Timeline for Drawing pairs (planar graph, circle packing)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Jun 20, 2014 at 10:49 | history | suggested | VividD | CC BY-SA 3.0 |
added explanations in order to achieve even better clarity and usability for potential new readers
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| Jun 20, 2014 at 10:26 | review | Suggested edits | |||
| S Jun 20, 2014 at 10:49 | |||||
| Jun 20, 2014 at 9:25 | review | Suggested edits | |||
| Jun 20, 2014 at 10:01 | |||||
| Jun 20, 2014 at 8:46 | review | Suggested edits | |||
| Jun 20, 2014 at 9:10 | |||||
| May 14, 2014 at 10:57 | comment | added | Simon Woods |
The second version improves things by using constraints to insist that the circles on connected vertices touch each other. The original vertex positions go in as a starting point to FindMaximum, which seeks a local maximum (whereas NMaxmimize looks for a global optimum). It can still give unsatisfactory results, with overlapping circles for non-edges. I think this means that FindMaximum has found a local maximum which is not a global optimum. I guess this could be remedied with more constraints.
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| May 14, 2014 at 10:57 | comment | added | Simon Woods | The original algorithm is not very good - it doesn't constrain the circles on connected vertices to touch, it just attempts to minimize the gaps. At the same time it is trying to minimize the movement of the vertices from their initial positions (which is not really what we want to do). So it reaches a point where it will sacrifice the circle-packing in order to avoid rearranging the vertex positions. | |
| May 14, 2014 at 10:21 | comment | added | VividD | for your first method, I tried g = GraphData[{"BananaTree", {7, 4}}] , with all other code the same, the resulting circle pac is not entirely correct for some reason... | |
| May 14, 2014 at 9:40 | comment | added | VividD | Great application of Mathematica built-in optimisations! Thanks a lot! I am also curious why do you think that in FindMaximum vs NMaximize, FindMaximum wins for larger graphs? (Or maybe this is not the case?) | |
| May 13, 2014 at 12:09 | history | edited | Simon Woods | CC BY-SA 3.0 |
added 1725 characters in body
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| May 12, 2014 at 22:15 | history | answered | Simon Woods | CC BY-SA 3.0 |