Valued Authorization Policy Existence Problem

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.

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