Common Influence Join: A Natural Join Operation for Spatial Pointsets

We identify and formalize a novel join operator for two spatial pointsets P and Q. The common influence join (CIJ) returns the pairs of points (p,q),p isin P,q isin Q, such that there exists a location in space, being closer to p than to any other point in P and at the same time closer to q than to any other point in Q. In contrast to existing join operators between pointsets (i.e., e-distance joins and fc-closest pairs), CIJ is parameter- free, providing a natural join result that finds application in marketing and decision support. We propose algorithms for the efficient evaluation of CIJ, for pointsets indexed by hierarchical multi-dimensional indexes. We validate the effectiveness and the efficiency of these methods via experimentation with synthetic and real spatial datasets. The experimental results show that a non-blocking algorithm, which computes intersecting pairs of Voronoi cells on-demand, is very efficient in practice, incurring only slightly higher I/O cost than the theoretical lower bound cost for the problem.