Abstract

Given a set of n colored points in some d-dimensional Euclidean space, a bichromatic closest (resp. farthest) pair is a closest (resp. farthest) pair of points of dierent colors. We present ecient algorithms to maintain both a bichromatic closest pair and a bichromatic farthest pair when the the points are xed but they dynamically change color. We do this by solving the more general problem of maintaining a bichromatic edge of minimum (resp. maximum) weight in an undirected weighted graph with colored vertices, when vertices dynamically change color.

Citations