Embedding into the rectilinear plane in optimal O*(n^2)
Computational Geometry
2011-07-08 v1 Data Structures and Algorithms
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).
Cite
@article{arxiv.0910.1059,
title = {Embedding into the rectilinear plane in optimal O*(n^2)},
author = {Nicolas Catusse and Victor Chepoi and Yann Vaxès},
journal= {arXiv preprint arXiv:0910.1059},
year = {2011}
}
Comments
12 pages, 13 figures