Efficient MapReduce computation of topological relations for big geometries

The increasing amount of available spatial data leads to the development and spread of big data systems specifically tailored for the management and process of such kind of information. These systems usually apply a MapReduce paradigm which essentially computes the same operation on different chunks of independent data in parallel. Even if this solution fits well in most cases where the extension and complexity of each single spatial object is small w.r.t. the extension and complexity of the overall dataset, some problems arise when a dataset is composed of only few objects, each one with a great extension and complexity in terms of number of vertices. This problem is exacerbated during the computation of a spatial join or in general of topological relations. As already discussed in literature, a viable solution for this problem consists in subdividing the big and complex geometries into smaller and simpler ones before applying the MapReduce operations. This paper takes a step forward in this direction by examining how the topological relations computed on the parts can be efficiently recombined to obtain the topological relation between the two original objects.