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A new algorithm for rectilinear Steiner trees (RST) is presented. The proposed algorithm is based on successively constructing a vicinity structure from a rectilinear minimum spanning tree (MST) and generating a refined RST. The algorithm achieves an 8.5-10% average cost improvement over the rectilinear MST at a time complexity of O(n log n). To address specifically the linear programming approach of global routing the algorithm is modified to generate K trees.