Optimal Path Queries in Very Large Spatial Databases

Abstract

Researchers have been investigating the optimal route query problem for a long time. Optimal route queries are categorized as either unconstrained or constrained queries. Many main memory based algorithms have been developed to deal with the optimal route query problem. Among these, Dijkstra's shortest path algorithm is one of the most popular algorithms for the unconstrained route query problem. The constrained route query problem is more complicated than the unconstrained one, and some constrained route query problems such as the Traveling Salesman Problem and Hamiltonian Path Problem are NP-hard. There are many algorithms dealing with the constrained route query problem, but most of them only solve a specific case. In addition, all of them require that the entire graph resides in the main memory. Recently, due to the need of applications in very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), several disk-based algorithms have been derived by using divide-and-conquer techniques to solve the shortest path problem in a very large graph. However, until now little research has been conducted on the disk-based constrained problem. <br /><br /> This thesis presents two algorithms: 1) a new disk-based shortest path algorithm (DiskSPNN), and 2) a new disk-based optimal path algorithm (DiskOP) that answers an optimal route query without passing a set of forbidden edges in a very large graph. Both algorithms fit within the same divide-and-conquer framework as the existing disk-based shortest path algorithms proposed by Ning Zhang and Heechul Lim. Several techniques, including query super graph, successor fragment and open boundary node pruning are proposed to improve the performance of the previous disk-based shortest path algorithms. Furthermore, these techniques are applied to the DiskOP algorithm with minor changes. The proposed DiskOP algorithm depends on the concept of collecting a set of boundary vertices and simultaneously relaxing their adjacent super edges. Even if the forbidden edges are distributed in all the fragments of a graph, the DiskOP algorithm requires little memory. Our experimental results indicate that the DiskSPNN algorithm performs better than the original ones with respect to the I/O cost as well as the running time, and the DiskOP algorithm successfully solves a specific constrained route query problem in a very large graph.