A clustering-based algorithm for the rectilinear steiner tree problem

Abstract

The Steiner Tree Problem is the determination of the shortest connecting length between a given set of points and additional points. The Rectilinear Steiner Tree Problem is the same as above but the connecting lines are confined to the horizontal or vertical lines only (L₁ metric). A cluster is a set of points that influence each other locally. This research gives a new algorithm based on a clustering metric that determines much less steiner points locally in a cluster as well as those external to it. The algorithm matches the worst-case time complexity of O(nlogn) of previous authors while giving better average results then theirs. In addition a Neural Solution to the Steiner problem in Networks, which is a graph-theoretic representation of the problem, is explored and its limitations presented.