Ring-constrained join: Deriving fair middleman locations from pointsets via a geometric constraint

Abstract

We introduce a novel spatial join operator, the ring-constrained join (RCJ). Given two sets P and Q of spatial points, the result of RCJ consists of pairs 〈p, q〉 (where p εP, q ε Q) satisfying an intuitive geometric constraint: the smallest circle enclosing p and q contains no other points in P, Q. This new operation has important applications in decision support, e.g., placing recycling stations at fair locations between restaurants and residential complexes. Clearly, RCJ is defined based on a geometric constraint but not on distances between points. Thus, our operation is fundamentally different from the conventional distance joins and closest pairs problems. We are not aware of efficient processing algorithms for RCJ in the literature. A brute-force solution requires computational cost quadratic to input size and it does not scale well for large datasets. In view of this, we develop efficient R-tree based algorithms for computing RCJ, by exploiting the characteristics of the geometric constraint. We evaluate experimentally the efficiency of our methods on synthetic and real spatial datasets. The results show that our proposed algorithms scale well with the data size and have robust performance across different data distributions. Copyright 2008 ACM.