Realizing Euclidean distance matrices by sphere intersection

Jorge Alencar; Carlile Lavor; Leo Liberti

doi:10.1016/j.dam.2018.06.003

Realizing Euclidean distance matrices by sphere intersection

Jorge Alencar
, Carlile Lavor
, Leo Liberti

Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais - IFSULDEMINAS
University of Campinas (UNICAMP)

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

Abstract

This paper presents the theoretical properties of an algorithm to find a realization of a (full) n×n Euclidean distance matrix in the smallest possible embedding dimension. Our algorithm performs linearly in n, and quadratically in the minimum embedding dimension, which is an improvement w.r.t. other algorithms.

Original language	English
Pages (from-to)	5-10
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	256
DOIs	https://doi.org/10.1016/j.dam.2018.06.003
Publication status	Published - 15 Mar 2019

Keywords

Distance geometry
Embedding dimension
Euclidean distance matrix
Sphere intersection

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10.1016/j.dam.2018.06.003

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title = "Realizing Euclidean distance matrices by sphere intersection",

abstract = "This paper presents the theoretical properties of an algorithm to find a realization of a (full) n×n Euclidean distance matrix in the smallest possible embedding dimension. Our algorithm performs linearly in n, and quadratically in the minimum embedding dimension, which is an improvement w.r.t. other algorithms.",

keywords = "Distance geometry, Embedding dimension, Euclidean distance matrix, Sphere intersection",

author = "Jorge Alencar and Carlile Lavor and Leo Liberti",

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year = "2019",

month = mar,

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doi = "10.1016/j.dam.2018.06.003",

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AU - Lavor, Carlile

AU - Liberti, Leo

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N2 - This paper presents the theoretical properties of an algorithm to find a realization of a (full) n×n Euclidean distance matrix in the smallest possible embedding dimension. Our algorithm performs linearly in n, and quadratically in the minimum embedding dimension, which is an improvement w.r.t. other algorithms.

AB - This paper presents the theoretical properties of an algorithm to find a realization of a (full) n×n Euclidean distance matrix in the smallest possible embedding dimension. Our algorithm performs linearly in n, and quadratically in the minimum embedding dimension, which is an improvement w.r.t. other algorithms.

KW - Distance geometry

KW - Embedding dimension

KW - Euclidean distance matrix

KW - Sphere intersection

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DO - 10.1016/j.dam.2018.06.003

M3 - Article

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SN - 0166-218X

VL - 256

SP - 5

EP - 10

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Realizing Euclidean distance matrices by sphere intersection

Abstract

Keywords

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