Information Systems and e-Business Management

, Volume 13, Issue 1, pp 69–106 | Cite as

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

  • Dominic Breuker
  • Patrick Delfmann
  • Hanns-Alexander Dietrich
  • Matthias Steinhorst
Original Article

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.

Keywords

Business process modeling Model collection management Model analysis Graph algorithms 

References

  1. 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 23:333–363CrossRefGoogle Scholar
  2. 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 115–128Google Scholar
  3. 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 33–44Google Scholar
  4. 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 85–94Google Scholar
  5. 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 326–341Google Scholar
  6. Batra D (2005) Conceptual data modeling patterns. J Database Manag 16:84–106CrossRefGoogle Scholar
  7. Becker J, Schütte R (2004) Handelsinformationssysteme. Redline Wirtschaft, FrankfurtGoogle Scholar
  8. 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, AustraliaGoogle Scholar
  9. 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 AfricaGoogle Scholar
  10. 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, WashingtonGoogle Scholar
  11. 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 31–42Google Scholar
  12. 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 1255–1258Google Scholar
  13. 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 343–354Google Scholar
  14. Beeri C, Eyal A, Kamenkovich S, Milo T (2008) Querying business processes with BP-QL. Inf Syst 33:477–507CrossRefGoogle Scholar
  15. 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 1245–1259Google Scholar
  16. Brzozowski JA (1962) Canonical regular expressions and minimal state graphs for definite events. Symposium on the mathematical theory of automata. New York, pp 529–561Google Scholar
  17. Cordella LP, Foggia P, Sansone C, Vento M (2004) A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans Pattern Anal Mach Intell 26:1367–1372CrossRefGoogle Scholar
  18. Curran TA, Keller G (1998) SAP R/3 business blueprint: business engineering mit den R/3-referenzprozessen. Addison-Wesley, BonnGoogle Scholar
  19. 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, ArizonaGoogle Scholar
  20. 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 157–168CrossRefGoogle Scholar
  21. 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 169–185Google Scholar
  22. Dijkman R, Dumas M, van Dongen B, Käärik R, Mendling J (2011a) Similarity of business process models: metrics and evaluation. Inf Syst 36:498–516CrossRefGoogle Scholar
  23. Dijkman R, Gfeller B, Küster J, Völzer H (2011b) Identifying refactoring opportunities in process model repositories. Inf Softw Technol 53:937–948CrossRefGoogle Scholar
  24. Dijkman R, La Rosa M, Reijers HA (2012) Managing large collections of business process models—current techniques and challenges. Comput Ind 63:91–97CrossRefGoogle Scholar
  25. Dumas M, García-Bañuelos L, Dijkman R (2009) Similarity search of business process models. IEEE Comput Soc Tech Comm Data Eng 32:23–28Google Scholar
  26. Dumas M, García-Bañuelos L, La Rosa M, Uba R (2013) Fast detection of exact clones in business process model repositories. Inf Syst 38:619–633CrossRefGoogle Scholar
  27. 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 20–37CrossRefGoogle Scholar
  28. 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 302–318Google Scholar
  29. 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 278–293Google Scholar
  30. 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 699–701Google Scholar
  31. 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 176–189Google Scholar
  32. 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 47:89–100CrossRefGoogle Scholar
  33. 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 436–444Google Scholar
  34. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company, New YorkGoogle Scholar
  35. 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 418–426CrossRefGoogle Scholar
  36. Gottschalk F, van der Aalst WMP, Jansen-Vullers MH, La Rosa M (2008b) Configurable workflow models. Int J Coop Inf Syst 17:177–221CrossRefGoogle Scholar
  37. Hallerbach A, Bauer T, Reichert M (2009) Capturing variability in business process models: the provop approach. J Softw Maint Evol Res Pract 22:519–546CrossRefGoogle Scholar
  38. 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 189–196CrossRefGoogle Scholar
  39. Hopcroft JE, Motwani R, Ullman JD (2008) Introduction to automata theory, languages, and computation. Pearson EducationGoogle Scholar
  40. Houy C, Fettke P, Loos P, Aalst WMP, Krogstie J (2011) Business process management in the large. Bus Inf Syst Eng 3:385–388CrossRefGoogle Scholar
  41. Huffman DA (1954) The synthesis of sequential switching circuits. J Frankl Inst 257:161–190CrossRefGoogle Scholar
  42. 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 402–409Google Scholar
  43. 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 56–63CrossRefGoogle Scholar
  44. 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 164–178Google Scholar
  45. 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 677–684Google Scholar
  46. 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 332–346Google Scholar
  47. Koch I (2001) Enumerating all connected maximal common subgraphs in two graphs. Theor Comput Sci 250:1–30CrossRefGoogle Scholar
  48. 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 535–546CrossRefGoogle Scholar
  49. 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 166–181Google Scholar
  50. 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 96–113CrossRefGoogle Scholar
  51. 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 38:7029–7040CrossRefGoogle Scholar
  52. La Rosa M, Dumas M, ter Hofstede AHM, Mendling J (2011b) Configurable multi-perspective business process models. Inf Syst 36:313–340CrossRefGoogle Scholar
  53. 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 22:1–42CrossRefGoogle Scholar
  54. Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions, and reversals. Sov Phys Dokl 10:707–710Google Scholar
  55. Levi G (1973) A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9:341–352CrossRefGoogle Scholar
  56. 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 344–362Google Scholar
  57. 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 19:159–203CrossRefGoogle Scholar
  58. 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 2–19Google Scholar
  59. Lu R, Sadiq S, Governatori G (2009) On managing business processes variants. Data Knowl Eng 68:642–664CrossRefGoogle Scholar
  60. 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 303–311Google Scholar
  61. 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 392–403Google Scholar
  62. McGregor JJ (1982) Backtrack search algorithms and the maximal common subgraph problem. Softw Pract Exp 12:23–34CrossRefGoogle Scholar
  63. Mendling J, Simon C (2006) Business process design by view integration. In: Eder J, Dustdar S (eds) Business process management workshops. Springer, Berlin, pp 55–64CrossRefGoogle Scholar
  64. 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 113–130Google Scholar
  65. 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 64:312–329CrossRefGoogle Scholar
  66. 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 306–321Google Scholar
  67. Nijssen S, Kok JN (2005) The gaston tool for frequent subgraph mining. Electron Notes Theor Comput Sci 127:77–87CrossRefGoogle Scholar
  68. Nijssen S, Kok JN (2006) Frequent subgraph miners: runtimes don’t say everything. international workshop on mining and learning with graphs (MLG 2006), pp 173–180Google Scholar
  69. Object Management Group (2003) Common warehouse metamodel 1.1. http://www.omg.org/spec/CWM/1.1/
  70. 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 5:42–62CrossRefGoogle Scholar
  71. 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 289–300CrossRefGoogle Scholar
  72. 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 149–166CrossRefGoogle Scholar
  73. 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 199–214Google Scholar
  74. Rahm E, Bernstein PA (2001) A survey of approaches to automatic schema matching. VLDB J 10:334–350CrossRefGoogle Scholar
  75. Reijers HA, Mans RS, van der Toorn RA (2009) Improved model management with aggregated business process models. Data Knowl Eng 68:221–243CrossRefGoogle Scholar
  76. Reijers HA, Mendling J, Dijkman RM (2011) Human and automatic modularizations of process models to enhance their comprehension. Inf Syst 36:881–897CrossRefGoogle Scholar
  77. Rosemann M (2006) Potential pitfalls of process modeling: part A. Bus Process Manag J 12:249–254CrossRefGoogle Scholar
  78. Rosemann M, van der Aalst WMP (2007) A configurable reference modelling language. Inf Syst 32:1–23CrossRefGoogle Scholar
  79. 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 1297–1300Google Scholar
  80. Scheer A-W (1992) Architecture of integrated information systems: foundations of enterprise modelling. Springer, BerlinCrossRefGoogle Scholar
  81. 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 1251–1254Google Scholar
  82. 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 1491–1494Google Scholar
  83. Sun S, Kumar A, Yen J (2006) Merging workflows: a new perspective on connecting business processes. Decis Support Syst 42:844–858CrossRefGoogle Scholar
  84. Thomas O, Fellmann MA (2009) Semantic process modeling—design and implementation of an ontology-based representation of business processes. Bus Inf Syst Eng 1:438–451CrossRefGoogle Scholar
  85. Ullmann JR (1976) An algorithm for subgraph isomorphism. J ACM 23:31–42CrossRefGoogle Scholar
  86. Van der Aalst WMP (1998) The APPLICATION OF PETRI NETS TO WORKflOW MANAGEMENT. J Circuits Syst Comput 08:21–66CrossRefGoogle Scholar
  87. Van der Aalst WMP (2013) Business process management: a comprehensive survey. ISRN Softw Eng 2013:1–37CrossRefGoogle Scholar
  88. 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 137–150CrossRefGoogle Scholar
  89. Wang J, Jin T, Wong RK, Wen L (2013) Querying business process model repositories—a survey of current approaches and issues. World Wide WebGoogle Scholar
  90. Weber B, Reichert M, Mendling J, Reijers HA (2011) Refactoring large process model repositories. Comput Ind 62:467–486CrossRefGoogle Scholar
  91. 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 267–282Google Scholar
  92. Welling R (2011) A performance analysis on maximal common subgraph algorithms. In: 15th Twente Student Conference on IT., Enschede, NetherlandsGoogle Scholar
  93. Wynn M, Verbeek HMW, van der Aalst WMP, ter Hofstede AHM, Edmond D (2009) Business process verification—finally a reality! Bus Process Manag J 15:74–92CrossRefGoogle Scholar
  94. Yan X, Han J (2002) gSpan: graph-based substructure pattern mining. IEEE international conference on data mining. IEEE Comput. Soc, Maebashi City, Japan, pp 721–724Google Scholar
  95. Yan Z, Dijkman R, Grefen P (2012) Fast business process similarity search. Distrib Parallel Databases 30:105–144CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Dominic Breuker
    • 1
  • Patrick Delfmann
    • 1
  • Hanns-Alexander Dietrich
    • 1
  • Matthias Steinhorst
    • 1
  1. 1.WWU Muenster - ERCISMuensterGermany

Personalised recommendations