@TechReport{Dartmouth:TR2005-538, author = {Robert Scot Drysdale and Clifford Stein and David P. Wagner}, title = {{An O(n^{5/2} log n) Algorithm for the Rectilinear Minimum Link-Distance Problem in Three Dimensions (Extended Abstract)}}, institution = {Dartmouth College, Computer Science}, address = {Hanover, NH}, number = {TR2005-538}, year = {2005}, month = {May}, URL = {http://www.cs.dartmouth.edu/reports/TR2005-538.pdf}, comment = { Submitted to CCCG 2005 }, abstract = { In this paper we consider the Rectilinear Minimum Link-Distance Problem in Three Dimensions. The problem is well studied in two dimensions, but is relatively unexplored in higher dimensions. We solve the problem in O(B n log n) time, where n is the number of corners among all obstacles, and B is the size of a BSP decomposition of the space containing the obstacles. It has been shown that in the worst case B = Theta(n^{3/2}), giving us an overall worst case time of O(n^{5/2} log n). Previously known algorithms have had worst-case running times of Omega(n^3). } }