Searching for Multiple Mobile Users

The problem of searching for mobile users in cellular networks is addressed in this study. Previous studies addressing this issue have focused on the problem of searching for a single user. As it is shown in this study, the problem of maximizing the expected rate of successful searches under delay and bandwidth constraints is NP-hard. When the potential locations of different users overlap, the derivation of an optimal concurrent search for many independent users from a set of optimal single user searches is NP-hard, In reality, a cellular network has to serve many competing search requests sharing a limited bandwidth. Since the problem of maximizing the expected rate of successful searches under delay and bandwidth constraints is NP-hard, this study proposes a heuristic algorithm, that is optimal for most probable cases, and its worst case running time complexity is O(n(log n + C log C)), where n is the number of mobile users that must be found, and C is the number of their potential locations.The approximation ratio of the proposed search algorithm is less than 2. That is, the expected number of searches is always less than twice the number of searches expected from an optimal search algorithm. Even under the worst case condition, the proposed method can potentially increase the expected rate of successful searches by 100 percent in comparison to the existing search strategy currently used by cellular networks. Moreover, the proposed search strategy outperforms a greedy search strategy that considers only the users' location probabilities and ignores their deadline constraints. Under certain conditions, the expected rate of successful searches generated by the proposed method is twice the equivalent rate generated by the greedy search strategy. In addition, the proposed search strategy outperforms a heuristic algorithm that searches around the user last known location.