Efficient minimum spanning tree construction without Delaunay triangulation

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 (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(nlogn) sweep-line algorithm to construct a rectilinear minimum spanning tree without using Delaunay triangulation. 2002 Elsevier Science B.V. All rights reserved.

• Type: Conference
• Year: 2001
• Where: ASPDAC
• Authors: Hai Zhou, Narendra V. Shenoy, William Nicholls
• Keywords: ASPDAC 2001, Delaunay Triangulation, Hardware, Minimum Spanning Tree, Minimum Total Length