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Rectilinear steiner trees: Efficient special‐case algorithms
Author(s) -
Aho A. V.,
Garey M. R.,
Hwang F. K.
Publication year - 1977
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230070104
Subject(s) - steiner tree problem , rectangle , mathematics , degree (music) , algorithm , boundary (topology) , combinatorics , tree (set theory) , set (abstract data type) , time complexity , plane (geometry) , computer science , discrete mathematics , geometry , mathematical analysis , programming language , physics , acoustics
A minimal rectilinear Steiner tree for a set A of points in the plane is a tree which interconnects A using horizontal and vertical lines of shortest possible total length. Such trees have potential application to wire layout for printed circuits. Unfortunately, at present no practical algorithm is known for constructing these trees in general. We present two algorithms, each requiring a number of operations proportional to only a low degree polynomial in the number of points to be interconnected, for the special cases in which all the points of A lie on a small number of parallel lines or on the boundary of a rectangle.