10.1184/R1/6622361.v1 John Louis Bentley John Louis Bentley Michael I. Shamos Michael I. Shamos Geometric Intersection Problems Carnegie Mellon University 1976 Software Research 1976-01-01 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/Geometric_Intersection_Problems/6622361 We investigate a divide-and-conquer technique in multidimensional space which decomposes a geometric problem on N points in k dimensions into two problems on N/2 points in k dimensions plus a single problem on N points in k-1 dimension. Special structure of the subproblems is exploited to obtain an algorithm for finding the two closest of N points in O(N log N) time in any dimension. Related results are discussed, along with some conjectures and unsolved geometric problems.