Efficient Evaluation of Location Predicates for Access Control Systems

Often, mobile access to services needs to be controlled based on the current location of a user. However, typically the user location is only available in form of an uncertainty area. Up to now, underlying location checks have been conducted using computationally demanding numerical integration. In this paper, an algorithm is presented for efficiently evaluating location predicates that are defined as containment checks on rectangular areas with user locations described as circular uncertainty areas. We propose to precompute the probability of being inside a small sample location for expectable uncertainty areas for a number of relative positions to that sample. For evaluating the containment check, the precomputed information is used to estimate the probability of being inside the rectangular area. Furthermore, an improvement of the algorithm to a constant complexity is proposed by using summed area tables. A practical evaluation showed that the runtime could be improved by two orders of magnitude in comparison to numerical integration for maximum absolute errors less than 1%.