Embedding into the rectilinear plane in optimal O*(n2)
Abstract
We present an optimal O*(n2) time algorithm for deciding if a metric space (X,d) on n points can be isometrically embedded into the plane endowed with the l1-metric. It improves the O*(n2 log2 n) time algorithm of J. Edmonds (2008). Together with some ingredients introduced by J. Edmonds, our algorithm uses the concept of tight span and the injectivity of the l1-plane. A different O*(n2) time algorithm was recently proposed by D. Eppstein (2009).
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