On the basic properties and the structure of power cells

Elisabetta Allevi; Juan Enrique Martínez Legaz; R. Riccardi

doi:10.1007/s10957-024-02435-0

On the basic properties and the structure of power cells

Elisabetta Allevi, Juan Enrique Martínez Legaz, R. Riccardi

Department of Economics and Economic History

University of Brescia

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

Abstract

Given a set T⊆R ⁿ and a nonnegative function r defined on T, we consider the power of x∈R ⁿ with respect to the sphere with center t∈T and radius rt, that is, p _rx,t:=x-t ²-r ²t, with · denoting the Euclidean distance. The corresponding power cell of s∈T is the set (Formula presented.) We study the structure of such cells and investigate the assumptions on r that allow for generalizing known results on classical Voronoi cells.

Original language	English
Pages (from-to)	1246-1262
Number of pages	17
Journal	Journal of Optimization Theory and Applications
Volume	203
DOIs	https://doi.org/10.1007/s10957-024-02435-0
Publication status	Published - 15 May 2024

Keywords

51M20
52A20
52B11
52C22
Power cell
Structure of power cells
Voronoi diagram

Access to Document

10.1007/s10957-024-02435-0Licence: CC BY

https://ddd.uab.cat/record/293059Licence: CC BY

Cite this

@article{0c7e8de33e914573b3fb503d4dc12f17,

title = "On the basic properties and the structure of power cells",

abstract = "Given a set T⊆R n and a nonnegative function r defined on T, we consider the power of x∈R n with respect to the sphere with center t∈T and radius rt, that is, p rx,t:=x-t 2-r 2t, with · denoting the Euclidean distance. The corresponding power cell of s∈T is the set (Formula presented.) We study the structure of such cells and investigate the assumptions on r that allow for generalizing known results on classical Voronoi cells.",

keywords = "51M20, 52A20, 52B11, 52C22, Power cell, Structure of power cells, Voronoi diagram",

author = "Elisabetta Allevi and \{Mart{\'i}nez Legaz\}, \{Juan Enrique\} and R. Riccardi",

year = "2024",

month = may,

day = "15",

doi = "10.1007/s10957-024-02435-0",

language = "English",

volume = "203",

pages = "1246--1262",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

}

TY - JOUR

T1 - On the basic properties and the structure of power cells

AU - Allevi, Elisabetta

AU - Martínez Legaz, Juan Enrique

AU - Riccardi, R.

PY - 2024/5/15

Y1 - 2024/5/15

N2 - Given a set T⊆R n and a nonnegative function r defined on T, we consider the power of x∈R n with respect to the sphere with center t∈T and radius rt, that is, p rx,t:=x-t 2-r 2t, with · denoting the Euclidean distance. The corresponding power cell of s∈T is the set (Formula presented.) We study the structure of such cells and investigate the assumptions on r that allow for generalizing known results on classical Voronoi cells.

AB - Given a set T⊆R n and a nonnegative function r defined on T, we consider the power of x∈R n with respect to the sphere with center t∈T and radius rt, that is, p rx,t:=x-t 2-r 2t, with · denoting the Euclidean distance. The corresponding power cell of s∈T is the set (Formula presented.) We study the structure of such cells and investigate the assumptions on r that allow for generalizing known results on classical Voronoi cells.

KW - 51M20

KW - 52A20

KW - 52B11

KW - 52C22

KW - Power cell

KW - Structure of power cells

KW - Voronoi diagram

UR - https://www.scopus.com/pages/publications/85193077454

UR - https://www.mendeley.com/catalogue/cad86d03-9e6e-32bc-9642-fcaffe2060bc/

UR - https://portalrecerca.uab.cat/en/publications/0c7e8de3-3e91-4573-b3fb-503d4dc12f17

U2 - 10.1007/s10957-024-02435-0

DO - 10.1007/s10957-024-02435-0

M3 - Article

SN - 0022-3239

VL - 203

SP - 1246

EP - 1262

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

ER -

On the basic properties and the structure of power cells

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this