Linear Separability in Spatial Databases

Abstract

Given two point sets $R$ and $B$ in the plane, with cardinalities $m$ and $n$, respectively, and each set stored in a separate R-tree, we present an algorithm to decide whether $R$ and $B$ are linearly separable. Our algorithm exploits the structure of the R-trees, loading into the main memory only relevant data, and runs in $O(m\log m + n\log n)$ time in the worst case. As experimental results, we implement the proposed algorithm and executed it on several real and synthetic point sets, showing that the percentage of nodes of the R-trees that are accessed and the memory usage are low in these cases. We also present an algorithm to compute the convex hull of $n$ planar points given in an R-tree, running in $O(n\log n)$ time in the worst case.