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

The fixed parameter tractable (FPT) approach is a powerful tool in tackling computationally hard problems.  In this paper, we link FPT results to classic artificial intelligence (AI) techniques to show how they complement each other.  Specifically, we consider the workflow satisfiability problem (WSP) which asks whether there exists an assignment of authorised users to the steps in a workflow specification, subject to certain constraints on the assignment.  It was shown by Cohen et al. (JAIR 2014) that WSP restricted to the class of user-independent constraints (UI), covering many practical cases, admits FPT algorithms, i.e. can be solved in time exponential only in the number of steps k and polynomial in the number of users n.  Since usually k << n in WSP, such FPT algorithms are of great practical interest. We present a new interpretation of the FPT nature of the WSP with UI constraints giving a decomposition of the problem into two levels.  Exploiting this two-level split, we develop a new FPT algorithm that is by many orders of magnitude faster than the previous state-of-the-art WSP algorithm and also has only polynomial-space complexity.  We also introduce new pseudo-Boolean (PB) and Constraint Satisfaction (CSP) formulations of the WSP with UI constraints which efficiently exploit this new decomposition of the problem and raise the novel issue of how to use general-purpose solvers to tackle FPT problems in a fashion that meets FPT efficiency expectations.  In our computational study, we investigate, for the first time, the phase transition (PT) properties of the WSP, under a model for generation of random instances.  We show how PT studies can be extended, in a novel fashion, to support empirical evaluation of scaling of FPT algorithms

Solving the Workflow Satisfiability Problem using General Purpose Solvers

The workflow satisfiability problem (WSP) is a well-studied problem in access control seeking allocation of authorised users to every step of the workflow, subject to workflow specification constraints. It was noticed that the number $k$ of steps is typically small compared to the number of users in the real-world instances of WSP; therefore $k$ is considered as the parameter in WSP parametrised complexity research. While WSP in general was shown to be W[1]-hard, WSP restricted to a special case of user-independent (UI) constraints is fixed-parameter tractable (FPT). However, restriction to the UI constraints might be impractical. To efficiently handle non-UI constraints, we introduce the notion of branching factor of a constraint. As long as the branching factors of the constraints are relatively small and the number of non-UI constraints is reasonable, WSP can be solved in FPT time. Extending the results from Karapetyan et al. (2019), we demonstrate that general-purpose solvers are capable of achieving FPT-like performance on WSP with arbitrary constraints when used with appropriate formulations. This enables one to tackle most of practical WSP instances. While important on its own, we hope that this result will also motivate researchers to look for FPT-aware formulations of other FPT problems.Comment: Associated data: http://doi.org/10.17639/nott.711

Workflow Satisfiability Problem with User-Independent Constraints: Instances, Instance Generator and Algorithms

Source code and data for the publication: Daniel Karapetyan, Andrew J. Parkes, Gregory Gutin, Andrei Gagarin. Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints. To appear in Journal of Artificial Intelligence Research. Includes: - Source code of an instance generator for the Workflow Satisfiability Problem with User-Independent Constraints (WSP) (part of the C# tool) - Parameters of benchmark instances - Benchmark instances with solutions - Source code of the Pattern Backtracking Algorithm (PBT) (part of the C# tool) - Translator of WSP instances into Pseudo-Boolean formulation (part of the C# tool) - Translator of WSP instances into Constraint Satisfaction Problem formulation (CspRunner.py