An optimal Steiner tree algorithm for a net whose terminals lie onthe perimeter of a rectangle
Cohoon, J.P.
Richards, D.S.
Salowe, J.S.
Dept. of Comput. Sci., Virginia Univ., Charlottesville, VA;
Abstract
Given a set of input points, the rectilinear Steiner tree problem
is to find a minimal-length tree consisting of vertical and horizontal
line segments that connects the input points, where it is possible to
add new points to minimize the length of the tree. The restricted
Steiner tree problem in which all the input points lie on the boundary
of a rectangle frequently occurs in VLSI physical design. Since the
fastest published algorithm is cubic in the size of the point set, VLSI
designers have been forced to use heuristic approximations to the length
of the Steiner tree for this problem. A simple, practical, linear-time
exact algorithm for finding the Steiner tree for points lying on the
boundary of a rectangle which obviates the need for some heuristic
algorithms in VLSI design is presented. The analysis of the algorithm is
based on the use of a tie-breaking rule that should prove useful for
other Steiner tree problems
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