Algorithms for Processing of Spatial Queries using R-trees. The Closest Pairs Query and its Application on Spatial Databases

This thesis addresses the problem of finding the K closest pairs between two spatial datasets (the so-called, K Closest Pairs Query, K-CPQ), where each set is stored in an index structure belonging in the R-tree family. There are two different techniques for solving this kind of distance-based query. The first is the incremental approach [HjS98, SML00], which computes the operation in the sense that the result elements are reported one-by-one in ascending order of distance. The second is the non-incremental alternative that we present in this thesis, which computes the operation reporting the K elements of the result all together at the end of the algorithm. Branch-and-bound has been the most successful technique for the design of algorithms that obtain the result of queries over tree-like structures. In this thesis, a general branch-and-bound algorithmic schema for obtaining the K optimal solutions of a given problem is proposed. Moreover, based on distance functions between two MBRs in the multidimensional Euclidean space, we propose a pruning heuristic and two updating strategies for minimizing the pruning distance, in order to use them in the design of three nonincremental branch-and-bound algorithms for K-CPQ between spatial objects stored in two Rtrees. Two of those approaches are recursive, following a Depth-First searching strategy and one is iterative, obeying a Best-First traversal policy. The plane-sweep method and the search ordering are used as optimization techniques for improving the naive approaches. Besides, a number of interesting extensions of the K-CPQ (K-Self-CPQ, Semi-CPQ, K-FPQ (the K Farthest Pairs Query), etc.) are discussed. An extensive performance study is also presented. This study is based on experiments performed with real spatial datasets. A wide range of values for the basic parameters affecting the performance of the algorithms is examined. The outcome of these studies is the designation of the algorithm that wins the performance award for each setting of parameter values. An experimental study of the behavior of the proposed K-CPQ branch-and-bound algorithms in terms of scalability of the dataset sizes and the value of K is also included. Finally, our non-incremental algorithms have been adapted to perform the simulation of the incremental closest pairs query.