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 , ⋯ , q M - 1 } and finds the object p ∗ that minimizes 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 ϕ ( 0 < ϕ ≤ 1 ) and finds the object p ∗ and the set of query objects Q ϕ ∗ that minimize g { d ( p ∗ , q i ) , q i ∈ Q ϕ ∗ } , where Q ϕ ∗ can be any subset of Q of size ϕ | Q | . This study proposes an efficient 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 NN , used the Euclidean distance based on the two-dimensional coordinates of objects when choosing an R-tree node that most potentially contains p ∗ . However, since the Euclidean distance is significantly different from the actual shortest-path distance between objects, IER- 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 NN ; the performance (execution time) of the proposed algorithm was improved by up to 10.87 times without loss of accuracy.