Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem

• Published in: Algorithmica Vol. 75; no. 2; pp. 383 - 402
• Main Authors: Gutin, Gregory, Kratsch, Stefan, Wahlström, Magnus
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2016
• Subjects: 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; Workflow satisfiability problem; Parameterized complexity; Kernelization
• ISSN: 0178-4617; 1432-0541
• DOI: 10.1007/s00453-015-9986-9

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.