Algorithms for the workflow satisfiability problem engineered for counting constraints

David Cohen, Jason Crampton, Andrei Gagarin, Gregory Gutin, Mark Jones

Research output: Contribution to journalArticlepeer-review

89 Downloads (Pure)


The workflow satisfiability problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification that satisfies the constraints in the specification. The problem is NP-hard in general, but several subclasses of the problem are known to be fixed-parameter tractable (FPT) when parameterized by the number of steps in the specification. In this paper, we consider the WSP with user-independent counting constraints, a large class of constraints for which the WSP is known to be FPT. We describe an efficient implementation of an FPT algorithm for solving this subclass of the WSP and an experimental evaluation of this algorithm. The algorithm iteratively generates all equivalence classes of possible partial solutions until, whenever possible, it finds a complete solution to the problem. We also provide a reduction from a WSP instance to a pseudo-Boolean (PB) SAT instance. We apply this reduction to the instances used in our experiments and solve the resulting PB SAT problems using SAT4J, a PB SAT solver. We compare the performance of our algorithm with that of SAT4J and discuss which of the two approaches would be more effective in practice.
Original languageEnglish
Pages (from-to)3–24
Number of pages22
JournalJournal of Combinatorial Optimization
Issue number1
Early online date19 Apr 2015
Publication statusPublished - Jul 2016


  • Workflow satisfiability problem (WSP); fixed-parameter tractability (FPT); algorithm engineering; reduction to the pseudo-Boolean SAT problem; user-independent constraints

Cite this