Computational geometry: an introduction
Computational geometry: an introduction
Skip lists: a probabilistic alternative to balanced trees
Communications of the ACM
Introduction to algorithms
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
Finding obstacle-avoiding shortest paths using implicit connection graphs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Highly scalable algorithms for rectilinear and octilinear Steiner trees
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
FOARS: FLUTE based obstacle-avoiding rectilinear steiner tree construction
Proceedings of the 19th international symposium on Physical design
Proceedings of the 16th Asia and South Pacific Design Automation Conference
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Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least ω(n2) time. More efficient approaches find a minimum spanning tree only among edges in the Delaunay triangulation of the points. However, Delaunay triangulation is not well defined in rectilinear distance. In this paper, we first establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural definition and not necessarily a Delaunay triangulation. Based on this framework, we then design an O(n log n) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay triangulation.