Optimal Rectilinear Steiner Minimal Trees in O (n22.62n) Time
نویسندگان
چکیده
This paper presents an algorithm that computes an optimal rectilinear Steiner minimal tree of n points in at most O(n 2 2:62 n) time. For instances small enough to solve in practice, this time bound is provably faster than any previous algorithm, and improves the previous best bound for practically solvable instances, which is O(n3 n). Experimental evidence is also presented that demonstrates that the algorithm is fast in practice as well|much faster, in fact, than its worst-case time complexity suggests. As part of the analysis, it is proven that the number of full sets on a set of n terminals is at most O(n1:62 n).
منابع مشابه
The Steiner tree problem for terminals on the boundary of a rectilinear polygon
Given a simple rectilinear polygon P with k sides and n terminals on its boundary, we present an O(k 3 n)-time algorithm to compute the minimal rectilinear Steiner tree lying inside P interconnecting the terminals. We obtain our result by proving structural properties of a selective set of minimal Steiner trees and exploiting them in a dynamic programming algorithm.
متن کاملA Fast Algorithm for Computing Optimal Rectilinear Steiner Trees for Extremal Point Sets1
We present an eecient algorithm to compute an optimal rectilinear Steiner tree for extremal point sets. A point set is extremal if every point in it lies on the boundary of a rectilinear convex hull of the point set. Our algorithm can be used to construct minimum-length connection for multi-terminal nets in homotopic routing in VLSI layout design. The previous best algorithms run in O(k 4 n) ti...
متن کاملA new exact algorithm for rectilinear Steiner trees
Given a nite set V of points in the plane (called terminals), the rectilinear Steiner minimal tree is a shortest network of horizontal and vertical lines connecting all the terminals of V. The decision form of this problem has been shown to be NP-complete 8]. A new algorithm is presented that computes provably optimal Steiner trees using the \FST concatenation" approach. In the \FST generation"...
متن کاملThumbnail Rectilinear Steiner Trees - VLSI, 1995. Proceedings., Fifth Great Lakes Symposium on
The rectilinear Steiner tree problem i s t o find a manimum-length set of horizontal and vertical line segments that interconnect a given set of points in $he plane. Here we study the thumbnail rectilinear S te iner tree problem, where the inpvt points are drawn f r o m a small integer grid. Specifically, we devise a full-set decomposition algorithm for computing opt ima l thumbnail rectalinear...
متن کاملRectilinear Steiner Tree Minimization on a Workstation
We describe a series of optimizations to Dreyfus and Wagner's dynamic program for nding a Steiner minimal tree on a graph. Our interest is in nding rectilinear Steiner minimal trees on k pins, for which the Dreyfus and Wagner algorithm runs in O(k 2 3 k) time. The original, unoptimized, code was hopelessly I/O-bound for k > 17, even on a workstation with 16 megabytes of main memory. Our optimiz...
متن کامل