Abstract
The aim of this work is to study the Simplex Cover (SC) problem, which is to determine whether a given simplex is covered by spheres centered at its vertices. We show that the SC problem is equivalent to a global optimization problem. We investigate its characteristics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aurenhammer F.: Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991). doi:10.1145/116873.116880
Casado L.G., Hendrix E.M.T., García I.: Infeasibility spheres for finding robust solutions of blending problems with quadratic constraints. J. Glob. Optim. 39(2), 215–236 (2007). doi:10.1007/s10898-006-9072-6
Edelsbrunner, H.: The union of balls and its dual shape. In: SCG’93: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp. 218–231, ACM, New York, USA (1993)
Gavrilova, M., Rokne, J.: An efficient algorithm for construction of the power diagram from the voronoi diagram in the plane. Int. J. Comput. Math. 61, 49–61 (1997) http://pages.cpsc.ucalgary.ca/~marina
Hendrix E.M.T., Casado L.G., García I.: The semi-continuous quadratic mixture design problem: description and branch-and-bound approach. Eur. J. Oper. Res. 191(3), 803–815 (2008). doi:10.1016/j.ejor.2007.01.056
Sadri, B.: Surface and medial axis topology through distance flows induced by discrete samples. PhD thesis, University of Illinois, Urbana, Illinois (2006). http://www.cs.duke.edu/~sadri
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work has been funded by grants from the Spanish Ministry of Science and Innovation (TIN2008-01117), Junta de Andalucía (P06-TIC-01426, P08-TIC-3518), in part financed by the European Regional Development Fund (ERDF). Eligius Hendrix is a fellow of the Spanish “Ramon y Cajal” contract program, co-financed by the European Social Fund. B.G.-Tóth was supported by the János Bolyai fellowship of the Hungarian Academy of Sciences.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Casado, L.G., García, I., Tóth, B.G. et al. On determining the cover of a simplex by spheres centered at its vertices. J Glob Optim 50, 645–655 (2011). https://doi.org/10.1007/s10898-010-9524-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-010-9524-x