[R] circle fill problem

[Robin Hankin]

Hello Ingmar

In Kepler's sphere packing problem the
spheres are not allowed to overlap, which
would suggest to me that different tactics should
perhaps be used.

Mini's problem is formally a "cover problem", and
the sphere packing problem is a "packing problem".
The two are related, but tend not to have direct
relevance to one another.

Also be aware that Kepler's conjecture refers to the
packing fraction limit as  the space available tends to
infinity.

My understanding is that Kepler's conjecture has now been
proved beyond all reasonable doubt, but how to use this in
Mini's problem is not clear to me.


rksh


On 8 Feb 2007, at 09:21, Ingmar Visser wrote:

> Robin & Mini,
> For those interested, googling for the 'orange packing problem' as it
> is known, or more officially the sphere packing problems gives you
> quite a few hits on these and similar problems.
> So at least the 3-d case the problem has been solved (I imagine the
> problem is easier in 2-d ...)
> hth, Ingmar
>
> On 8 Feb 2007, at 09:52, Robin Hankin wrote:
>
>> Mini
>>
>> This is a hard problem in general.
>>
>> Recreational mathematics has wrestled with
>> this and similar problems over the years; the
>> general field is the "set cover problem" but
>> in your case the sets are uncountably infinite
>> (and there are uncountably many of them).
>>
>> I would be surprised if your problem were not NP complete.
>>
>>
>> HTH
>>
>>
>> Robin
>>
>>
>> On 8 Feb 2007, at 05:15, MINI GHOSH wrote:
>>
>>> Dear R user,
>>>
>>> I want to know is there a way to find the minimum
>>> number of circles (of given radius) required to fill a
>>> given area (say rectangular) where overlapping of
>>> circles is allowed.
>>>
>>> Thanks,
>>> Regards,
>>> Mini Ghosh
>>>
>>> ______________________________________________
>>> R-help at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posting-
>>> guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>> --
>> Robin Hankin
>> Uncertainty Analyst
>> National Oceanography Centre, Southampton
>> European Way, Southampton SO14 3ZH, UK
>>   tel  023-8059-7743
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-
>> guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting- 
> guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743