Efficient Nearest-Neighbor Query and Clustering of Planar Curves

Boris Aronov, Omrit Filtser, Michael Horton, Matthew J. Katz, Khadijeh Sheikhan

Abstract: We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let \(\mathcal {C}\) be a set of n polygonal curves, each of size m. In the nearest-neighbor problem, the goal is to construct a compact data structure over \(\mathcal {C}\), such that, given a query curve Q, one can efficiently find the curve in \(\mathcal {C}\) closest to Q. In the center problem, the goal is to find a curve Q, such that the maximum distance between Q and the curves in \(\mathcal {C}\) is minimized. We use the well-known discrete Fréchet distance function, both under \(L_\infty \) and under \(L_2\), to measure the distance between two curves.