Influential facilities placement over moving objects

In this paper we propose and study the problem of k -Collective influential facility placement over moving object. Specifically, given a set of candidate locations, a group of moving objects, each of which is associated with a collection of reference points, as well as a budget k , we aim to mine a group of k locations, the combination of whom can influence the most number of moving objects. We show that this problem is NP-hard and present a basic hill-climb algorithm, namely GreedyP. We prove this method with (1- 1/e) approximation ratio. One core challenge is to identify and reduce the overlap of the influence from different selected locations to maximize the marginal benefits. Therefore, the GreedyP approach may be very costly when the number of moving objects is large. In order to address the problem, we also propose another GreedyPS algorithm based on FM-sketch technique, which maps the moving objects to bitmaps such that the marginal benefit can be easily observed through bit-wise operations. Through this way, we are able to save more than a half running time while preserving the result quality. We further present a pair of extensions to the problem, namely k -Additional and k -Eliminative Influential Facility Placement problems. We also present corresponding approximate solutions towards both extensions and theoretically show that results of both algorithms are guaranteed. Experiments on real datasets verify the efficiency and effectiveness for all these algorithms comparing with baselines.