How often should you clean your room?

• Published in 2013
• Added on 2014-09-02

We introduce and study a combinatorial optimization problem motivated by the question in the title. In the simple case where you use all objects in your room equally often, we investigate asymptotics of the optimal time to clean up in terms of the number of objects in your room. In particular, we prove a logarithmic upper bound, solve an approximate version of this problem, and conjecture a precise logarithmic asymptotic.

Links

• http://arxiv.org/abs/1305.1984
• http://arxiv.org/pdf/1305.1984v2

Other information

BibTeX entry

@article{Martin2013,
	key = {Martin2013},
	type = {article},
	title = {How often should you clean your room?},
	author = {Martin, Kimball and Shankar, Krishnan},
	abstract = {We introduce and study a combinatorial optimization problem motivated by the question in the title. In the simple case where you use all objects in your room equally often, we investigate asymptotics of the optimal time to clean up in terms of the number of objects in your room. In particular, we prove a logarithmic upper bound, solve an approximate version of this problem, and conjecture a precise logarithmic asymptotic.},
	comment = {},
	date_added = {2014-09-02},
	date_published = {2013-05-01},
	urls = {http://arxiv.org/abs/1305.1984,http://arxiv.org/pdf/1305.1984v2},
	collections = {Easily explained},
	month = {may},
	pages = 28,
	url = {http://arxiv.org/abs/1305.1984 http://arxiv.org/pdf/1305.1984v2},
	year = 2013,
	archivePrefix = {arXiv},
	eprint = {1305.1984},
	primaryClass = {math.CO},
	urldate = {2014-09-02}
}