2 research outputs found

    Tight lower bounds for the Workflow Satisfiability Problem based on the Strong Exponential Time Hypothesis

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    The Workflow Satisfiability Problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification, subject to certain constraints on the assignment. The problem is NP-hard even when restricted to just not equals constraints. Since the number of steps kk is relatively small in practice, Wang and Li (2010) introduced a parametrisation of WSP by kk. Wang and Li (2010) showed that, in general, the WSP is W[1]-hard, i.e., it is unlikely that there exists a fixed-parameter tractable (FPT) algorithm for solving the WSP. Crampton et al. (2013) and Cohen et al. (2014) designed FPT algorithms of running time O(2k)O^*(2^{k}) and O(2klog2k)O^*(2^{k\log_2 k}) for the WSP with so-called regular and user-independent constraints, respectively. In this note, we show that there are no algorithms of running time O(2ck)O^*(2^{ck}) and O(2cklog2k)O^*(2^{ck\log_2 k}) for the two restrictions of WSP, respectively, with any c<1c<1, unless the Strong Exponential Time Hypothesis fails
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