On Steiner tree problem with 45° routing

Author

Lee, D.T. ; Shen, Chin-Fang ; Ding, Cheng-Liang

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Northwestern Univ., Evanston, IL, USA

Volume

3

fYear

1995

fDate

30 Apr-3 May 1995

Firstpage

1680

Abstract

We consider Steiner minimal trees (SMT) in the plane where the orientations of interconnection are restricted to be either horizontal, vertical or of slopes +1 and -1. We derive a ratio, 1/4-2√2 which we conjecture to be the Steiner ratio for 45°-SMT. We provide a method to find an optimal 45°-SMT for 3 or 4 points by analyzing its topological connections. For arbitrary point set of size n we present an O(n log n) time heuristic based on the notions of 45° minimum spanning tree and Delaunay triangulation. Empirical results compared with the rectilinear and Euclinear cases are given

Keywords

circuit layout; computational geometry; mesh generation; network routing; network topology; trees (mathematics); 45° routing; Delaunay triangulation; Steiner minimal trees; Steiner tree problem; interconnection orientations; minimum spanning tree; topological connections; Crosstalk; Geometry; Manufacturing; Routing; Steiner trees; Surface-mount technology; Vectors; Very large scale integration; Visualization; Wires;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1995. ISCAS '95., 1995 IEEE International Symposium on

Conference_Location

Seattle, WA

Print_ISBN

0-7803-2570-2

Type

conf

DOI

10.1109/ISCAS.1995.523734

Filename

523734