Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem - Gutin, Gregory; Kratsch, Stefan; Wahlström, Magnus (Algorithmica, 2016)
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.