An algorithm for realizing Euclidean distance matrices

Jorge Alencar; Tibérius Bonates; Carlile Lavor; Leo Liberti

doi:10.1016/j.endm.2015.07.066

An algorithm for realizing Euclidean distance matrices

Jorge Alencar, Tibérius Bonates, Carlile Lavor, Leo Liberti

Research output: Contribution to journal › Article › peer-review

Abstract

We present an efficient algorithm to find a realization of a (full) n×. n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worst-case running time. Our algorithm performs cubically in n (and linearly when the dimension is fixed, which happens in most applications).

Original language	English
Pages (from-to)	397-402
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	50
DOIs	https://doi.org/10.1016/j.endm.2015.07.066
Publication status	Published - 1 Dec 2015

Keywords

Distance geometry
EDM
Embedding dimension
Sphere interesection

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10.1016/j.endm.2015.07.066

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abstract = "We present an efficient algorithm to find a realization of a (full) n×. n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worst-case running time. Our algorithm performs cubically in n (and linearly when the dimension is fixed, which happens in most applications).",

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AU - Alencar, Jorge

AU - Bonates, Tibérius

AU - Lavor, Carlile

AU - Liberti, Leo

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We present an efficient algorithm to find a realization of a (full) n×. n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worst-case running time. Our algorithm performs cubically in n (and linearly when the dimension is fixed, which happens in most applications).

AB - We present an efficient algorithm to find a realization of a (full) n×. n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worst-case running time. Our algorithm performs cubically in n (and linearly when the dimension is fixed, which happens in most applications).

KW - Distance geometry

KW - EDM

KW - Embedding dimension

KW - Sphere interesection

U2 - 10.1016/j.endm.2015.07.066

DO - 10.1016/j.endm.2015.07.066

M3 - Article

AN - SCOPUS:84953399278

SN - 1571-0653

VL - 50

SP - 397

EP - 402

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

An algorithm for realizing Euclidean distance matrices

Abstract

Keywords

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