Quantitative Helly-type theorems via sparse approximation
We prove the following sparse approximation result for polytopes. Assume that Q is a polytope in John's position. Then there exist at most 2d vertices of Q whose convex hull Q' satisfies Q subset of -2d(2) Q'. As a consequence, we retrieve the best bound for the quantitative Helly-typ...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2023
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| Sorozat: | DISCRETE AND COMPUTATIONAL GEOMETRY
70 No. 4 |
| Tárgyszavak: | |
| doi: | 10.1007/s00454-022-00441-5 |
| mtmt: | 32257228 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/29682 |
| LEADER | 01645nab a2200253 i 4500 | ||
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| 008 | 240227s2023 hu o 0|| eng d | ||
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| 024 | 7 | |a 10.1007/s00454-022-00441-5 |2 doi | |
| 024 | 7 | |a 32257228 |2 mtmt | |
| 040 | |a SZTE Publicatio Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 2 | |a Hugo Almendra-Hernández Víctor | |
| 245 | 1 | 0 | |a Quantitative Helly-type theorems via sparse approximation |h [elektronikus dokumentum] / |c Hugo Almendra-Hernández Víctor |
| 260 | |c 2023 | ||
| 300 | |a 1707-1714 | ||
| 490 | 0 | |a DISCRETE AND COMPUTATIONAL GEOMETRY |v 70 No. 4 | |
| 520 | 3 | |a We prove the following sparse approximation result for polytopes. Assume that Q is a polytope in John's position. Then there exist at most 2d vertices of Q whose convex hull Q' satisfies Q subset of -2d(2) Q'. As a consequence, we retrieve the best bound for the quantitative Helly-type result for the volume, achieved by Brazitikos, and improve on the strongest bound for the quantitative Helly-type theorem for the diameter, shown by Ivanov and Naszodi: We prove that given a finite family F of convex bodies in R-d with intersection K, we may select at most 2d members of F such that their intersection has volume at most (cd)(3d)(/2) vol K, and it has diameter at most 2d(2) diam K, for some absolute constant c > 0. | |
| 650 | 4 | |a Matematika | |
| 700 | 0 | 1 | |a Ambrus Gergely |e aut |
| 700 | 0 | 1 | |a Kendall Matthew |e aut |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/29682/1/quanthelly_final.pdf |z Dokumentum-elérés |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/29682/3/32257228_megjelent.pdf |z Dokumentum-elérés |