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 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 \in Γ allows no polynomial kernelization in k+m unless the polynomial hierarchy collapses.

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