## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, November 03, 2016, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Gregory Gutin (Royal Holloway University of London)

## A Multivariate Approach for Checking Resiliency in Access Control

In recent years, several combinatorial problems were introduced in the area of access control. Typically, such problems deal with an authorization policy, seen as a relation $UR \subseteq Users \times Resources$, where $(u, r) \in UR$ means that user u is authorized to access resource r. Li, Tripunitara and Wang (2009) introduced the Resiliency Checking Problem (RCP), in which we are given an authorization policy, a subset of resources $P$, as well as integers $s \ge 0$, $d \ge 1$ and $t \geq 1$. It asks whether upon removal of any set of at most $s$ users, there still exist $d$ pairwise disjoint sets of at most $t$ users such that each set has collectively access to all resources in $P$. This problem possesses several parameters which appear to take small values in practice. We thus analyze the parameterized complexity of RCP with respect to these parameters, by considering all possible combinations of $|P|, s, d, t$. In all cases, we are able to settle whether the problem is in FPT, XP, W[2]-hard, para-NP-hard or para-coNP-hard. The main theorem to prove FPT can be used for other applications.

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