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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).

Note: Submitted to CCCG 2005

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   Robert Scot Drysdale, Clifford Stein, and David P. Wagner, "An O(n^{5/2} log n) Algorithm for the Rectilinear Minimum Link-Distance Problem in Three Dimensions (Extended Abstract)." Dartmouth Computer Science Technical Report TR2005-538, May 2005.

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