Numbering action vertices in workflow graphs

Zoltán Ádám Mann

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 3, page 591-600
  • ISSN: 1641-876X

Abstract

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Workflow graphs, consisting of actions, events, and logical switches, are used to model business processes. In order to easily identify the actions within a workflow graph, it is useful to number them in such a way that the numbering reflects the structure of the workflow. However, available tools offer only rudimental numbering schemes. In the paper, a set of natural requirements is defined that a logical numbering should fulfill. It is investigated under what conditions there is an appropriate numbering at all, when it is uniquely defined by the set of requirements, and when it can be computed efficiently. It is shown that for an important special class of workflow graphs, namely, structured workflow graphs, the answer to all these questions is affirmative. For general workflow graphs, a set of requirements is presented that can always be fulfilled, but the numbering is not necessarily unique. An algorithm based on a depth-first search can be used to compute an appropriate numbering efficiently.

How to cite

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Zoltán Ádám Mann. "Numbering action vertices in workflow graphs." International Journal of Applied Mathematics and Computer Science 20.3 (2010): 591-600. <http://eudml.org/doc/208010>.

@article{ZoltánÁdámMann2010,
abstract = {Workflow graphs, consisting of actions, events, and logical switches, are used to model business processes. In order to easily identify the actions within a workflow graph, it is useful to number them in such a way that the numbering reflects the structure of the workflow. However, available tools offer only rudimental numbering schemes. In the paper, a set of natural requirements is defined that a logical numbering should fulfill. It is investigated under what conditions there is an appropriate numbering at all, when it is uniquely defined by the set of requirements, and when it can be computed efficiently. It is shown that for an important special class of workflow graphs, namely, structured workflow graphs, the answer to all these questions is affirmative. For general workflow graphs, a set of requirements is presented that can always be fulfilled, but the numbering is not necessarily unique. An algorithm based on a depth-first search can be used to compute an appropriate numbering efficiently.},
author = {Zoltán Ádám Mann},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {workflow graph; flowchart; event-driven process chain; numbering; depth-first search},
language = {eng},
number = {3},
pages = {591-600},
title = {Numbering action vertices in workflow graphs},
url = {http://eudml.org/doc/208010},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Zoltán Ádám Mann
TI - Numbering action vertices in workflow graphs
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 3
SP - 591
EP - 600
AB - Workflow graphs, consisting of actions, events, and logical switches, are used to model business processes. In order to easily identify the actions within a workflow graph, it is useful to number them in such a way that the numbering reflects the structure of the workflow. However, available tools offer only rudimental numbering schemes. In the paper, a set of natural requirements is defined that a logical numbering should fulfill. It is investigated under what conditions there is an appropriate numbering at all, when it is uniquely defined by the set of requirements, and when it can be computed efficiently. It is shown that for an important special class of workflow graphs, namely, structured workflow graphs, the answer to all these questions is affirmative. For general workflow graphs, a set of requirements is presented that can always be fulfilled, but the numbering is not necessarily unique. An algorithm based on a depth-first search can be used to compute an appropriate numbering efficiently.
LA - eng
KW - workflow graph; flowchart; event-driven process chain; numbering; depth-first search
UR - http://eudml.org/doc/208010
ER -

References

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  1. Cormen, T.H., Leiserson, C.E., Rivest, R.L. and Stein, C. (2001). Introduction to Algorithms, MIT Press, Cambridge, MA. Zbl1047.68161
  2. Kiepuszewski, B., ter Hofstede, A. and van der Aalst, W. (2003). Fundamentals of control flow in workflows, Acta Informatica 39(3): 143-209. Zbl1060.68079
  3. Microsoft Corporation (2010). Microsoft Office Visio: Number the shapes in a flowchart, http://office.microsoft.com/en-us/visio/HP866500731033.aspx. 
  4. RFF Electronics (2004). RFFlow user's guide, http://www.rff.com. 
  5. Scheer, A.-W. (2000). ARIS-Business Process Modeling, Springer, Berlin. 
  6. Scheer, A.-W., Thomas, O. and Adam, O. (2005). Process modeling using event-driven process chains, in M. Dumas, W.M.P. van der Aalst and A.H.M. ter Hofstede (Eds.), Process-Aware Information Systems, John Wiley & Sons, Hoboken, NJ, pp. 119-145. 
  7. van der Aalst, W.M.P. (1999). Formalization and verification of event-driven process chains, Information and Software Technology 41(10): 639-650. 
  8. Vanhatalo, J., Völzer, H. and Koehler, J. (2009). The refined process structure tree, Data & Knowledge Engineering 68(9): 793-818. 
  9. Weber, I., Hoffmann, J. and Mendling, J. (2008). Beyond soundness: On the semantic consistency of executable process models, Proceedings of the 6th European Conference on Web Services, Dublin, Ireland, pp. 102-111. 

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