论文信息 - Embedding into the rectilinear plane in optimal O(n2) time

Embedding into the rectilinear plane in optimal O(n2) time

In this paper, we present an optimal O(n^2) time algorithm for deciding whether a metric space (X,d) on n points can be isometrically embedded into the plane endowed with the l"1-metric. It improves the O(n^2log^2n) time algorithm of Edmonds (2008) [9]. Together with some ingredients introduced by Edmonds, our algorithm uses the concept of tight span and the injectivity of the l"1-plane. A different O(n^2) time algorithm was recently proposed by Eppstein (2009) [10].

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