Heuristics for the minimum rectilinear Steiner tree problem: new algorithms and a computational study
نویسندگان
چکیده
منابع مشابه
New algorithms for the rectilinear Steiner tree problem
We discuss a new approach to constructing the rectilinear Steiner tree (RST) of a given set of points in the plane, starting from a minimum spanning tree (MST). The main idea in our approach is to find layouts for the edges of the MST, so as to maximize the overlaps between the layouts, thus minimizing,the cost (i.e., wire length) of the resulting rectilinear Steiner tree. We describe two algor...
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The classical Steiner tree problem requires a shortest tree spanning a given vertex subset within a graph G = (V, E). An important variant is the Steiner tree problem in rectilinear metric. Only recently two algorithms were found which achieve better approximations than the “traditional” one with a factor of 3/2. These algorithms with an approximation ratio of 11/8 are quite slow and run in tim...
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Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. We consider the rectilinear instances of the TSP, i.e. TSP instances where the points lie in the plane and the distance between two points is the l1 distance. We propose a fixed-parameter algorithm for the Rectilinear TSP running in O ( nh7 ...
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The Steiner tree problem is to nd the tree with minimal Euclidean length spanning a set of xed points in the plane, given the ability to add points (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an eecient method for computing a locally optimal tree with a given topology. The rst systematically inserts S...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1993
ISSN: 0166-218X
DOI: 10.1016/0166-218x(93)90010-l