α-Probabilistic flexible aggregate nearest neighbor search in road networks using landmark multidimensional scaling

In spatial database and road network applications, the search for the nearest neighbor (NN) from a given query object q is the most fundamental and important problem. Aggregate nearest neighbor (ANN) search is an extension of the NN search with a set of query objects $$Q = \{ q_0, \dots , q_{M-1} \}$$ Q = { q 0 , ⋯ , q M - 1 } and finds the object $$p^*$$ p ∗ that minimizes $$g \{ d(p^*, q_i), q_i \in Q \}$$ g { d ( p ∗ , q i ) , q i ∈ Q } , where g (max or sum) is an aggregate function and d() is a distance function between two objects. Flexible aggregate nearest neighbor (FANN) search is an extension of the ANN search with the introduction of a flexibility factor $$\phi \, (0 < \phi \le 1)$$ ϕ ( 0 < ϕ ≤ 1 ) and finds the object $$p^*$$ p ∗ and the set of query objects $$Q^*_\phi $$ Q ϕ ∗ that minimize $$g \{ d(p^*, q_i), q_i \in Q^*_\phi \}$$ g { d ( p ∗ , q i ) , q i ∈ Q ϕ ∗ } , where $$Q^*_\phi $$ Q ϕ ∗ can be any subset of Q of size $$\phi |Q|$$ ϕ | Q | . This study proposes an efficient $$\alpha $$ α -probabilistic FANN search algorithm in road networks. The state-of-the-art FANN search algorithm in road networks, which is known as IER-$$k\hbox {NN}$$ k NN , used the Euclidean distance based on the two-dimensional coordinates of objects when choosing an R-tree node that most potentially contains $$p^*$$ p ∗ . However, since the Euclidean distance is significantly different from the actual shortest-path distance between objects, IER-$$k\hbox {NN}$$ k NN looks up many unnecessary nodes, thereby incurring many calculations of ‘expensive’ shortest-path distances and eventually performance degradation. The proposed algorithm transforms road network objects into k-dimensional Euclidean space objects while preserving the distances between them as much as possible using landmark multidimensional scaling (LMDS). Since the Euclidean distance after LMDS transformation is very close to the shortest-path distance, the lookup of unnecessary R-tree nodes and the calculation of expensive shortest-path distances are reduced significantly, thereby greatly improving the search performance. As a result of performance comparison experiments conducted for various real road networks and parameters, the proposed algorithm always achieved higher performance than IER-$$k\hbox {NN}$$ k NN ; the performance (execution time) of the proposed algorithm was improved by up to 10.87 times without loss of accuracy.

On Top-k Weighted Sum Aggregate Nearest and Farthest Neighbors in the L1 Plane

In this paper, we study top-[Formula: see text] aggregate (or group) nearest neighbor queries using the weighted Sum operator under the [Formula: see text] metric in the plane. Given a set [Formula: see text] of [Formula: see text] points, for any query consisting of a set [Formula: see text] of [Formula: see text] weighted points and an integer [Formula: see text], [Formula: see text], the top-[Formula: see text] aggregate nearest neighbor query asks for the [Formula: see text] points of [Formula: see text] whose aggregate distances to [Formula: see text] are the smallest, where the aggregate distance of each point [Formula: see text] of [Formula: see text] to [Formula: see text] is the sum of the weighted distances from [Formula: see text] to all points of [Formula: see text]. We build an [Formula: see text]-size data structure in [Formula: see text] time, such that each top-[Formula: see text] query can be answered in [Formula: see text] time. We also obtain other results with trade-off between preprocessing and query. Even for the special case where [Formula: see text], our results are better than the previously best work, which requires [Formula: see text] preprocessing time, [Formula: see text] space, and [Formula: see text] query time. In addition, for the one-dimensional version of this problem, our approach can build an [Formula: see text]-size data structure in [Formula: see text] time that can support [Formula: see text] time queries. Further, we extend our techniques to answer the top-[Formula: see text] aggregate farthest neighbor queries, with the same bounds.

A Trajectory Privacy Preserving Scheme in the CANNQ Service for IoT

Nowadays, anyone carrying a mobile device can enjoy the various location-based services provided by the Internet of Things (IoT). ‘Aggregate nearest neighbor query’ is a new type of location-based query which asks the question, ‘what is the best location for a given group of people to gather?’ There are numerous, promising applications for this type of query, but it needs to be done in a secure and private way. Therefore, a trajectory privacy-preserving scheme, based on a trusted anonymous server (TAS) is proposed. Specifically, in the snapshot queries, the TAS generates a group request that satisfies the spatial K-anonymity for the group of users—to prevent the location-based service provider (LSP) from an inference attack—and in continuous queries, the TAS determines whether the group request needs to be resent by detecting whether the users will leave their secure areas, so as to reduce the probability that the LSP reconstructs the users’ real trajectories. Furthermore, an aggregate nearest neighbor query algorithm based on strategy optimization, is adopted, to minimize the overhead of the LSP. The response speed of the results is improved by narrowing the search scope of the points of interest (POIs) and speeding up the prune of the non-nearest neighbors. The security analysis and simulation results demonstrated that our proposed scheme could protect the users’ location and trajectory privacy, and the response speed and communication overhead of the service, were superior to other peer algorithms, both in the snapshot and continuous queries.