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Valued Authorization Policy Existence Problem
arXiv - CS - Data Structures and Algorithms Pub Date : 2021-06-10 , DOI: arxiv-2106.05761
Jason Crampton, Eduard Eiben, Gregory Gutin, Daniel Karapetyan, Diptapriyo Majumdar

Problems of satisfiability and resiliency in workflows have been widely studied in the last decade. Recent work has shown that many such problems may be viewed as special cases of the authorization policy existence problem (APEP), which returns an authorization policy if one exists and 'No' otherwise. A solution may not exist because of the restrictions imposed by the base authorization relation and constraints that form part of the input to APEP. However, in many practical settings it would be more useful to obtain a 'least bad' policy than just a 'No', where 'least bad' is characterized by some numerical value associated with the policy indicating the extent to which the policy violates the base authorization relation and constraints. Accordingly, we introduce the Valued APEP, which returns an authorization policy of minimum weight, where the (non-negative) weight is determined by the constraints violated by the returned solution (and is 0 if all constraints are satisfied). We then establish a number of results concerning the parameterized complexity of Valued APEP. We prove that the problem is fixed-parameter tractable if the set of constraints satisfies two restrictions, but is intractable if only one of these restrictions holds. (Most constraints known to be of practical use satisfy these restrictions.) We introduce the notion of a user profile for a weighted constraint, which enables us to prove a powerful result, a corollary of which improves on known complexity results for APEP. Finally, we consider Valued APEP when restricted to particular sub-classes of constraints and show that instances of such problems can be reduced to the Valued WSP, enabling us to exploit known algorithms to solve these particular instances.

中文翻译:

值授权策略存在问题

在过去的十年中,工作流中的可满足性和弹性问题得到了广泛的研究。最近的工作表明,许多此类问题可以被视为授权策略存在问题 (APEP) 的特例,如果存在则返回授权策略,否则返回“否”。由于基本授权关系和构成 APEP 输入一部分的约束所施加的限制,解决方案可能不存在。然而,在许多实际环境中,获得“最不坏”的政策比仅仅“不”更有用,其中“最坏”的特征是与政策相关的一些数值,表明政策违反政策的程度基本授权关系和约束。因此,我们引入了有价值的 APEP,它返回一个最小权重的授权策略,其中(非负)权重由返回的解决方案违反的约束确定(如果满足所有约束,则为 0)。然后,我们建立了一些关于 Valued APEP 参数化复杂性的结果。我们证明,如果约束集满足两个限制,则问题是固定参数可处理的,但如果只有这些限制中的一个成立,则问题是难以处理的。(大多数已知具有实际用途的约束都满足这些限制。)我们为加权约束引入了用户配置文件的概念,这使我们能够证明一个强大的结果,其推论改进了 APEP 的已知复杂性结果。最后,
更新日期:2021-06-11
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