage 13, 69–106 (2015). https://doi.org/10.1007/s10257-014-0243-6

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