Journal ArticleDOI
Fast heuristic algorithms for rectilinear steiner trees
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An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques, and an extensive review of proposed heuristics is given.Abstract:
A fundamental problem in circuit design is how to connectn points in the plane, to make them electrically common using the least amount of wire. The tree formed, a Steiner tree, is usually constructed with respect to the rectilinear metric. The problem is known to be NP-complete; an extensive review of proposed heuristics is given. An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques. The algorithm can be modified to do sequential searching inO(n2) total time. However, it is shown that the latter approach runs inO(n3/2) expected time, forn points selected from anm×m grid. Empirical results are presented for problems up to 10,000 points.read more
Citations
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Journal ArticleDOI
Steiner tree problems
Frank K. Hwang,Dana Richards +1 more
TL;DR: A survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations.
Journal ArticleDOI
A new class of iterative Steiner tree heuristics with good performance
Andrew B. Kahng,Gabriel Robins +1 more
TL;DR: The method yields results that reduce wire length by up to 2% to 3% over the previous methods, and is the first heuristic which has been shown to have a performance ratio less than 3/2.
Journal ArticleDOI
Hierarchical Steiner tree construction in uniform orientations
Majid Sarrafzadeh,C.K. Wong +1 more
TL;DR: A hierarchical approach to Steiner tree construction in lambda -geometry is proposed and it is shown that given enough time, an optimal Steiners tree will be obtained.
Journal ArticleDOI
A heuristic for Euclidean and rectilinear Steiner problems
TL;DR: In this article, a heuristic for Euclidean and rectilinear Steiner problems is presented based on finding optimal Steiner solutions for connected subgraphs of the minimal spanning tree of the entire vertex set.
Proceedings ArticleDOI
A new class of Steiner tree heuristics with good performance: the iterated 1-Steiner approach
Andrew B. Kahng,Gabriel Robins +1 more
TL;DR: The authors iteratively find optimal Steiner points to be added to the layout of the rectilinear Steiner tree problem and give improved average-case performance, and also avoids the worst-case examples of existing approaches.
References
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Book
Data Structures and Network Algorithms
TL;DR: This paper presents a meta-trees tree model that automates the very labor-intensive and therefore time-heavy and therefore expensive process of manually selecting trees to grow in a graph.
Journal ArticleDOI
A fast algorithm for Steiner trees
TL;DR: The heuristic algorithm has a worst case time complexity of O(¦S¦¦V¦2) on a random access computer and it guarantees to output a tree that spans S with total distance on its edges no more than 2(1−1/l) times that of the optimal tree.
Journal ArticleDOI
Steiner Minimal Trees
E. N. Gilbert,H. O. Pollak +1 more
TL;DR: A Steiner minimal tree for given points in the plane is a tree which interconnects these points using lines of shortest possible total length as mentioned in this paper, where the length of the shortest possible line is chosen.
Journal Article
An approximate solution for the Steiner problem in graphs
H Takahashi,Matsuyama A +1 more
Journal ArticleDOI
On the History of the Minimum Spanning Tree Problem
Ron Graham,Pavol Hell +1 more
TL;DR: There are several apparently independent sources and algorithmic solutions of the minimum spanning tree problem and their motivations, and they have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century.