Skip to main content
SpringerLink
Log in

Parameterized Complexity of the Workflow Satisfiability Problem

  • Chapter
  • First Online:
Combinatorial Optimization and Graph Algorithms

Abstract

The problem of finding an assignment of authorized users to tasks in a workflow in such a way that all business rules are satisfied has been widely studied in recent years. What has come to be known as the workflow satisfiability problem is known to be hard, yet it is important to find algorithms that can solve the problem as efficiently as possible, because it may be necessary to solve the problem multiple times for the same instance of a workflow. Hence, the most recent work in this area has focused on finding optimal fixed-parameter algorithms to solve the problem. In this chapter, we summarize our recent results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In fact, NP-hardness result for the WSP is thus a restatement of this well-known result for CSP.

  2. 2.

    For a formal definition of FPT algorithms, see Sect. 2.3.

  3. 3.

    The Exponential Time Hypothesis [37] states that 3-SAT cannot be solved by an algorithm of running time \(O^*(2^{o(n)})\), where n is the number of variables in the input CNF formula.

  4. 4.

    The Strong Exponential Time Hypothesis [36] states that

    $$ \lim _{t \rightarrow \infty } \inf \{c \ge 0:\ t\text {-SAT has an algorithm in time } O(2^{cn})\} = 1. $$
  5. 5.

    This notion was introduced by Cohen et al. [18] in a different but equivalent form; our definition is from [40].

References

  1. American National Standards Institute. in ANSI INCITS 359-2004 for Role Based Access Control (2004)

    Google Scholar 

  2. A. Armando, S. Ponta, Model checking of security-sensitive business processes, in eds. By P. Degano, J.D. Guttman, Formal Aspects in Security and Trust. Lecture Notes in Computer Science, vol. 5983 (Springer, 2009), pp. 66–80

    Google Scholar 

  3. L. Barto, M. Kozik, Constraint satisfaction problems solvable by local consistency methods. J. ACM 61(1), 3 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. D.A. Basin, S.J. Burri, G. Karjoth, Obstruction-free authorization enforcement: aligning security with business objectives, in CSF (IEEE Computer Society, 2011), pp. 99–113

    Google Scholar 

  5. N. Beldiceanu, M. Carlsson, J.-X. Rampon, Global Constraint Catalog, 2nd edn. (revision a). Technical Report T2012:03, Swedish Institute of Computer Science (2012)

    Google Scholar 

  6. E. Bertino, E. Ferrari, V. Atluri, The specification and enforcement of authorization constraints in workflow management systems. ACM Trans. Inf. Syst. Secur. 2(1), 65–104 (1999)

    Article  Google Scholar 

  7. C. Bessière, J.-C. Régin, R.H.C. Yap, Y. Zhang, An optimal coarse-grained arc consistency algorithm. Artif. Intell. 165(2), 165–185 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Björklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion-exclusion. SIAM J. Comput. 39(2), 546–563 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Bodirsky, J. Nešetřil, Constraint satisfaction with countable homogeneous templates. J. Logic Comput. 16, 359–373 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. D.F.C. Brewer, M.J. Nash, The Chinese wall security policy, in IEEE Symposium on Security and Privacy (IEEE Computer Society, 1989), pp. 206–214

    Google Scholar 

  11. A. Bulatov, A dichotomy theorem for constraints on a three-element set, in Proceedings 43rd IEEE Symposium on Foundations of Computer Science, FOCS’02 (IEEE Computer Society, 2002), pp. 649–658

    Google Scholar 

  12. A. Bulatov, Tractable conservative constraint satisfaction problems, in Proceedings 18th IEEE Symposium on Logic in Computer Science, LICS’03 (Ottawa, Canada, 2003), pp. 321–330

    Google Scholar 

  13. A. Bulatov, P. Jeavons, A. Krokhin, Classifying the complexity of constraints using finite algebras. SIAM J. Comput. 34(3), 720–742 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. A.A. Bulatov, On the CSP dichotomy conjecture, in eds. By A.S. Kulikov, N.K. Vereshchagin, Proceedings of the Computer Science-Theory and Applications-6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Lecture Notes in Computer Science, vol. 6651 (Springer, 2011), pp. 331–344

    Google Scholar 

  15. A.A. Bulatov, V. Dalmau, A simple algorithm for Mal’tsev constraints. SIAM J. Comput. 36(1), 16–27 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. A.A. Bulatov, D. Marx, The complexity of global cardinality constraints. in Proceedings of the 24th Annual IEEE Symposium on Logic in Computer Science, LICS 2009, 11-14 August 2009, Los Angeles, CA, USA (IEEE Computer Society, 2009), pp. 419–428

    Google Scholar 

  17. D. Cohen, J. Crampton, A. Gagarin, G. Gutin, M. Jones, Engineering algorithms for workflow satisfiability problem with user-independent constraints, in eds. By J. Chen, J. Hopcroft, J. Wang, Frontiers in Algorithmics, FAW 2014. Lecture Notes in Computer Science, vol. 8497 (Springer, 2014), pp. 48–59

    Google Scholar 

  18. D. Cohen, J. Crampton, A. Gagarin, G. Gutin, M. Jones, Iterative plan construction for the workflow satisfiability problem problem. J. Artif. Intell. Res. (JAIR) 51, 555–577 (2014)

    MathSciNet  MATH  Google Scholar 

  19. D. Cohen, P. Jeavons, P. Jonsson, M. Koubarakis, Building tractable disjunctive constraints. J. ACM 47, 826–853 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. M.C. Cooper, D.A. Cohen, P. Jeavons, Characterising tractable constraints. Artif. Intell. 65(2), 347–361 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Crampton, A reference monitor for workflow systems with constrained task execution, in eds. By E. Ferrari, G.-J. Ahn, SACMAT (ACM, 2005), pp. 38–47

    Google Scholar 

  22. J. Crampton, R. Crowston, G. Gutin, M. Jones, M.S. Ramanujan, Fixed-parameter tractability of workflow satisfiability in the presence of seniority constraints, in eds. By M.R. Fellows, X. Tan, B. Zhu, FAW-AAIM. Lecture Notes in Computer Science, vol. 7924 (Springer, 2013), pp. 198–209

    Google Scholar 

  23. J. Crampton, A.V. Gagarin, G. Gutin, M. Jones, On the workflow satisfiability problem with class-independent constraints, in 10th International Symposium on Parameterized and Exact Computation, IPEC 2015. LIPIcs, vol. 43 (2015), pp. 66–77

    Google Scholar 

  24. J. Crampton, A.V. Gagarin, G. Gutin, M. Jones, M.M. Wahlström, On the workflow satisfiability problem with class-independent constraints for hierarchical organizations. ACM Trans. Priv. Secur. 19(3), 8:1–8:29 (2016)

    Google Scholar 

  25. J. Crampton, G. Gutin, D. Karapetyan, Valued workflow satisfiability problem, in Proceedings of the 20th ACM Symposium on Access Control Models and Technologies (SACMAT 2015) (2015), pp. 3–13

    Google Scholar 

  26. J. Crampton, G. Gutin, D. Karapetyan, R. Watrigant, The bi-objective workflow satisfiability problem and workflow resiliency. J. Comput. Secur. 25(1), 83–115 (2017)

    Article  Google Scholar 

  27. J. Crampton, G. Gutin, A. Yeo, On the parameterized complexity and kernelization of the workflow satisfiability problem. ACM Trans. Inf. Syst. Secur. 16(1), 4 (2013)

    Article  Google Scholar 

  28. M. Cygan, F. Fomin, L. Kowalik, D. Lokshtanov, D. Marx, M. Pilipczuk, M. Pilipczuk, S. Saurabh, Parameterized Algorithms (Springer, 2015)

    Google Scholar 

  29. V. Dalmau, A new tractable class of constraint satisfaction problems, in Proceedings 6th International Symposium on Artificial Intelligence and Mathematics (2000)

    Google Scholar 

  30. R.G. Downey, M.R. Fellows, Fundamentals of Parameterized Complexity (Springer, New York, 2013)

    Google Scholar 

  31. R.G. Downey, M.R. Fellows, Fundamentals of Parameterized Complexity, Texts in Computer Science (Springer, 2013)

    Google Scholar 

  32. P. Erdős, P. Turán, On a problem of sidon in additive number theory, and on some related problems. J. Lond. Math. Soc. s1-16(4), 212–215 (1941)

    Google Scholar 

  33. G. Gutin, S. Kratsch, M. Wahlström, Polynomial kernels and user reductions for the workflow satisfiability problem. Algorithmica 75, 383–402 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Gutin, M. Wahlström, Tight lower bounds for the workflow satisfiability problem based on the strong exponential time hypothesis. Inf. Process. Lett. 116(3), 223–226 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  35. C. Han, C.-H. Lee, Comments on Mohr and Henderson’s path consistency algorithm. Artif. Intell. 36, 125–130 (1988)

    Article  MATH  Google Scholar 

  36. R. Impagliazzo, R. Paturi, On the complexity of \(k\)-sat. J. Comput. Syst. Sci. 62(2), 367–375 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  37. R. Impagliazzo, R. Paturi, F. Zane, Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63(4), 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  38. P.G. Jeavons, M.C. Cooper, Tractable constraints on ordered domains. Artif. Intell. 79(2), 327–339 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  39. J. Joshi, E. Bertino, U. Latif, A. Ghafoor, A generalized temporal role-based access control model. IEEE Trans. Knowl. Data Eng. 17(1), 4–23 (2005)

    Article  Google Scholar 

  40. D. Karapetyan, A.V. Gagarin, G. Gutin, Pattern backtracking algorithm for the workflow satisfiability problem with user-independent constraints, in Proceedings of the Frontiers in Algorithmics-9th International Workshop, FAW 2015, Guilin, China, July 3–5 (2015), pp. 138–149

    Google Scholar 

  41. D. Karapetyan, A.J. Parkes, G. Gutin, A. Gagarin, Pattern-based approach to the workflow satisfiability problem with user-independent constraints, in CoRR (2016), arxiv:abs/1604.05636

  42. A. Krokhin, P. Jeavons, P. Jonsson, Reasoning about temporal relations: the tractable subalgebras of Allen’s interval algebra. J. ACM 50, 591–640 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  43. D. Le Berre, A. Parrain, The SAT4J library, release 2.2. J. Satisf. Bool. Model. Comput. 7, 59–64 (2010)

    Google Scholar 

  44. F. Rossi, P.V. Beek, T. Walsh, Handbook of Constraint Programming (Foundations of Artificial Intelligence) (Elsevier Science Inc., New York, NY, USA, 2006)

    Google Scholar 

  45. R.S. Sandhu, E.J. Coyne, H.L. Feinstein, C.E. Youman, Role-based access control models. IEEE Comput. 29(2), 38–47 (1996)

    Article  Google Scholar 

  46. T.J. Schaefer, The complexity of satisfiability problems, in Proceedings 10th ACM Symposium on Theory of Computing, STOC’78 (1978), pp. 16–226

    Google Scholar 

  47. Q. Wang, N. Li, Satisfiability and resiliency in workflow authorization systems. ACM Trans. Inf. Syst. Secur. 13(4), 40 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    D. Cohen, J. Crampton, G. Gutin & M. Wahlström

Authors
  1. D. Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Crampton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Gutin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Wahlström
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Wahlström .

Editor information

Editors and Affiliations

  1. National Institute of Informatics , Tokyo, Japan

    Takuro Fukunaga

  2. National Institute of Informatics , Tokyo, Japan

    Ken-ichi Kawarabayashi

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this chapter

Cite this chapter

Cohen, D., Crampton, J., Gutin, G., Wahlström, M. (2017). Parameterized Complexity of the Workflow Satisfiability Problem. In: Fukunaga, T., Kawarabayashi, Ki. (eds) Combinatorial Optimization and Graph Algorithms. Springer, Singapore. https://doi.org/10.1007/978-981-10-6147-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6147-9_5

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6146-2

  • Online ISBN: 978-981-10-6147-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation