An O(n^{5/2} log n) Algorithm for the Rectilinear Minimum Link-Distance Problem in Three Dimensions (Extended Abstract)

Authors

Robert Scot Drysdale, Dartmouth CollegeFollow
Clifford Stein, Columbia University
David P. Wagner, Dartmouth College

Document Type

Technical Report

Publication Date

5-1-2005

Technical Report Number

TR2005-538

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).

Comments

Submitted to CCCG 2005

Dartmouth Digital Commons Citation

Drysdale, Robert Scot; Stein, Clifford; and Wagner, David P., "An O(n^{5/2} log n) Algorithm for the Rectilinear Minimum Link-Distance Problem in Three Dimensions (Extended Abstract)" (2005). Computer Science Technical Report TR2005-538. https://digitalcommons.dartmouth.edu/cs_tr/270