An Optimal Solution for the Muffin Problem

• Published in 2019
• Added on 2020-08-17

The muffin problem asks us to divide $m$ muffins into pieces and assign each of those pieces to one of $s$ students so that the sizes of the pieces assigned to each student total $m/s$, with the objective being to maximize the size of the smallest piece in the solution. We present a recursive algorithm for solving any muffin problem and demonstrate that it always produces an optimal solution.

Links

• http://arxiv.org/abs/1907.08726v2
• http://arxiv.org/pdf/1907.08726v2

Other information

BibTeX entry

@article{AnOptimalSolutionfortheMuffinProblem,
	key = {AnOptimalSolutionfortheMuffinProblem},
	type = {article},
	title = {An Optimal Solution for the Muffin Problem},
	author = {Richard E. Chatwin},
	abstract = {The muffin problem asks us to divide {\$}m{\$} muffins into pieces and assign each
of those pieces to one of {\$}s{\$} students so that the sizes of the pieces assigned
to each student total {\$}m/s{\$}, with the objective being to maximize the size of
the smallest piece in the solution. We present a recursive algorithm for
solving any muffin problem and demonstrate that it always produces an optimal
solution.},
	comment = {},
	date_added = {2020-08-17},
	date_published = {2019-12-07},
	urls = {http://arxiv.org/abs/1907.08726v2,http://arxiv.org/pdf/1907.08726v2},
	collections = {attention-grabbing-titles,food,fun-maths-facts,protocols-and-strategies},
	url = {http://arxiv.org/abs/1907.08726v2 http://arxiv.org/pdf/1907.08726v2},
	year = 2019,
	urldate = {2020-08-17},
	archivePrefix = {arXiv},
	eprint = {1907.08726},
	primaryClass = {math.CO}
}