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.