The user authorization query (UAQ) problem determines whether there exists an optimum set of roles to be activated to provide a set of permissions requested by a user. It has been deemed as a key issue for efficiently handling user's access requests in role-based access control (RBAC). Unfortunately, the weight is a value attached to a permission/role representing its importance, should be introduced to UAQ, has been ignored. In this paper, we propose a comprehensive definition of the weighted UAQ (WUAQ) problem with the role-weighted-cardinality and permission-weighted-cardinality constraints. Moreover, we study the computational complexity of different subcases of WUAQ, and show that many instances in each subcase are intractable. In particular, inspired by the idea of the genetic algorithm, we propose an algorithm to approximate solve an intractable subcase of the WUAQ problem. An important observation is that this algorithm can be efficiently modified to handle the other subcases of the WUAQ problem. The experimental results show the advantage of the proposed algorithm, which is especially fit for the case that the computational overhead is even more important than the accuracy in a large-scale RBAC system.

Traffic signal phase and timing (TSPaT) information is valuable for various applications, such as velocity advisory systems, navigation systems, collision warning systems, and so forth. In this paper, we focus on learning baseline timing cycle lengths for fixed-time traffic signals. The cycle length is the most important parameter among all timing parameters, such as green lengths. We formulate the cycle length learning problem as a period estimation problem using a sparse set of noisy observations, and propose the most frequent approximate greatest common divisor (MFAGCD) algorithms to solve the problem. The accuracy performance of our proposed algorithms is experimentally evaluated on both simulation data and the real taxi GPS trajectory data collected in Shanghai, China. Experimental results show that the MFAGCD algorithms have better sparsity and outliers tolerant capabilities than existing cycle length estimation algorithms.