New Lower Bounds for Hopcroft's Problem (Extended Abstract)

We establish new lower bounds on the complexity of the following basic geometric problem, attributed to John Hopcroft: Given a set of n points and m hyperplanes in JR.d, is any point cent ained in any hyperplane? We define a general class of partitioning algorithms, and show that in the worst case, for all m and n, any such algorithm requires time Q(n log m… CONTINUE READING