Efficient ϵ-Approximate k-Flexible Aggregate Nearest Neighbor Search for Arbitrary ϵ in Road Networks

Abstract

Recently, complicated spatial search algorithms have emerged as spatial-information-based applications, such as location-based services (LBS), and have become very diverse and frequent. The aggregate nearest neighbor (ANN) search is an extension of the existing nearest neighbor (NN) search; it finds the object p* that minimizes G{d(p*,qi),qi∈Q} from a set Q of M (≥1) query objects, where G is an aggregate function and d() is the distance between two objects. The flexible aggregate nearest neighbor (FANN) search is an extension of the ANN search by introducing flexibility factor ϕ(0<ϕ≤1); it finds the object p* that minimizes G{d(p*,qi),qi∈Qϕ} from Qϕ, a subset of Q with |Qϕ|=ϕ|Q|. This paper proposes an efficient ϵ-approximate k-FANN (k≥1) search algorithm for an arbitrary approximation ratio ϵ (≥1) in road networks. In general, ϵ-approximate algorithms are expected to give an improved search performance at the cost of allowing an error ratio of up to the given ϵ. Since the optimal value of ϵ varies greatly depending on applications and cases, the approximate algorithm for an arbitrary ϵ is essential. We prove that the error ratios of the approximate FANN objects returned by our algorithm do not exceed the given ϵ. To the best of our knowledge, our algorithm is the first ϵ-approximate k-FANN search algorithm in road networks for an arbitrary ϵ. Through a series of experiments using various real-world road network datasets, we demonstrated that our approximate algorithm always outperformed the previous state-of-the-art exact algorithm and that the error ratios of the approximate FANN objects were significantly lower than the given ϵ value.