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The corresponding power cell of $$s\\in T$$<\/jats:tex-math>\n \n s<\/mml:mi>\n \u2208<\/mml:mo>\n T<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is the set $$\\begin{aligned} C_{T}^{r}(s):=\\{x\\in {\\mathbb {R}}^{n}:{ p_r}(x,s)\\le {p_r}(x,t),\\ \\text{ for } \\text{ all }\\ t\\in T\\}. \\end{aligned}$$<\/jats:tex-math>\n \n \n \n \n \n \n C<\/mml:mi>\n \n T<\/mml:mi>\n <\/mml:mrow>\n r<\/mml:mi>\n <\/mml:msubsup>\n \n (<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n :<\/mml:mo>\n =<\/mml:mo>\n \n {<\/mml:mo>\n x<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n R<\/mml:mi>\n <\/mml:mrow>\n n<\/mml:mi>\n <\/mml:msup>\n :<\/mml:mo>\n \n p<\/mml:mi>\n r<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2264<\/mml:mo>\n \n p<\/mml:mi>\n r<\/mml:mi>\n <\/mml:msub>\n \n (<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n t<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n ,<\/mml:mo>\n \n \n for<\/mml:mtext>\n \n \n all<\/mml:mtext>\n \n \n t<\/mml:mi>\n \u2208<\/mml:mo>\n T<\/mml:mi>\n }<\/mml:mo>\n <\/mml:mrow>\n .<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:disp-formula>We study the structure of such cells and investigate the assumptions on r<\/jats:italic> that allow for generalizing known results on classical Voronoi cells.<\/jats:p>","DOI":"10.1007\/s10957-024-02435-0","type":"journal-article","created":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T06:01:40Z","timestamp":1715752900000},"page":"1246-1262","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Basic Properties and the Structure of Power Cells"],"prefix":"10.1007","volume":"203","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4914-9124","authenticated-orcid":false,"given":"Elisabetta","family":"Allevi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6845-6202","authenticated-orcid":false,"given":"Juan Enrique","family":"Mart\u00ednez-Legaz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1038-180X","authenticated-orcid":false,"given":"Rossana","family":"Riccardi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,15]]},"reference":[{"key":"2435_CR1","doi-asserted-by":"publisher","DOI":"10.1109\/TMC.2023.3305714","author":"E Ao","year":"2023","unstructured":"Ao, E., Xin, S., Li, F., Tu, C., Wang, W.: Efficient capacity constrained assignment for dynamic network coverage. 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