Timeline for Hemisphere containing the maximum number of points scattered on a sphere
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2023 at 1:01 | history | reopened |
Joseph Van Name Alex M. Yemon Choi Jukka Kohonen LeechLattice |
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| Apr 7, 2023 at 17:14 | comment | added | Joseph Van Name | Someone asked a question about equivalent to this again. mathoverflow.net/questions/444144/… I wonder why this question was upvoted but closed the first time, but it attracted multiple answers, upvotes, and upvoted answers the second time. I think it is an interesting mathematical question even if is best solved using inexact algorithms.. | |
| Apr 7, 2023 at 17:13 | comment | added | Joseph Van Name | @mlk I have tried your approach with random points placed on the sphere, but I was able to get much better results using other approaches including gradient ascent (faster), simulated annealing (slower), or evolutionary algorithms (slower). | |
| Apr 7, 2023 at 17:07 | review | Reopen votes | |||
| Apr 21, 2023 at 1:01 | |||||
| Dec 18, 2022 at 1:53 | review | Reopen votes | |||
| Jan 17, 2023 at 1:56 | |||||
| Dec 17, 2022 at 22:52 | comment | added | Stefan Kohl♦ | Please do not post the same question simultaneously on both Math.SE and MO, in order to avoid duplication of efforts. | |
| Dec 17, 2022 at 22:50 | history | closed | Stefan Kohl♦ | Not suitable for this site | |
| Nov 28, 2022 at 0:29 | comment | added | Joseph O'Rourke | Another way to phrase your question: Find an optimal $2$-cluster partition via hyperplanes through the origin. This may help in searches. | |
| Nov 24, 2022 at 3:33 | comment | added | RobPratt | Cross-posted: math.stackexchange.com/questions/4583251/… | |
| Nov 23, 2022 at 18:40 | comment | added | Ali | @mlk: thank you. The problem with such approach, as you mentioned, is the pathological configurations which happen easily once we don't have a unimodal distribution of the directions. I was hoping of an algorithm that keeps including/excluding points until some type of convergence is reached. | |
| Nov 23, 2022 at 10:55 | comment | added | mlk | I guess a quick $O(n)$ heuristic would be to pick the hyperplane that is normal to the vector pointing from the origin to the center of mass. I can think of some pathologic configurations where this fails spectacularly, but for more generic configurations, it should yield a good first approximation. | |
| Nov 23, 2022 at 8:14 | comment | added | Ali | Yes, my preference is with faster algorithms, even if they are inexact. Also, the problem should have been considered before, but I yet have not found any relative content. | |
| Nov 23, 2022 at 8:07 | comment | added | Timothy Budd | If the points are in general position, there is a simple bruteforce algorithm in $O(n^k)$ time: simply consider all hemispheres that have their boundary aligned with a $(k-1)$-tuple of the points. Are you looking for some faster? | |
| Nov 23, 2022 at 7:40 | history | asked | Ali | CC BY-SA 4.0 |