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

Karapetyan, Daniel; J. Parkes, Andrew; Gutin, Gregory; Gagarin, Andrei


Daniel Karapetyan

Gregory Gutin

Andrei Gagarin


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 less than less than 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.

Journal Article Type Article
Publication Date Sep 5, 2019
Journal Journal of Artificial Intelligence Research
Print ISSN 1076-9757
Publisher AI Access Foundation
Peer Reviewed Peer Reviewed
Volume 66
Pages 85-122
APA6 Citation Karapetyan, D., J. Parkes, A., Gutin, G., & Gagarin, A. (2019). Pattern-Based Approach to the Workflow Satisfiability Problem with User-Independent Constraints. Journal of Artificial Intelligence Research, 66, 85-122.
Keywords Artificial Intelligence; Computational Complexity
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