@inproceedings{3065b9e0f88d4901b6ff8d11828bb4be,
title = "Distance geometry on the sphere",
abstract = "The Distance Geometry Problem asks whether a given weighted graph has a realization in a target Euclidean space ℝK which ensures that the Euclidean distance between two realized vertices incident to a same edge is equal to the given edge weight. In this paper we look at the setting where the target space is the surface of the sphere SK−1. We show that the Distance Geometry Problem is almost the same in this setting, as long as the distances are Euclidean. We then generalize a theorem of G{\"o}del about the case where the distances are spherical geodesics, and discuss a method for realizing cliques geodesically on a K-dimensional sphere.",
author = "Leo Liberti and Grzegorz Swirszcz and Carlile Lavor",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2016.; 18th Japan Conference on Discrete and Computational Geometry and Graphs, JCDCGG 2015 ; Conference date: 14-09-2015 Through 16-09-2015",
year = "2016",
month = jan,
day = "1",
doi = "10.1007/978-3-319-48532-4\_18",
language = "English",
isbn = "9783319485317",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "204--215",
editor = "Toshinori Sakai and Hiro Ito and Jin Akiyama",
booktitle = "Discrete and Computational Geometry and Graphs - 18th Japan Conference, JCDCGG 2015, Revised Selected Papers",
}