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. Several bespoke algorithms have been constructed for solving the WSP, optimised to deal with constraints (business rules) of particular types. It is natural to see the WSP as a subclass of the Constraint Satisfaction Problem (CSP) in which the variables are tasks and the domain is the set of users. What makes the WSP distinctive as a CSP is that we can assume that the number of tasks is very small compared to the number of users. This is in sharp contrast with traditional CSP models where the domain is small and the number of variables is very large. As such, it is appropriate to ask for which constraint languages the WSP is fixed-parameter tractable (FPT), parameterized by the number of tasks. This novel approach to the WSP, using techniques for CSP, has enabled us to generalise and unify existing algorithms. Rather than considering algorithms for specific constraints, we design a generic algorithm which is a fixed-parameter algorithm for several families of workflow constraints considered in the literature. We have identified a new FPT constraint language, user-independent constraint, that includes many of the constraints of interest in business processing systems. We are also able to prove that the union of FPT languages remains FPT if they satisfy a simple compatibility condition. In this paper we present our generic algorithm, in which plans are grouped into equivalence classes, each class being associated with a pattern. We demonstrate that our generic algorithm has running time O * (2 k log k ), where k is the number of tasks, for the language of user-independent constraints. We also show there is no algorithm of running time O * (2 o(k log k) ) for user-independent constraints unless the Exponential Time Hypothesis fails.
Cohen et al. REF apply techniques from CSP to the Workflow Satisfiability Problem (WSP)-that is, deciding whether a plan exists for assinging task to authorized users in a given business process.
Iterative Plan Construction for the Workflow Satisfiability Problem
Journal of Artificial Intelligence Research 51 (2014), pp.555-577
Computer Science