Abstract
Given a set S of n points in the plane, we define a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G = (V; E), where the vertex set V corresponds to points from S and a set of steiner points S′, and the edges in E correspond to horizontal or vertical line segments connecting points in S ∪ S′. A Manhattan network can also be thought of as a 1-spanner (for the L 1-metric) for the points in S.
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