Tight Lower Bounds for the Workflow Satisfiability Problem Based on the Strong Exponential Time Hypothesis

• Published in: arXiv.org
• Main Authors: Gutin, Gregory, Wahlstrom, Magnus
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.08.2015
• Subjects: Algorithms; Hypotheses; Lower bounds; Parameterization; Run time (computers); Workflow
• ISSN: 2331-8422

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 \(k\) is relatively small in practice, Wang and Li (2010) introduced a parametrisation of WSP by \(k\). 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 \(O^*(2^{k})\) and \(O^*(2^{k\log_2 k})\) 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 \(O^*(2^{ck})\) and \(O^*(2^{ck\log_2 k})\) for the two restrictions of WSP, respectively, with any \(c<1\), unless the Strong Exponential Time Hypothesis fails.