Estimations of Covering Functionals of Convex Bodies Based on Relaxation Algorithm

Man Yu, Yafang Lv, Yanping Zhao, Chan He and Senlin Wu ()
Additional contact information
Man Yu: School of Mathematics, North University of China, Taiyuan 030051, China
Yafang Lv: School of Navigation, Wuhan University of Technology, Wuhan 430063, China
Yanping Zhao: School of Mathematics, North University of China, Taiyuan 030051, China
Chan He: School of Mathematics, North University of China, Taiyuan 030051, China
Senlin Wu: School of Mathematics, North University of China, Taiyuan 030051, China

Mathematics, 2023, vol. 11, issue 9, 1-15

Abstract: Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a long-standing open problem from convex and discrete geometry. In this paper, we transform this problem into a vertex p -center problem (VPCP). An exact iterative algorithm is introduced to solve the VPCP by making adjustments to the relaxation-based algorithm mentioned by Chen and Chen in 2009. The accuracy of this algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean disc, simplices, and the regular octahedron. A better lower bound of the covering functional with respect to 7 of 3-simplices is presented.

Keywords: Hadwiger’s covering problem; covering functional; vertex p-center problem; relaxation algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/9/2000/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/9/2000/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:9:p:2000-:d:1130925

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().