Unhelpful framing news, now. A University of Michigan of press release begins:
A hidden facet of a math problem that goes back to timeworn Sanskrit manuscripts has just been exposed by nanotechnology researchers at the University of Michigan and the University of Connecticut.
What Glotzer et al have actually done is changed the rules of the classical packing problem a bit, to suit an application they had in mind. Maybe the person writing the press release is a Platonist.
Anyway, the problem is called filling, and it is to find the best way to fill a space with overlapping shapes placed entirely inside it.
In the paper, they only consider filling 2D polygons with arbitrarily-sized discs. They show that the centres of the discs always lie on a “skeleton” (a $1$-skeleton to you and me), and claim the solutions to their problem have applications in radiation treatment, electronics and protein modelling.
I’d be amazed if nobody’s thought about this problem before. The authors are a physicist, a biologist and an engineer, that’s all I’m saying. It does look like a very useful problem for them to have a solution to.
Astonishingly, the press release doesn’t bother to link to the paper itself, which is in Physical Review Letters. It especially doesn’t link to the freely-available arXiv preprint. It does deign to give the name of the paper, however. The “timeworn Sanskrit manuscripts” are not mentioned again after that ridiculous lead paragraph.
Paper: Optimal Filling of Shapes