Timeline for $\varepsilon$-net of a $d$-dimensional unit ball formed by power set of $V = \{+1, 0 -1\}^d$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2020 at 16:38 | comment | added | Christian Chapman | Purely out of curiosity where did you find this set $V_{sum}$? | |
| Oct 17, 2020 at 7:15 | comment | added | YCor | The "surface of the unit ball" is usually called the "unit sphere". | |
| Oct 17, 2020 at 5:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 19, 2020 at 7:02 | comment | added | M. Winter | It is hard to say anything useful for general $S$. Are you looking for a feasible algorithm to compute such an upper bounds (or exact value) or do you have some restrictions on the $S$. In full generality, $|S|$ could be ${v,-v}$ and the maximal isolation is 2. Maybe one can say more if we lower bound $|S|$, but because there are many ways to duplicate vectors this will be probably not too helpful. | |
| Jun 19, 2020 at 5:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 20, 2020 at 5:29 | comment | added | Pedro Juan Soto | What is the motivation behind asking this question? Is there a specific application you have in mind? | |
| May 20, 2020 at 4:16 | answer | added | Pedro Juan Soto | timeline score: 2 | |
| May 17, 2020 at 8:08 | history | edited | YCor | CC BY-SA 4.0 |
edited title
|
| May 17, 2020 at 8:07 | comment | added | usercsw | @domotorp, there would be some $\varepsilon$ such that any vector on the surface of the $d$-dimensional unit ball is at a distance at most $\varepsilon$ from one of the vectors in $V_{\text{sum}}$ right? That's the reason I am calling it an $\varepsilon$-net. | |
| May 17, 2020 at 6:35 | history | edited | usercsw | CC BY-SA 4.0 |
deleted 12 characters in body
|
| May 16, 2020 at 8:13 | history | edited | usercsw | CC BY-SA 4.0 |
edited body
|
| May 16, 2020 at 7:46 | history | edited | YCor | CC BY-SA 4.0 |
changed tags, formatting
|
| May 16, 2020 at 7:16 | history | edited | Wlod AA | CC BY-SA 4.0 |
isolation
|
| May 16, 2020 at 6:05 | history | asked | usercsw | CC BY-SA 4.0 |