Optimal binary space partitions for orthogonal objects
Journal of Algorithms
Rectilinear paths among rectilinear obstacles
Discrete Applied Mathematics
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
IEEE Transactions on Computers
Binary Space Partitions for Axis-Parallel Segments, Rectangles, and Hyperrectangles
Discrete & Computational Geometry
Computing a shortest k-link path in a polygon
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Faster algorithms for minimum-link paths with restricted orientations
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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In this paper we consider the Rectilinear Minimum Link Path Problem among rectilinear obstacles in three dimensions. The problem is well studied in two dimensions, but is relatively unexplored in higher dimensions. We solve the problem in O(@bnlogn) time, where n is the number of corners among all obstacles, and @b is the size of a binary space partition (BSP) decomposition of the space containing the obstacles. There exist methods to find a BSP where in the worst-case @b=@Q(n^3^/^2), giving us an overall worst-case time of O(n^5^/^2logn). Previously known algorithms have had worst-case running times of @W(n^3).