Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem
The workflow satisfiability problem ( wsp ) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a plan —an assignment of tasks to authorized users—such...
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| Vydáno v: | Algorithmica Ročník 75; číslo 2; s. 383 - 402 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
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01.06.2016
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| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
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| Abstract | The
workflow satisfiability problem
(
wsp
) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a
plan
—an assignment of tasks to authorized users—such that all constraints are satisfied. The
wsp
is, in fact, the
conservative constraint satisfaction problem
(i.e., for each variable, here called
task
, we have a unary authorization constraint) and is, thus,
NP
-complete. It was observed by Wang and Li (ACM Trans Inf Syst Secur 13(4):40,
2010
) that the number
k
of tasks is often quite small and so can be used as a parameter, and several subsequent works have studied the parameterized complexity of
wsp
regarding parameter
k
. We take a more detailed look at the kernelization complexity of
wsp
(
Γ
) when
Γ
denotes a finite or infinite set of allowed constraints. Our main result is a dichotomy for the case that all constraints in
Γ
are regular: (1) We are able to reduce the number
n
of users to
n
′
≤
k
. This entails a kernelization to size poly
(
k
)
for finite
Γ
, and, under mild technical conditions, to size poly
(
k
+
m
)
for infinite
Γ
, where
m
denotes the number of constraints. (2) Already
wsp
(
R
) for some
R
∈
Γ
allows no polynomial kernelization in
k
+
m
unless the polynomial hierarchy collapses. |
|---|---|
| AbstractList | The
workflow satisfiability problem
(
wsp
) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a
plan
—an assignment of tasks to authorized users—such that all constraints are satisfied. The
wsp
is, in fact, the
conservative constraint satisfaction problem
(i.e., for each variable, here called
task
, we have a unary authorization constraint) and is, thus,
NP
-complete. It was observed by Wang and Li (ACM Trans Inf Syst Secur 13(4):40,
2010
) that the number
k
of tasks is often quite small and so can be used as a parameter, and several subsequent works have studied the parameterized complexity of
wsp
regarding parameter
k
. We take a more detailed look at the kernelization complexity of
wsp
(
Γ
) when
Γ
denotes a finite or infinite set of allowed constraints. Our main result is a dichotomy for the case that all constraints in
Γ
are regular: (1) We are able to reduce the number
n
of users to
n
′
≤
k
. This entails a kernelization to size poly
(
k
)
for finite
Γ
, and, under mild technical conditions, to size poly
(
k
+
m
)
for infinite
Γ
, where
m
denotes the number of constraints. (2) Already
wsp
(
R
) for some
R
∈
Γ
allows no polynomial kernelization in
k
+
m
unless the polynomial hierarchy collapses. |
| Author | Wahlström, Magnus Gutin, Gregory Kratsch, Stefan |
| Author_xml | – sequence: 1 givenname: Gregory surname: Gutin fullname: Gutin, Gregory organization: Royal Holloway, University of London – sequence: 2 givenname: Stefan surname: Kratsch fullname: Kratsch, Stefan email: kratsch@cs.uni-bonn.de organization: TU Berlin – sequence: 3 givenname: Magnus surname: Wahlström fullname: Wahlström, Magnus organization: Royal Holloway, University of London |
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| Keywords | Workflow satisfiability problem Parameterized complexity Kernelization |
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| PublicationTitle | Algorithmica |
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| References | CohenDCramptonJGagarinAGutinGJonesMIterative plan construction for the workflow satisfiability problemJ. Artif. Intell. Res.20145155557732864751315.68145 CramptonJGutinGYeoAOn the parameterized complexity and kernelization of the workflow satisfiability problemACM Trans. Inf. Syst. Secur.2013161410.1145/2487222.2487226 BertinoEBonattiPAFerrariETRBAC: a temporal role-based access control modelACM Trans. Inf. Syst. Secur.20014319123310.1145/501978.501979 Crampton, J., Crowston, R., Gutin, G., Jones, M., Ramanujan, M.S.: Fixed-parameter tractability of workflow satisfiability in the presence of seniority constraints. In: FAW-AAIM, volume 7924 of LNCS, pp. 198–209. Springer (2013) JoshiJBertinoELatifUGhafoorAA generalized temporal role-based access control modelIEEE Trans. Knowl. Data Eng.200517142310.1109/TKDE.2005.1 SandhuRSCoyneEJFeinsteinHLYoumanCERole-based access control modelsIEEE Comput.1996292384710.1109/2.485845 Hermelin, D., Kratsch, S., Soltys, K., Wahlström, M., Wu, X.: A completeness theory for polynomial (Turing) kernelization. In: IPEC, volume 8246 of LNCS, pp. 202–215. Springer (2013) Cohen, D., Crampton, J., Gagarin, A., Gutin, G., Jones, M.: Engineering algorithms for workflow satisfiability problem with user-independent constraints. In: FAW 2014, volume 8497 of LNCS, pp. 48–59. Springer (2014) WangQLiNSatisfiability and resiliency in workflow authorization systemsACM Trans. Inf. Syst. Secur.20101344010.1145/1880022.1880034 BertinoEFerrariEAtluriVThe specification and enforcement of authorization constraints in workflow management systemsACM Trans. Inf. Syst. Secur.1999216510410.1145/300830.300837 DomMLokshtanovDSaurabhSKernelization lower bounds through colors and idsACM Trans. Algorithms201411213328356810.1145/2650261 Crampton, J.: A reference monitor for workflow systems with constrained task execution. In: SACMAT, pp. 38–47. ACM (2005) DellHvan MelkebeekDSatisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapsesJ. ACM201461423325006910.1145/26296201321.68274 American National Standards Institute. ANSI INCITS 359-2004 for role based access control (2004) Lokshtanov, D., Misra, N., Saurabh, S.: Kernelization—preprocessing with a guarantee. In: The Multivariate Algorithmic Revolution and Beyond, volume 7370 of LNCS, pp. 129–161. Springer (2012) DowneyRodney GFellowsMichael RFundamentals of Parameterized Complexity. Texts in Computer Science2013BerlinSpringer10.1007/978-1-4471-5559-106236169 Betzler, N., Bredereck, R., Niedermeier, R.: Partial kernelization for rank aggregation: theory and experiments. In: IPEC, volume 6478 of LNCS, pp. 26–37. Springer (2010) Q Wang (9986_CR17) 2010; 13 J Joshi (9986_CR14) 2005; 17 9986_CR15 RS Sandhu (9986_CR16) 1996; 29 E Bertino (9986_CR3) 1999; 2 9986_CR13 M Dom (9986_CR11) 2014; 11 9986_CR8 Rodney G Downey (9986_CR12) 2013 E Bertino (9986_CR2) 2001; 4 D Cohen (9986_CR6) 2014; 51 H Dell (9986_CR10) 2014; 61 9986_CR1 J Crampton (9986_CR9) 2013; 16 9986_CR7 9986_CR4 9986_CR5 |
| References_xml | – reference: Crampton, J., Crowston, R., Gutin, G., Jones, M., Ramanujan, M.S.: Fixed-parameter tractability of workflow satisfiability in the presence of seniority constraints. In: FAW-AAIM, volume 7924 of LNCS, pp. 198–209. Springer (2013) – reference: SandhuRSCoyneEJFeinsteinHLYoumanCERole-based access control modelsIEEE Comput.1996292384710.1109/2.485845 – reference: WangQLiNSatisfiability and resiliency in workflow authorization systemsACM Trans. Inf. Syst. Secur.20101344010.1145/1880022.1880034 – reference: Crampton, J.: A reference monitor for workflow systems with constrained task execution. In: SACMAT, pp. 38–47. ACM (2005) – reference: Betzler, N., Bredereck, R., Niedermeier, R.: Partial kernelization for rank aggregation: theory and experiments. In: IPEC, volume 6478 of LNCS, pp. 26–37. Springer (2010) – reference: DowneyRodney GFellowsMichael RFundamentals of Parameterized Complexity. Texts in Computer Science2013BerlinSpringer10.1007/978-1-4471-5559-106236169 – reference: Lokshtanov, D., Misra, N., Saurabh, S.: Kernelization—preprocessing with a guarantee. In: The Multivariate Algorithmic Revolution and Beyond, volume 7370 of LNCS, pp. 129–161. Springer (2012) – reference: BertinoEBonattiPAFerrariETRBAC: a temporal role-based access control modelACM Trans. Inf. Syst. Secur.20014319123310.1145/501978.501979 – reference: American National Standards Institute. ANSI INCITS 359-2004 for role based access control (2004) – reference: DomMLokshtanovDSaurabhSKernelization lower bounds through colors and idsACM Trans. Algorithms201411213328356810.1145/2650261 – reference: CohenDCramptonJGagarinAGutinGJonesMIterative plan construction for the workflow satisfiability problemJ. Artif. Intell. Res.20145155557732864751315.68145 – reference: BertinoEFerrariEAtluriVThe specification and enforcement of authorization constraints in workflow management systemsACM Trans. Inf. Syst. Secur.1999216510410.1145/300830.300837 – reference: Cohen, D., Crampton, J., Gagarin, A., Gutin, G., Jones, M.: Engineering algorithms for workflow satisfiability problem with user-independent constraints. In: FAW 2014, volume 8497 of LNCS, pp. 48–59. Springer (2014) – reference: DellHvan MelkebeekDSatisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapsesJ. ACM201461423325006910.1145/26296201321.68274 – reference: CramptonJGutinGYeoAOn the parameterized complexity and kernelization of the workflow satisfiability problemACM Trans. Inf. Syst. Secur.2013161410.1145/2487222.2487226 – reference: Hermelin, D., Kratsch, S., Soltys, K., Wahlström, M., Wu, X.: A completeness theory for polynomial (Turing) kernelization. In: IPEC, volume 8246 of LNCS, pp. 202–215. Springer (2013) – reference: JoshiJBertinoELatifUGhafoorAA generalized temporal role-based access control modelIEEE Trans. Knowl. Data Eng.200517142310.1109/TKDE.2005.1 – ident: 9986_CR4 doi: 10.1007/978-3-642-17493-3_5 – volume: 51 start-page: 555 year: 2014 ident: 9986_CR6 publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.4435 – volume: 11 start-page: 13 issue: 2 year: 2014 ident: 9986_CR11 publication-title: ACM Trans. Algorithms – volume: 17 start-page: 4 issue: 1 year: 2005 ident: 9986_CR14 publication-title: IEEE Trans. Knowl. Data Eng. doi: 10.1109/TKDE.2005.1 – ident: 9986_CR1 – volume: 61 start-page: 23 issue: 4 year: 2014 ident: 9986_CR10 publication-title: J. ACM doi: 10.1145/2629620 – volume: 4 start-page: 191 issue: 3 year: 2001 ident: 9986_CR2 publication-title: ACM Trans. Inf. Syst. Secur. doi: 10.1145/501978.501979 – volume: 29 start-page: 38 issue: 2 year: 1996 ident: 9986_CR16 publication-title: IEEE Comput. doi: 10.1109/2.485845 – ident: 9986_CR15 doi: 10.1007/978-3-642-30891-8_10 – ident: 9986_CR5 doi: 10.1007/978-3-319-08016-1_5 – volume: 13 start-page: 40 issue: 4 year: 2010 ident: 9986_CR17 publication-title: ACM Trans. Inf. Syst. Secur. doi: 10.1145/1880022.1880034 – ident: 9986_CR13 doi: 10.1007/978-3-319-03898-8_18 – volume-title: Fundamentals of Parameterized Complexity. Texts in Computer Science year: 2013 ident: 9986_CR12 doi: 10.1007/978-1-4471-5559-1 – ident: 9986_CR7 doi: 10.1145/1063979.1063986 – ident: 9986_CR8 doi: 10.1007/978-3-642-38756-2_21 – volume: 2 start-page: 65 issue: 1 year: 1999 ident: 9986_CR3 publication-title: ACM Trans. Inf. Syst. Secur. doi: 10.1145/300830.300837 – volume: 16 start-page: 4 issue: 1 year: 2013 ident: 9986_CR9 publication-title: ACM Trans. Inf. Syst. Secur. doi: 10.1145/2487222.2487226 |
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| Snippet | The
workflow satisfiability problem
(
wsp
) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to... |
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| StartPage | 383 |
| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation |
| Title | Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem |
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