Timeline for Techniques for showing optimality of given packing
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2013 at 5:31 | answer | added | Yuichiro Fujiwara | timeline score: 1 | |
| Aug 20, 2013 at 18:50 | comment | added | Turbo | Actually angels and pin ringed the idea of a million nanomachines on a pinhead in a US printed annual yearbook of inventions and advances in science in $'88$. | |
| Aug 20, 2013 at 18:46 | comment | added | Turbo | There are many many. over steifel manifolds, over finite graphs and over different metrics as well...... are there uniform techniques to tame the beast? | |
| Aug 20, 2013 at 18:45 | comment | added | Will Jagy | JAS, angels is what came to mind. However, all I know from your list is lattice sphere packings, and even that gets unwieldy as the dimension rises. For my purposes, it was actually coverings that were the important concept... Let's see, i would agree that the literature is scattered, if you include problems with boundaries, or non-lattice packings, etc. | |
| Aug 20, 2013 at 18:36 | comment | added | Turbo | Hmm atleast a million at last count in year book of inventions in $'88$. Come on I think neglecting suboptimal packings is important. Most of the techniques are scattered around. I could not find a coherent list. | |
| Aug 20, 2013 at 18:35 | comment | added | Will Jagy | Also, how many angels can dance on the head of a pin? In his 1667 tract The Reasons of the Christian Religion, Baxter reviews opinions on the materiality of angels from ancient times, concluding: And Schibler with others, maketh the difference of extension to be this, that Angels can contract their whole substance into one part of space, and therefore have not partes extra partes. Whereupon it is that the Schoolmen have questioned how many Angels may fit upon the point of a Needle?". –Richard Baxter | |
| Aug 20, 2013 at 15:24 | answer | added | Robert Israel | timeline score: 1 | |
| Aug 20, 2013 at 14:30 | comment | added | Turbo | @S.Carnahan As I understand linear programming provides upper bounds (please correct if I am wrong). As such they could be used to show sub-optimality of given packing if the bound is tight. | |
| Aug 20, 2013 at 14:01 | history | edited | Turbo | CC BY-SA 3.0 |
deleted 3 characters in body
|
| Aug 20, 2013 at 13:54 | comment | added | Steve Huntsman | For the sphere surface case, I am not aware of anything better than equilibrating point charges on the surface with uniformly random initial conditions. Unless there is a better way, it's not clear to me how a given instance of this could be shown to be optimal. | |
| Aug 20, 2013 at 13:38 | comment | added | S. Carnahan♦ | I don't think there are general methods that work for all packings. However, sometimes you can get good results using linear programming bounds. This was used for kissing numbers by Odlyzko (and possibly others), and for lattice packings by Cohn-Elkies and Cohn-Kumar. | |
| Aug 20, 2013 at 13:19 | history | asked | Turbo | CC BY-SA 3.0 |