Embedding into the rectilinear plane in optimal O*(n^2)

Abstract : We present an optimal O*(n^2) time algorithm for deciding if 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^2 log^2 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 l_1-plane. A different O*(n^2) time algorithm was recently proposed by D. Eppstein (2009).
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Contributor : Nicolas Catusse <>
Submitted on : Wednesday, February 19, 2014 - 11:33:42 AM
Last modification on : Friday, April 12, 2019 - 10:18:03 AM

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Nicolas Catusse, Victor Chepoi, Yann Vaxès. Embedding into the rectilinear plane in optimal O*(n^2). Theoretical Computer Science, Elsevier, 2011, 412 (22), pp.2425-2433. ⟨10.1016/j.tcs.2011.01.038⟩. ⟨hal-00949183⟩

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