Iterative Plan Construction for the Workflow Satisfiability Problem
Abstract
The \emph{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 \emph{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 {\em 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 fixedparameter tractable (FPT), parameterized by the number of tasks. We have identified a new FPT constraint language, userindependent 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 \emph{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 userindependent constraints. We also show that there is no algorithm of running time $O^*(2^{o(k\log k)})$ for userindependent constraints unless the Exponential Time Hypothesis fails.
 Publication:

arXiv eprints
 Pub Date:
 June 2013
 arXiv:
 arXiv:1306.3649
 Bibcode:
 2013arXiv1306.3649C
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Journal of Artificial Intelligence Research 51 (2014), pp.555577