Showing papers on "Prim's algorithm published in 1981"
TL;DR: A linear time approximation algorithm for the weighted set-covering problem is presented and produces a solution of weight which is at most twice the weight of an optimal solution.
450 citations
TL;DR: An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented and is shown to be as good as the previous O( n4) algorithm in achieving reductions in the ratio SMT/MST of the given vertex set.
Abstract: An O(n log n) heuristic for the Euclidean Steiner Minimal Tree (ESMT) problem is presented. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the Delaunay triangulation, then “recomposes” the suboptimal Steiner Minimal Tree (SMT) according to the Voronoi diagram and Minimum Spanning Tree (MST) of the point set. The ESMT algorithm was implemented in FORTRAN-IV and tested on a number of randomly generated point sets in the plane drawn from a uniform distribution. Comparison of the O(n log n) algorithm with an O(n4) algorithm clearly indicates that the O(n log n) algorithm is as good as the previous O(n4) algorithm in achieving reductions in the ratio SMT/MST of the given vertex set. This is somewhat surprising since the O(n4) algorithm considers more potential Steiner points and alternative tree configurations.
86 citations