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Given a set S of n points, a weight function w to associate a non-negative weight to each point in S, a positive integer k ≥1, and a real number ϵ> 0, we present algorithms for computing a spanner network G(S, E) for the metric space (S, d_w) induced by the weighted points in S. The weighted distance function d_w on the set S of points is defined as follows: for any p, q ∈S, d_w(p, q) is equal to w(p) + d_π(p, q) + w(q) if p q, otherwise, d_w(p, q) is 0. Here, d_π(p, q) is the EuclideanarXiv:2011.03354v1 fatcat:bjmwwrc42vcbvaon5rowr7vjy4