Scalable Method for k Optimal Meeting Points (k-OMP) Computation in the Road Network Databases

Given a set of points Q on a road network G = (V,E), an optimal meeting point (OMP) query offers a point on a road network with the smallest sum-of-distances (SoD) to all the points in Q. For example, a travel agency may issue OMP query to decide the location for a tourist bus to pick up the tourists thus minimizing the total travel cost for tourist. The OMP problem has been well studied in the Euclidean space. The currently available algorithms for solving this problem in the context of road networks are still not efficient for the practical applications and are in-memory algorithms which do not guarantee the scalability for the large road databases. Further, the most of the research work has been carried out around the single point OMP; however, the k-OMP problem on the road network setting is still unexplored. In this paper, we are proposing multiple variants of the scalable external-memory based algorithms for computing the optimal meeting point. There are mainly three variants of the proposed grid based algorithms i.e. Basic Grid based, Hierarchical Grid based and Greedy Centroid based OMP search. Later we used single point OMP as a start point to explore the k points OMP using breadth first search. The I/O optimized spatial grids are loaded from the secondary storage as and when required and hence the I/O complexity is reduced to O(N/B) as opposed to O(N) in the existing methods; where B is the average number of road vertices of the grid block. Extensive experiments are conducted on both real and synthetic datasets.