Timeline for What is the expected minimum total matching distance between two partitions of identically and independently distributed points?
Current License: CC BY-SA 4.0
16 events
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| Sep 14, 2023 at 7:09 | answer | added | kaleidoscop | timeline score: 0 | |
| Mar 8, 2019 at 10:05 | history | edited | YCor |
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| Mar 8, 2019 at 9:49 | answer | added | Gilles Mordant | timeline score: 2 | |
| Dec 15, 2018 at 6:15 | comment | added | fedja | @FedorPetrov Someone thinks it is "not research level" (you can see what people think by pushing the close button yourself, just do not submit your vote at the very end). I'd rather abstain from commenting further... | |
| Dec 15, 2018 at 5:38 | comment | added | Fedor Petrov | I just wonder: why close vote. | |
| Dec 15, 2018 at 4:50 | review | Close votes | |||
| Dec 15, 2018 at 16:37 | |||||
| Dec 15, 2018 at 3:35 | history | edited | Guoyang Qin | CC BY-SA 4.0 |
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| S Dec 15, 2018 at 2:59 | history | suggested | Josiah Park | CC BY-SA 4.0 |
updated link to publicly accessible source
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| Dec 15, 2018 at 2:54 | review | Suggested edits | |||
| S Dec 15, 2018 at 2:59 | |||||
| Dec 15, 2018 at 2:44 | comment | added | Guoyang Qin | @JosiahPark The numerical simulation is a way out. However, I have more interest in the analytic derivation. Good news is there are papers that have deeply investigated this problem, and one has provided the formula as $E_N=\frac{\ln{N}}{2\pi N}+\frac{\gamma}{N}+o(\frac{1}{N})$ for a quadratic distance version. However, as mentioned in the question description, it is heavily based on statistical mechanics, I failed to understand how it works, so I am unable to modify or expand it for my research purpose. | |
| Dec 15, 2018 at 2:37 | comment | added | Josiah Park | You might try to simulate things numerically, although it seems likely that someone should have considered the problem by now and written up some estimates. | |
| Dec 15, 2018 at 2:36 | comment | added | Guoyang Qin | @JosiahPark Yep, I noticed the problem too, the result is really impressive, which reminds me of the $\pi$ derived from Buffon's needle problem. However, the distances between the vehicles and riders are correlated due to triangle inequality restriction, therefore, this problem might be more complicated. | |
| Dec 15, 2018 at 2:27 | comment | added | Josiah Park | A really interesting related problem asks a similar question for uniform weights on the edges instead. In that problem what is asked is for the minimum-cost perfect matching in the complete $n\times n$ bipartite graph $K_{n,n}$ with i.i.d. edge weights, say uniform on $[0, 1]$. Somewhat suprisingly, Aldous in 2001 showed the optimal cost converges to $\zeta(2)=\frac{\pi^2}{6}$ as $n\rightarrow \infty$. | |
| Dec 15, 2018 at 2:10 | history | edited | Guoyang Qin | CC BY-SA 4.0 |
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| Dec 15, 2018 at 2:05 | review | First posts | |||
| Dec 15, 2018 at 2:56 | |||||
| Dec 15, 2018 at 2:04 | history | asked | Guoyang Qin | CC BY-SA 4.0 |