Polynomial Kernels and User Reductions for the Workflow Satisfiability Problem

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 userssuch 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 (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.

Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints

“…The proposition is closely related to known methods in kernelisation[31]; however, due to the lack of space we do not want to pursue that here.…”